A systematic benchmarking framework and dual-view optimization strategy for single-cell DNA methylation imputation

Abstract

Single-cell DNA methylation (scDNAm) profiling is revolutionizing our understanding of epigenetic control of gene expression, but its accurate analysis is severely hindered by extreme data sparsity. While imputation methods have undergone remarkable development in recent years, a rigorous benchmark to guide method selection remains absent. We established the first systematic benchmarking framework for scDNAm imputation, subjecting five state-of-the-art methods to a comprehensive evaluation across 13 published experimental scDNAm datasets. Performance was systematically assessed across seven critical dimensions: accuracy, sensitivity to data characteristics, scalability, robustness to data splitting strategies, inter-dataset generalizability, convergence behavior, and computational efficiency. Through rigorous statistical analysis, we dissected the influence of intrinsic data attributes and model architectures on the fidelity of scDNAm imputation to provide guidance for selecting appropriate methods for given scenarios. Furthermore, based on the benchmark-identified limitations, we proposed a dual-view strategy to address the performance bottlenecks of existing methods: at the model view, we developed BridgeCpG, an ensemble strategy to integrate complementary modeling strengths to overcome single-model limitations; at the data view, we introduced an adaptive divide-and-conquer strategy to partition highly heterogeneous datasets into several homogeneous subsets amenable to accurate imputation, followed by aggregating the sub-results. This integrated framework, spanning both model and data views, delivers quantitative analyses, scenario-aware selection guidelines, and targeted innovative strategies, establishing a rigorous, enabling foundation for accurate, high-throughput, and scalable next-generation single-cell epigenomic analysis.

Introduction

Epigenetic modifications, particularly DNA methylation at CpG dinucleotides, serve as a fundamental regulatory mechanism governing cellular differentiation, genomic stability, and transcriptional programs [1–5]. Elucidating these epigenetic landscapes is critical for understanding diverse biological processes, ranging from embryonic development to oncogenesis. The recent advent of single-cell DNA methylation (scDNAm) sequencing methods, such as scBS-seq [6] and snmC-seq [7], has revolutionized the field [8–10], empowering researchers to dissect epigenetic heterogeneity at an unprecedented resolution. However, profiling the methylome presents a formidable high-dimensional challenge, as exemplified by the human methylome, which encompasses >28 million CpG sites [11, 12]. The stochastic nature of sequencing and the minute amounts of genomic DNA per cell result in pervasive data sparsity, where loss of sequencing coverage often exceeds 95% [13]. This extreme sparsity severely fragments the methylome landscape, obscuring lineage-specific signals and hindering downstream analyses [14–16]. Consequently, computational imputation has emerged as an indispensable prerequisite to recover missing information and reconstruct complete epigenetic profiles.

To overcome these inherent limitations, imputation methods have evolved rapidly, transitioning from traditional statistical approaches to advanced deep learning paradigms. Initial efforts sought to recover missing signals by exploiting local correlations between neighboring CpG sites or global similarities among cells [17]. Subsequently, machine-learning methods emerged as powerful alternatives. A prominent example is CaMelia [18], which strategically employs the CatBoost gradient boosting framework to capture both local genomic patterns and global intercellular similarities [19]. Machine learning–based approaches explicitly model statistical dependencies, making them particularly effective for small-scale datasets with adequate statistical information to support inference.

However, as dataset sizes and biological complexities have increased, the limitations of traditional machine-learning methods, specifically their inability to model complex and nonlinear genomic contexts, have become apparent. This has catalyzed a paradigm shift toward deep learning architectures. DeepCpG [20] pioneered this transition by utilizing convolutional neural networks (CNNs) and bidirectional gated recurrent units (GRUs) to extract features from DNA sequences. Building on this foundation, more sophisticated architectures emerged to capture long-range dependencies. CpG Transformer [14] adapted the self-attention mechanism [21] to model global interactions across distal genomic regions. Introducing a topological perspective, GraphCpG [15] reformulated the problem using graph convolutional networks (GCNs [22]), modeling cells and CpG sites as nodes to explicitly learn spatial distribution topologies. Most recently, MambaCpG [16] integrated selective state-space models (Mamba [23]), promising linear-time sequence modeling to handle the expanding scale of genomic data. These deep learning models have demonstrated superior capacity in learning latent representations from massive datasets.

Despite this methodological proliferation, the field currently faces a critical bottleneck: the lack of a systematic, scenario-specific benchmarking framework [24] to guide method selection. Existing evaluations are predominantly confined to the original method papers, which typically focus on overall accuracy metrics under favorable and self-selected conditions. For instance, feature-based methods like CaMelia emphasize computational efficiency on small-scale datasets, leaving their scalability limits on larger scale matrices unexplored. Meanwhile, deep learning models such as DeepCpG [20] are often validated on homogeneous cell lines like mouse embryonic stem cells (mESCs [6]) to ensure convergence. Collectively, these limited comparisons fail to address three fundamental challenges inherent to practical scDNAm applications. First, current studies often prioritize architectural novelty over biological fidelity, failing to define the performance boundaries where models deteriorate due to intrinsic data characteristics like extreme sparsity or class imbalance [25]. Second, there is a scalability dilemma [13]. On one hand, while scRNA-seq imputation methods operate within a defined space of ~20 000 genes with continuous read counts [26–29], the scDNAm landscape is far more expansive, encompassing ~28 million CpG sites in the human genome [11, 12] and ~20 million CpG sites in the mouse genome [6]. This extremely high dimensionality uniquely distinguishes scDNAm from other omics modalities, making the imputation of just 500 cells computationally equivalent to processing nearly 70 000 transcriptomic profiles [29–32]. Consequently, large-scale scDNAm datasets impose prohibitive computational costs on existing methods, frequently resulting in memory overflows. On the other hand, without sufficient training examples to support representation learning, applying deep learning models to data-sparse small-scale datasets causes these models to fall into severe overfitting. This is consistent with the predictions of neural scaling laws: deep learning models require adequate data volume to mitigate overfitting and attain robust generalization [33–35]. Third, the black-box nature of deep neural networks obscures their inference logic, leaving researchers uncertain whether imputed values reflect true biological signals or technical artifacts [25, 36]. Critically, current computational frameworks typically restrict imputation to the exclusive use of a single standalone model, offering no alternative strategy to improve results when the primary model underperforms, leaving researchers without recourse to recover biologically meaningful signals.

In this study, we present the first systematic benchmarking framework dedicated to scDNAm imputation methods. Instead of relying solely on accuracy, we comprehensively assess existing methods to identify their specific weaknesses under complex biological conditions. We evaluated five state-of-the-art methods across 13 published experimental scDNAm datasets spanning diverse tissues. Our evaluation dissects performance across seven critical dimensions: (1) Accuracy, assessing fundamental imputation precision across diverse biological contexts; (2) Sensitivity to data characteristics, quantifying how intrinsic data attributes impact model efficacy; (3) Sensitivity to scalability, evaluating model capacity across varying dataset magnitudes, ranging from limited inputs to moderate-scale matrices; (4) Robustness to data splitting strategies, evaluating performance stability across diverse data splitting scenarios; (5) Inter-dataset generalizability, testing the capability to transfer learned patterns across distinct datasets; (6) Convergence behavior, analyzing training dynamics across epochs to characterize model convergence stability and optimal training round requirements; and (7) Computational efficiency, quantifying execution time and memory usage across diverse scenarios.

To resolve the limitations of single-model frameworks and recover signals where existing approaches underperform, we leverage our benchmarking insights to propose a dual-view remediation strategy. At the model view, we developed BridgeCpG, an interpretable ensemble framework designed for challenging scenarios where individual models underperform. By dynamically integrating the long-range dependency of CpG Transformer, the topological structure of GraphCpG, and the state-space modeling of MambaCpG via a LightGBM-based meta-learner [37], BridgeCpG achieves superior robustness. At the data view, to address the issue where high entropy leads to poor imputation performance, we propose an adaptive divide-and-conquer strategy. This approach structurally decomposes massive, heterogeneous datasets into multiple homogeneous clusters with minimized intra-cluster variance, ensuring high-accuracy imputation within each individual cluster, while avoiding the prohibitive graphics processing unit (GPU) memory overhead associated with global modeling. Finally, we synthesize our findings into a practical decision guide, empowering researchers to select the optimal imputation strategy tailored to their specific data constraints and computational resources. Crucially, by systematically dissecting the architectural strengths and inherent bottlenecks of state-of-the-art imputation methods, our evaluation establishes actionable guidance for method development tailored to scDNAm imputation model developers, thereby facilitating the rational design and performance optimization of next-generation imputation frameworks. Collectively, this study establishes a robust methodological foundation for scDNAm analysis, bridging the gap between sparse sequencing data and deep biological interpretation. An overview of the overall study design is presented in Fig. 1.

Figure 1.

Overview of the systematic benchmarking framework and methodological advancements for scDNAm imputation. (a) The pipeline of our benchmark study, including the evaluation workflow, 13 published experimental scDNAm datasets, and 7 core dimensions for comprehensive performance assessment of state-of-the-art imputation methods. (b) Two optimization strategies for existing method bottlenecks: left, BridgeCpG, a LightGBM-based meta-learner integrating top-performing models to boost imputation robustness; right, a divide-and-conquer strategy decomposing heterogeneous datasets for parallel high-fidelity imputation. (c) Method selection guide. Synthesis of benchmarking insights into a quantitative decision framework.

Materials and methods

Data collection

Our benchmark analysis was performed on a comprehensive collection of 13 scDNAm datasets, ranging from small-scale studies to large-scale datasets. These datasets were curated from published studies [6, 8, 38–44] and encompass both human and mouse systems, covering diverse biological contexts such as early embryonic development, hematopoietic lineages, liver tissue, and germ cells, while spanning diverse sequencing technologies (scBS-seq [6], scRRBS-seq [45], scNOMe-seq [40], scCOOL-seq [46], and snmC-seq [7]). Key characteristics of all curated datasets are summarized in Table 1 and Supplementary Table S1. The GSM accession numbers of the individual cells used for the hCLP, hCMP, and hGMP datasets are provided in Supplementary Table S4.

Table 1.

Summary of scDNAm datasets employed in this study, sorted by cell count in ascending order.

Data name	GEO accession	Cell number	Protocol	Sparsity (10−1)	Species	Cell type/tissue	Role in this study
mESC_2i	GSE56879	12	scBS-Seq	8.3790	Mus musculus	mESCs	Primary benchmark dataset
mOocyte	GSE56879	12	scBS-Seq	8.2580	M. musculus	Oocyte	Primary benchmark dataset
mESC_Ser	GSE56879	20	scBS-Seq	8.5140	M. musculus	mESCs	Primary benchmark dataset
hCLP	GSE87197	20	scBS-seq	8.3770	Homo sapiens	Lymphoid	Primary benchmark dataset
hCMP	GSE87197	20	scBS-seq	8.2580	H. sapiens	Myeloid	Primary benchmark dataset
hGMP	GSE87197	20	scBS-seq	8.5520	H. sapiens	Macrophage	Primary benchmark dataset
hHCC	GSE65364	26	scRRBS-Seq	9.1160	H. sapiens	Hepatocellular carcinoma	Primary benchmark dataset
hCellLine	GSE83882	30	scNOMe-seq	9.4260	H. sapiens	Hematopoietic cell lines	Primary benchmark dataset
hMK	GSE87197	71	scBS-seq	9.2610	H. sapiens	Megakaryocyte	Primary benchmark dataset
hHSC	GSE87197	108	scBS-seq	8.8970	H. sapiens	Hematopoietic stem cell	Primary benchmark dataset
hMLP	GSE87197	152	scBS-seq	8.6950	H. sapiens	Immature lymphoid progenitor	Primary benchmark dataset
hEmbryo	GSE100272	285	scCOOL-seq	9.1310	H. sapiens	Early embryos	Primary benchmark dataset
hPGC	GSE107714	461	scBS-seq	7.2020	H. sapiens	Primordial germ cells	Primary benchmark dataset
hFC	GSE97179	2313	snmC-seq	–	H. sapiens	Frontal cortex neurons	D&C validation dataset
mBrain_Atlas	GSE132489	103 982	snmC-seq2	–	M. musculus	Mouse brain atlas	D&C validation dataset

This collection comprises 13 datasets utilized for imputation benchmarking and two datasets for validating the divide-and-conquer strategy. Notably, hFC and mBrain_Atlas have an extremely large cell count, making them unsuitable for direct imputation and difficult-to-compute metrics including sparsity (marked as “–”).

The datasets we selected exhibit diverse biological heterogeneity and coverage profiles, enabling us to evaluate imputation performance in different scenarios. This primary collection includes three mouse embryonic datasets [6] derived from mouse embryonic stem cells grown in serum (mESC_Ser), mouse embryonic stem cells grown in 2i medium (mESC_2i), and mouse oocytes (mOocyte). It also incorporates six human hematopoietic differentiation datasets [38]: human common lymphoid progenitors (hCLP), human common myeloid progenitors (hCMP), human granulocyte-macrophage progenitors (hGMP), human megakaryocytes (hMK), human hematopoietic stem cells (hHSC), and human immature multi-lymphoid progenitors (hMLP). Furthermore, we utilized human hepatocellular carcinoma (hHCC) [39], human lymphoblastoid cell lines (hCellLine) [40], human early embryos (hEmbryo) [41], and human primordial germ cells (hPGC) [42] to evaluate imputation fidelity and generalizability across various biological contexts.

Beyond standard performance benchmarking, we specifically selected two large-scale datasets to illustrate the feasibility of applying the divide-and-conquer partitioning workflow to large and heterogeneous scDNAm datasets: the Human Frontal Cortex Neurons dataset (hFC) [8] and the Mouse Brain Atlas (mBrain_Atlas) [43] (see “Adaptive divide-and-conquer strategy resolves heterogeneity bottlenecks” section for more details). For details on data preprocessing, see Supplementary Text S1.

Imputation methods

We evaluated five representative imputation methods encompassing two distinct computational paradigms: (1) a gradient boosting-based machine-learning method CaMelia and (2) deep representation learning methods, including DeepCpG, CpG Transformer, GraphCpG, and MambaCpG. To ensure a fair baseline comparison, all models were executed using their default hyperparameter configurations. Key architectural characteristics and input specifications are summarized in Table 2. Additional considerations regarding software environments and input differences are provided in Supplementary Text S2.

Table 2.

Description of the five imputation methods utilized for scDNAm data.

Methods	Language	Deep learning	Framework versions	Compatible CUDA version	Underlying model	Input
DeepCpG	Python	Yes	TensorFlow 1.15	10	CNN and GRU	scDNAm data; DNA sequence
CaMelia	Python	No	/	/	CatBoost	scDNAm data; one available bulk methylation data
CpG Transformer	Python	Yes	PyTorch 1.10	11.3	Transformer	scDNAm data; DNA sequence
GraphCpG	Python	Yes	PyTorch 1.9	11.1	GCN	scDNAm data
MambaCpG	Python	Yes	PyTorch 2.0	11.8	Mamba	scDNAm data; DNA sequence

Notably, framework versions are reported for reproducibility; runtime and memory performance may be affected by framework-level optimizations and underlying software environments. Note: CaMelia uses bulk methylation profiles as supplementary input, which are not required by the other methods and may provide an advantage in direct performance comparisons. Therefore, its results should be interpreted with this input difference in mind.

CaMelia [18]: Utilizing a CatBoost-based gradient boosting framework [19], CaMelia integrates local and global intercellular methylation similarities with DNA sequence features to perform genome-wide imputation. The method operates on chromosome-specific cell-by-site matrices supplemented by corresponding bulk methylation profiles.

DeepCpG [20]: This method employs a multimodal deep learning architecture that fuses CNNs for extracting DNA sequence motifs with bidirectional GRUs for capturing spatial dependencies across neighboring CpG sites. Inputs consist of cell-by-region matrices binned into genomic windows.

CpG Transformer [14]: Adapting the transformer architecture [21], this method utilizes axial attention mechanisms to model long-range dependencies within methylation patterns. It processes standard NPZ-formatted inputs containing methylation states, genomic positions, and encoded DNA sequences.

GraphCpG [15]: GraphCpG reframes imputation as a link prediction task within a graph topology. It leverages GNNs to model high-order interactions between CpG sites and cells [22], operating independently of DNA sequence data. The method utilizes the same NPZ input format as CpG Transformer.

MambaCpG [16]: Incorporating a bidirectional state-space model architecture (Mamba) [23], MambaCpG efficiently captures long-range dependencies through linear-complexity sequence modeling. It processes fused representations of methylation matrices and DNA sequence embeddings, sharing the unified NPZ input format used by CpG Transformer and GraphCpG.

Benchmarking metrics and intrinsic data characteristic metrics

To systematically evaluate imputation fidelity, we employed 10 metrics stratified into three analytical dimensions. First, overall performance metrics (accuracy (ACC), area under the receiver operating characteristic curve (AUC), Matthews correlation coefficient (MCC)) assessed the global consistency of predictions against ground truth. Second, we independently evaluated the model’s dual performance in recognizing both positive methylated signals and negative unmethylated backgrounds, using class-specific recognition metrics ( true positive rate (TPR), F1 score (F1), true negative rate (TNR)). Finally, to mitigate validation bias from class imbalance, we introduced balanced composite scores (Comprehensive score, Positive recognition, Negative recognition, Overall score) (Supplementary Text S3).

In parallel, to systematically characterize the intrinsic data characteristics of scDNAm datasets, we selected a total of five metrics. They are as follows: Sparsity for evaluating the sparsity of methylation data; Average methylation rate for reflecting the global methylation level of the sample; Coverage complexity for measuring the uniformity of CpG locus coverage; Methylation variance for quantifying the dispersion of methylation rates across individual cells; and Shannon entropy for characterizing the epigenetic heterogeneity of the sample (Supplementary Text S4). Especially, previous studies have demonstrated that Shannon entropy can quantify the randomness, stochasticity, and diversity of DNA methylation patterns, thereby providing an information-theoretic measure of epigenetic heterogeneity [47–50]. In subsequent experiments, we will leverage these properties of Shannon entropy to conduct our analyses.

Benchmarking results

Systematic benchmarking unveils a data-difficulty-dependent performance landscape and algorithmic bottlenecks

Dataset splitting and training strategy

To ensure comparability and fairness across all experimental results, we implemented a consistent and rigorous chromosome hold-out strategy throughout our study, which is fully aligned with the species-specific default settings of MambaCpG [16] for both mouse and human datasets, and meanwhile adheres to the well-validated gold-standard benchmarking framework for genomic prediction models [51].

Specifically, in benchmarking experiments, we employed this unified hold-out scheme across both species: for the mouse dataset, chromosomes chr1–9 and chr11–19 constituted the training set, while chr10 served as the held-out independent test set; for the human dataset, chromosomes chr1–9 and chr11–22 were used for model training, with chr10 retained as the test set. All analyses were restricted to autosomes, with sex chromosomes excluded per standard field practices to avoid confounding effects from sex-specific methylation patterns. This whole-chromosome hold-out design eliminates data leakage inherent to random splits and enables an unbiased and robust assessment of model generalizability [20] (“Reliability assessment and the impact of train-test splitting strategies” section).

During testing, we randomly masked 20% of CpG sites with observed methylation states within the held-out test chromosome for evaluation, with the masking ratio kept consistent with CpG Transformer [14]. The same masked positions were shared across all methods to ensure strictly comparable evaluation conditions. For deep learning methods, we adopted 30 epochs as a common training budget for the primary benchmark. Consistent with our empirical profiling of training dynamics (“Computational costs and training stability” section), the performance of most methods showed only limited changes after ~20 training epochs.

Result analysis

To establish a rigorous performance benchmark across diverse biological contexts, we conducted a systematic evaluation of five state-of-the-art methods, CaMelia, DeepCpG, CpG Transformer, GraphCpG, and MambaCpG, across 13 datasets. To ensure a fair and unbiased baseline comparison, all models were strictly executed using their default hyperparameter configurations. To ensure a comprehensive assessment, we quantified model fidelity using 10 specific metrics: ACC, AUC, MCC, Comprehensive score (averaging ACC, AUC, and MCC), F1, TPR, Positive recognition (averaging TPR and F1), TNR, Negative recognition (based on TNR), and Overall score (averaging all six fundamental metrics). All aggregate scores are normalized to the range of 0–1, based on which the color mapping is implemented (see Supplementary Texts S3 for more details). The aggregated comprehensive performance scores of each imputation method across all successfully processed datasets are shown in Fig. 2a, while the aggregated comprehensive scores for each dataset across all cells and all metrics are presented in Fig. 2b.

Figure 2.

Performance landscape and determinants of scDNAm imputation methods. (a) Comprehensive performance evaluation of the five tested imputation methods. Since successfully processed datasets vary by method, aggregate scores cannot be treated as a fully consistent global ranking. (b) Aggregated imputation performance across the 13 scDNAm datasets. (c) Performance distribution of imputation methods on representative datasets stratified by difficulty level. Violin plots illustrate the distribution of evaluation metrics (ACC, AUC, TPR, TNR, F1, MCC) for each method on “Simple” datasets (mOocyte, hCLP), “Intermediate” datasets (mESC_2i, hCellLine), and “Challenging” datasets (hHSC, hMK). Notably, for panels (a) and (b), the displayed aggregate scores are normalized to a scale of 0–1.

As shown in Fig. 2a, CaMelia and CpG Transformer achieved the highest overall comprehensive scores across the 10 evaluation metrics. However, relying solely on these aggregate statistics may be misleading, as they mask a critical underlying issue: imputation models exhibited dramatic performance divergence across individual datasets, with extremely poor consistency in predictive performance. Crucially, this cross-dataset variability was not random, but was driven by the intrinsic statistical characteristics of each dataset. To systematically dissect the impact of intrinsic data properties on imputation efficacy, we therefore stratified the full benchmark suite into distinct tiers based on quantitative data and performance metrics. Specifically, we selected two core metrics as our stratification criteria: the observed overall accuracy levels of tested methods on each dataset and the performance variance across different methods. Using these criteria, we categorized the full benchmark suite into three distinct tiers (Supplementary Table S1). The first tier represents the simple data-difficulty level (e.g. mOocyte, hCLP), where all methods can universally achieve high accuracy. The second represents the intermediate data-difficulty level (e.g. mESC_2i, hCellLine), where performance varies significantly across methods. The third represents the challenging data-difficulty level (e.g. hHSC, hMK), where most methods fail to capture valid signals. These challenging data conditions underscore the urgent need for more robust predictive solutions. We further computed separate aggregated comprehensive performance scores for each imputation method across the three dataset tiers (Supplementary Fig. S1a and Table S1).

To facilitate direct comparison of method rankings and detailed results across data-difficulty levels, we additionally provide a summary in Supplementary Table S2. In addition, dataset-level characteristics, quantified by the averaged benchmark metrics across all evaluated imputation methods, are summarized in Supplementary Table S3. In the following analyses, we further characterize these data-difficulty levels from two complementary perspectives: intrinsic biological complexity and dataset-scale settings (“Intrinsic determinants of imputation performance” and “Impact of sample size on imputation stability” sections).

Further examination of the violin plots (Fig. 2c and Supplementary Fig. S1b) highlights the distinct behavioral characteristics of each method. DeepCpG showed limited applicability, restricted primarily to small-scale settings with minimal sparsity. For instance, while DeepCpG maintained robust performance on the hCLP dataset comprising 20 cells, it could not run successfully on the moderate-scale hMK dataset containing 71 cells due to its excessive computational burden with increasing cell counts. In contrast, GraphCpG and MambaCpG exhibited marked volatility with wide and inconsistent performance ranges, performing well in specific contexts but degrading significantly in others. Notably, CpG Transformer distinguished itself by maintaining consistently high median scores with minimal variance, indicating superior stability across diverse scenarios.

Most importantly, we uncovered a universal computational barrier inherent to all current architectures. Specifically, on whole-genome sequencing datasets exceeding 500 cells (e.g. hFC), none of the evaluated methods could complete the imputation task within a 72-h window under standard parameter settings. This computational bottleneck demonstrates that while methods like CaMelia and CpG Transformer excel in imputation tasks, existing state-of-the-art strategies remain fundamentally inadequate for the emerging scale of comprehensive, high-throughput methylome profiling.

Intrinsic determinants of imputation performance

We further performed a quantitative analysis of data characteristics to identify the main drivers of imputation performance. First, Shannon entropy serves as a core metric for biological complexity, as higher entropy reflects more heterogeneous and dispersed methylation landscapes across cells, indicating stronger epigenetic diversity within the population [47–49]. Based on this rationale, we stratified datasets into low (0.00–0.50), medium (0.50–1.50), and high (>1.50) entropy groups (see Supplementary Table S1 for more details) and calculated the average positive recognition rate for each group (Fig. 3a). We observed that the low-entropy group exhibited significantly higher recognition rates compared to the medium- and high-entropy groups. This indicates that data complexity critically influences imputation performance; as internal data disorder increases, it becomes increasingly difficult for models to extract effective features.

Figure 3.

Quantitative profiling of intrinsic data characteristic drivers. (a) Stacked bar plots visualizing the mean positive recognition score of methods across datasets stratified by Shannon entropy levels (high, medium, low). (b) Visualization of methylation rates, Shannon entropy, and corresponding mean prediction accuracy across datasets. (c) Performance sensitivity to specific data properties: left, line plots of ACC versus sparsity ratio; middle, line plots of MCC versus coverage per cell; right, composite plot of method-specific F1 scores (lines) and global average MCC (right y-axis) across increasing methylation rates of real datasets. (d) Dot plots comparing TPR and TNR distributions across datasets grouped by Shannon entropy levels. (e) Stacked bar plots illustrating the aggregate influence of data attributes on performance via regression and Pearson correlation analysis.

As a further analysis, we dissected the causal chain between intrinsic methylome characteristics and imputation model performance. We visualized the stepwise associations between genome-wide methylation rate distributions, Shannon entropy, and ACC across all datasets for this analysis in Fig. 3b, with datasets ordered from low to high entropy from bottom to top. We observed a three-tiered trend across the full dataset cohort: first, low-entropy datasets (e.g. mOocyte, hCMP) exhibited tightly concentrated, low-dispersion methylation rate distributions, paired with uniformly low Shannon entropy values (<1.00) and near-perfect model prediction ACC (generally >0.90). As the dispersion of methylation rate distributions increased markedly, which was evidenced by wider boxplot spans and a shift of the median toward intermediate methylation levels, Shannon entropy rose in a stepwise manner, reaching >1.5 in high-entropy datasets (e.g. hPGC, mESC_2i). Across entropy groups, model prediction accuracy showed an overall declining trend, with a relative decrease of >15% from the low-entropy to high-entropy groups. This consistent cross-dataset association provides evidence that biological heterogeneity, quantified by the Shannon entropy of the methylome, is a core intrinsic driver of imputation model performance, with elevated entropy directly impairing model prediction accuracy and reliability.

Subsequently, we analyzed three specific data properties individually (Fig. 3c). First, sparsity represents the degree of missing data. As illustrated in Fig. 3c left, we observed a significant decline in the ACC curve as dataset sparsity increases. This indicates that imputation performance is critically dependent on the degree of data sparsity. Next, CpG coverage per cell, defined as the proportion of genomic CpG loci successfully sequenced within an individual cell, explicitly quantifies the absolute density of available epigenetic signals. In Fig. 3c middle, we observed a clear upward trend in MCC scores as CpG coverage increases. This indicates that sufficient data density is a prerequisite for correct model decisions, and insufficient information directly limits model performance. Finally, the average methylation rate reflects the abundance of biological signals. In Fig. 3c right, we observed that while method-specific F1 scores generally rise with higher methylation rates, the global average MCC fluctuates complexly. This suggests that simply increasing the quantity of methylation signals improves positive-related metrics but does not guarantee a balanced classification ability between positives and negatives.

Furthermore, as shown in Fig. 3b, high-entropy datasets (e.g. hPGC) can yield deceptively high overall ACC, but perform markedly worse in other metrics such as MCC (see “Systematic benchmarking unveils a data-difficulty-dependent performance landscape and algorithmic bottlenecks” section). This result highlights the critical limitation of using ACC as the sole evaluation criterion. To address this, we assessed the balance between TPR and TNR across all datasets (Fig. 3d) and used dumbbell plots to directly visualize and quantify the divergence between these two metrics. We found that high-entropy datasets exhibited significant imbalance between TPR and TNR, with one metric notably elevated while the other was markedly reduced. For instance, the mESC_2i dataset showed a substantially higher TNR relative to TPR. In stark contrast, this divergence was drastically narrowed in low-entropy datasets, with TPR and TNR largely balanced. This observation uncovers a severe class bias in models trained on complex, high-entropy data: models preferentially predict the majority class to inflate overall accuracy while sacrificing sensitivity to detect biologically critical positive signals.

Finally, to quantify the determinants of imputation fidelity, we employed multivariate regression analysis and Pearson correlation coefficients to calculate the contribution weight of each data feature (Fig. 3e). The resulting feature importance ranking reveals that intrinsic data complexity, particularly sparsity and biological heterogeneity measured by Shannon entropy, impacts model performance more than simple data volume such as sequencing coverage or cell counts.

Impact of sample size on imputation stability

To systematically evaluate the adaptability and scalability of imputation methods to varying data scales, we assessed both computational efficiency and performance stability across a full spectrum of dataset sizes using a two-tiered experimental design. This two-tiered design assesses method adaptability and scalability across dataset sizes ranging from minimal single-cell inputs to large-scale datasets, while accounting for each method’s computational constraints. We selected the MCC and F1 as the primary metrics for all analyses, as they reflect the comprehensive performance of the models. In addition, to investigate whether the abnormally high ACC values were associated with cell count, we monitored dynamic changes in ACC specifically in the hPGC experiment, as this dataset represents a high-entropy moderate-scale scenario (corresponding to the high Shannon entropy level scenarios in “Intrinsic determinants of imputation performance” section).

First, to characterize scalability within the small-scale setting, we selected five representative datasets, mESC_2i, mESC_Ser, hCellLine, hHCC, and hCLP, and constructed incremental training subsets ranging from single cells to the full dataset volume. For each subset, we executed all applicable imputation methods and aggregated performance metrics to characterize how model performance changes with increasing cell numbers. Corresponding analysis of these small datasets (Fig. 4a) revealed distinct behavioral profiles across methods. CaMelia followed a unique pattern: it failed to process single-cell inputs (N = 1) and reached its peak performance with as few as three to five cells. However, in heterogeneous datasets such as mESC_2i and mESC_Ser, its MCC and F1 declined notably as the number of input cells increased, in stark contrast to its stable performance on the simpler hCLP dataset. In contrast, deep learning models (e.g. CpG Transformer and GraphCpG) can technically run on single-cell (N = 1) inputs, but their performance only stabilized once the sample size exceeded five cells.

Figure 4.

Evaluation of model scalability and reliability across diverse data splitting strategies. (a) Scalability of imputation methods. Line plots showing the scalability of methods with increasing cell numbers across five datasets (hHCC, mESC_2i, mESC_Ser, hCLP, and hCellLine). The x-axis represents the number of cells, and the y-axis represents MCC (upper) and F1 score (lower). (b) Bar plots showing the scalability of methods on the moderate-scale hPGC dataset. The x-axis represents the number of cells, and the y-axis represents MCC, F1, and ACC scores. (c) Reliability assessment of methods under different data splitting strategies with statistical significance analysis. Box plots compare the MCC and F1 distributions obtained from random splits versus chromosome-based splits on hCLP, mESC_Ser, and mESC_2i datasets. Notably, significance levels are defined as ns, P > .05; ^*, P ≤ .05; ^**, P ≤ .01; ^***, P ≤ .001.

Second, to investigate performance dynamics in the moderate-to-large-scale setting, we leveraged the hPGC dataset (461 cells) and generated subsets of 5, 10, 25, 50, 75, 100, 150, and 200 cells. This extended range was specifically designed to rigorously evaluate architectures, such as CpG Transformer, GraphCpG, and MambaCpG, enabling a rigorous evaluation of their stability under substantially larger cell counts. Average metrics were calculated for each subset size and visualized to facilitate a direct comparison of scalability patterns across different algorithmic approaches. Results from this moderate-to-large-scale benchmark (Fig. 4b) showed that the data volume reliance observed in small-scale experiments was even more pronounced here: deep learning models required a minimum of 50 cells to achieve stable performance. Once this threshold was crossed, all deep learning models maintained consistent and stable performance. Meanwhile, ACC was consistently high across all imputation methods tested on the hPGC dataset, validating the robustness of our aforementioned findings in “Intrinsic determinants of imputation performance” section.

Notably, GraphCpG exhibited the best scalability across all tested methods, uniquely demonstrating the capacity to process moderate-to-large matrices exceeding 400 cells (e.g. the full hPGC dataset with 461 cells). Conversely, CaMelia commonly failed to process datasets with >20 cells in these large cohorts due to prohibitive computational overhead, confirming its applicability is restricted exclusively to small-scale studies; importantly, within the range of small datasets it could stably process, CaMelia achieved the top predictive performance among all competing methods.

Reliability assessment and the impact of train-test splitting strategies

In the evaluation of imputation models, the strategy employed to split the dataset into training and test sets fundamentally dictates the reliability of the performance metrics. To rigorously validate the reliability of our performance evaluations and eliminate evaluation bias introduced by genomic data leakage, we systematically benchmarked the impact of two distinct train-test splitting strategies on DNA methylation imputation model performance: standard random genome-wide splits and biologically motivated chromosome-based hold-out splits. The two strategies are defined by their handling of genomic position information: random splitting distributes individual CpG sites across training and test sets without accounting for their genomic positions, while chromosome-based splitting strictly partitions full, non-overlapping chromosomes into separate training and held-out test sets.

For the chromosome-based hold-out approach, we adopted a setup fully consistent with that detailed in the preceding content (see “Dataset splitting and training strategy” section). For the random split approach, we divided the dataset into training and test sets at a 9:1 ratio randomly. This paired experimental design ensures a roughly consistent number of training samples between the two strategies to guarantee a fair comparison for assessing how the data splitting strategy affects model stability.

Across three tested datasets (mESC_2i, mESC_Ser, hCLP) and all evaluated models, we observed two consistent core trends (Fig. 4c): first, random splitting consistently produced significantly higher MCC and F1 scores, with markedly lower result variability (as evidenced by narrower interquartile ranges) relative to chromosome-based splits; second, every model exhibited pronounced performance declines when evaluated under the chromosome-based split framework, with the magnitude of decline directly reflecting the degree to which model performance relied on local CpG correlations.

As shown in Fig. 4c, the pattern of statistically significant inflation under random splitting is consistent with a data leakage mechanism in genomic prediction tasks. The mechanistic basis for this performance discrepancy is well established in DNA methylation imputation: adjacent CpG sites have highly correlated methylation states, and random splitting inevitably places highly similar neighboring sites in both training and test sets. This allows models to achieve spuriously high, inflated performance by leveraging these local genomic correlations, rather than learning genome-wide methylation regulatory patterns [52, 53]. In contrast, chromosome-based splits eliminate this data leakage source, resulting in more conservative, unbiased performance estimates and greater variability in results, as model performance is no longer inflated by easily accessible local correlations.

We further found that the severity of performance inflation from random splitting was modulated by the intrinsic biological heterogeneity of the dataset. The largest performance gaps between random and chromosome-based splits were observed in the highly heterogeneous mESC_2i and mESC_Ser datasets, while the relatively less complex hCLP dataset showed slightly reduced but still substantial discrepancies. Even in hCLP, the majority of models failed to maintain consistent performance under the chromosome-based split framework, confirming that performance overestimation induced by random splitting is a widespread issue across datasets of varying biological complexity.

Additionally, we identified stark differences in robustness to data splitting strategy across the evaluated models. CaMelia exhibited the strongest stability, with the smallest decline in performance between random and chromosome-based splits, closely followed by GraphCpG. DeepCpG displayed intermediate robustness. Conversely, CpG Transformer and MambaCpG showed strong sensitivity to splitting protocol, with severe drops in MCC under the chromosome-based split framework, as both architectures rely critically on long-range correlations between adjacent CpG sites for accurate prediction.

Finally, to determine if this splitting-induced performance bias is a universal phenomenon or specific to certain models, we performed experiments using a five-fold cross-validation training paradigm (see Supplementary Fig. S2). These experiments confirmed that the training results across cross-validation folds were highly stable with significantly smaller variance, which was lower than that observed under random splitting, further confirming the robustness and reproducibility of our findings.

Evaluation of the models’ inter-dataset generalizability and the impact of source training data

To validate the inter-dataset generalizability of the models and systematically dissect the core factors governing transfer performance, we established a rigorous evaluation framework comprising two complementary experimental designs. In the first phase, we conducted exhaustive pairwise transfer tests where models were fully trained on a single source dataset and evaluated on an independent target dataset within the same species context. For human data, transferability was assessed across hematopoietic progenitor populations (hCLP, hCMP, and hGMP), while for mouse data, evaluations spanned embryonic stages exhibiting varying degrees of heterogeneity (mESC_2i, mESC_Ser, and mOocyte). Crucially, to quantify the deterministic role of intrinsic data characteristics, we stratified source datasets based on our prior benchmarking profiling of Shannon entropy (see “Intrinsic determinants of imputation performance” section). Specifically, mOocyte, hCLP, hCMP, and hGMP were classified as information-rich, low-entropy datasets, characterized by low biological heterogeneity and relatively high coverage, whereas mESC_Ser and mESC_2i were classified as high-complexity, high-entropy datasets, characterized by severe epigenetic heterogeneity and extreme sparsity. This stratified design facilitated a systematic analysis of how the intrinsic fitness of the training data influences inter-dataset prediction performance.

We applied this pairwise transfer framework to systematically evaluate the boundaries of model transferability across all dataset pairs (Fig. 5a–c and Supplementary Fig. S3), which revealed significant differences in transfer robustness among the tested methods. CaMelia, which relies on explicit feature engineering, demonstrated the highest stability, maintaining high MCC scores across most transfer tasks. In contrast, deep learning architectures exhibited variable generalization capabilities. While CpG Transformer showed moderate adaptability, GraphCpG experienced a sharp decline in performance when transferred to new datasets. This sensitivity suggests that GraphCpG may overfit to the specific characteristics of the source dataset, limiting its utility in scenarios where training and test data come from different biological contexts.

Figure 5.

Generalization capability of imputation methods assessed by inter-dataset prediction. (a–c) Grouped bar plots compare the MCC and AUC of models trained on various source training datasets and evaluated on target datasets mESC_2i (a), mOocyte (b), and hCMP (c), including within-dataset baselines. In legends, “X for Y” means models trained on X and tested on Y; a single dataset name marks the within-dataset baseline. (d) Aggregated performance summaries for the inter-dataset generalization experiments. Left: average metric values across all imputation methods when the specified dataset (x-axis) serves as the singular training source, with models subsequently evaluated on the other target datasets. Right: average metric values across all imputation methods when the specified dataset (x-axis) serves as the evaluation target, predicted by models previously trained on the other source datasets.

Notably, beyond method-specific differences, the entropy of the training source emerged as a more critical determinant of generalization than the imputation method itself. As visualized in the metric composition analysis (Fig. 5d), models trained on low-entropy dataset mOocyte demonstrated superior transferability compared to those trained on high-entropy datasets such as mESC_2i. Strikingly, in specific scenarios involving DeepCpG and CpG Transformer, models trained on the low-entropy mOocyte dataset and transferred to the mESC_2i target actually outperformed models trained directly on the mESC_2i dataset itself (e.g. DeepCpG MCC: ~0.77 transfer versus ~0.35 self-trained). This suggests that robust biological patterns learned from low-entropy data can compensate for the inherent sparsity in high-entropy targets, offering a superior alternative to training on noisy local data. Conversely, high-entropy training sources consistently led to poor performance across all targets. For instance, evaluations on the mOocyte target yielded the highest average ACC (~0.89), followed by mESC_Ser (~0.85) and mESC_2i (~0.78). Collectively, these results underscore the critical importance of low-entropy source data for effective inter-dataset generalization.

Building on these findings, we next investigated whether increasing information volume via data integration strategies could further improve model generalizability, which constituted our second experimental design. We constructed three categories of mixed datasets to test this: intra-species human mixtures pooling distinct tissues, intra-species mouse mixtures, and inter-species mixtures combining human and mouse data. While intra-species integration followed standard procedures for constructing cell-by-site methylation matrices, cross-species integration presented a fundamental challenge due to the divergence of genomic coordinates and the lack of one-to-one CpG site alignment between species. Consequently, methods reliant on species-specific sequence contexts or strictly aligned genomic loci, specifically DeepCpG and CaMelia, were excluded from the inter-species experiments as their model architectures are incompatible with the disjoint feature spaces inherent to multi-species matrices. Across all integration tests, we found that simply increasing data volume by mixing datasets did not improve predictive performance. As evidenced by the bubble plot analysis (Fig. 6a), models trained on mixed datasets (e.g. mOocyte + mESC_2i) often underperformed those trained solely on the low-entropy subset (e.g. mOocyte). In cross-species training setups, models such as MambaCpG achieved a competitive accuracy of ~0.91 when trained on integrated human and mouse datasets (e.g. hCMP + mOocyte), yet still failed to surpass the performance of models trained exclusively on the low-entropy mOocyte dataset. These results indicate that noise inherent in high-entropy or divergent datasets interferes with the biological signals from low-entropy subsets, effectively hindering rather than improving predictive performance.

Figure 6.

Model performance under mixed-dataset training and fine-tuning. (a) Bubble plots display the ACC results of models trained on mixed datasets, including mouse-only, human-only, and cross-species (mouse and human) dataset combinations. (b–c) Grouped box plots compare the performance (ACC, AUC, and MCC) of CpG Transformer, GraphCpG, and MambaCpG models before (Org) and after fine-tuning (FT), across inter-dataset transfer and intra-dataset evaluation scenarios for mESC_2i, mESC_Ser, and mOocyte datasets.

Taken together, our analyses systematically characterized the inter-dataset generalizability of DNA methylation imputation models and identified core drivers of transfer performance across experimental contexts. We demonstrated that the entropy of the source training dataset is the primary determinant of inter-dataset generalization, outweighing the choice of imputation method, with low-entropy datasets enabling robust transfer even to sparse, heterogeneous target datasets. Additionally, we identified marked differences in transfer robustness across tested methods. Machine-learning methods are more stable across different test settings than deep learning models, which often overfit to the specific features of the source dataset. We further confirmed that unfiltered data pooling to increase sample volume does not enhance model generalizability and instead often degrades performance by introducing noise that disrupts the learning of robust biological patterns. These findings provide actionable, experimentally validated guidance for training data and imputation method selection in DNA methylation studies requiring inter-dataset generalization.

Impact of evaluation strategy and fine-tuning

While direct model transfer offers a convenient baseline for inter-dataset generalization, its performance is often limited by distributional differences between source and target datasets. To address this limitation, we employed a fine-tuning strategy where models pre-trained on the source dataset were further optimized on target data using a reduced learning rate. We conducted systematic fine-tuning experiments across differing data quality gradients, with two core aims: first, to assess whether fine-tuning the pre-trained models on target data could yield performance improvements beyond direct transfer; and second, to investigate the plasticity of pre-trained models and the bounds of transfer learning.

In inter-dataset and intra-dataset transfer evaluations, GraphCpG benefited the most from this fine-tuning strategy, achieving consistent and significant performance improvements across the vast majority of transfer tasks and all tested scenarios. Specifically, across ACC, AUC, and MCC metrics, GraphCpG exhibited a marked increase in median performance and reduced result variance after fine-tuning. This indicates that while graph models may struggle with direct zero-shot transfer, they are highly capable of adapting to the specific epigenetic characteristics of the target domain to substantially improve predictive performance. In contrast, sequence-based models CpG Transformer and MambaCpG showed scenario-dependent limited gains, with highly variable performance changes across different entropy gradients. When these models were pre-trained on low-entropy datasets (e.g. mOocyte) and fine-tuned on high-entropy targets (e.g. mESC_2i, mESC_Ser), fine-tuning often achieved negligible improvements or even a consistent decline in performance across the three metrics. This suggests that the robust biological patterns established during pre-training can be disrupted when adapted to a noisy, high-heterogeneity target domain.

Conversely, when pre-trained on high-entropy source datasets (e.g. mESC_2i) and fine-tuned on low-entropy target datasets (e.g. mOocyte), these models exhibited consistent and significant performance improvements across all three metrics. In low-entropy to another low-entropy inter-dataset transfer scenarios (e.g. hCLP to hCMP), fine-tuning yielded consistent moderate gains across the three metrics.

Taken together, our analysis reveals that the benefits of this fine-tuning strategy are not universal but depend heavily on the specific model architecture, as well as the entropy gradient between the pre-training source dataset and the fine-tuning target dataset, with fully consistent trends observed across all three evaluated performance metrics (ACC, AUC, and MCC; Fig. 6b and c).

Beyond accuracy metrics, we also evaluated the computational efficiency of transfer learning. Detailed monitoring of training epochs for the CpG Transformer model (see Supplementary Table S5) revealed that fine-tuning significantly accelerates model convergence. While training with random initialization typically required ~30 epochs to stabilize, fine-tuning a pre-trained model on the same target achieves convergence in as few as 7–9 epochs. This corresponds to a three- to four-fold reduction in computational time for target domains, confirming that fine-tuning is a highly efficient strategy for reusing pre-trained weights, allowing models to adapt to new contexts without the computational burden of training from scratch.

Computational costs and training stability

To systematically evaluate the computational efficiency of DNA methylation imputation methods across diverse data scenarios, we established a comprehensive benchmarking framework that controls for two primary variables, input dataset size and intrinsic dataset characteristics, with three complementary assessment dimensions to capture distinct computational profiles of tested methods. All evaluations were conducted on an NVIDIA RTX A6000 graphics processing unit with 48 GB of memory. For rigorous and fair cross-method comparison, we defined the computational time as the end-to-end execution duration of the imputation workflow, including preprocessing, training, and imputation. We designed three sets of computational efficiency experiments to systematically characterize the performance of all tested methods. Systematic profiling of computational resources across all experimental settings revealed the distinct scalability limits and efficiency profiles of each tested architecture (Fig. 7a). Our efficiency analysis demonstrated that computational cost depends not only on input cell count, but is also critically sensitive to the genomic coverage and intrinsic complexity of the dataset.

Figure 7.

Evaluation of computational efficiency and training convergence dynamics. (a) Computational time cost of methods under different scenarios. Left, running time for processing 20 cells across different datasets; middle, total imputation workflow time on the hEmbryo dataset with increasing cell numbers; right, total imputation workflow time on the mESC_2i dataset with increasing cell numbers. (b) Line plots showing the training dynamics of deep learning methods on mESC_2i and mESC_Ser datasets, with the x-axis representing training epochs and the y-axis representing the average value of all performance metrics for the full dataset.

Specifically, for the first set of experiments, we fixed the input cell count at 20 cells to isolate the impact of intrinsic dataset features. At this fixed 20-cell input level, all tested methods maintained low runtime on low-coverage, high-sparsity datasets (hHCC, hCellLine), while dramatic divergence in computational cost emerged on high-coverage, low-sparsity datasets (hCLP, hEmbryo). Specifically, CaMelia exhibited a distinct sensitivity to genomic site density, with its runtime increasing significantly on the high-coverage hCLP dataset; CpG Transformer and GraphCpG showed the lowest sensitivity to dataset complexity, maintaining stable and low runtime across all 20-cell datasets.

For the second set of experiments, we focused on small-scale settings (1 to 12 cells, mESC_2i dataset) to characterize method efficiency in ultra-low sample size settings. In this scenario, CaMelia, GraphCpG, and CpG Transformer maintained consistently low and stable runtime across the full cell count gradient, delivering optimal efficiency for ultra-small sample inputs. In contrast, DeepCpG and MambaCpG showed rapid linear growth in runtime with increasing cell numbers, reaching nearly 900 min at the maximum 12-cell input, with markedly inferior efficiency in small-scale settings.

For the third set of experiments, we assessed method scalability in moderate-to-large-scale settings (5 to 200 cells, hEmbryo dataset) to test performance in routine research scenarios. In this setting, deep learning models exhibited highly disparate scalability patterns. MambaCpG displayed pronounced nonlinear computational growth, with runtime increasing exponentially as cell numbers rose, exceeding 16 000 min at 200 cells, which identifies its computational burden as a major bottleneck for moderate-to-large-scale dataset applications. GraphCpG achieved the optimal linear scalability among all tested models, exhibiting a gradual and linear increase in runtime even on the 200-cell hEmbryo dataset.

Beyond overall computational efficiency and scalability, we further investigated the convergence behavior and training dynamics of deep learning–based imputation architectures. Four deep learning models underwent extended training for >10 epochs across four representative datasets (mESC_2i, mESC_Ser, hCellLine, hEmbryo), during which six performance metrics (ACC, AUC, TPR, TNR, F1, MCC) were recorded on the validation set after every training epoch. In terms of training dynamics, we observed that performance metrics for most models converged rapidly within the first few epochs (Fig. 7b and Supplementary Fig. S4), with distinct stability profiles across different architectures.

DeepCpG plateaued almost immediately after the first epoch, indicating that extended training failed to yield further performance improvements. In contrast, GraphCpG exhibited high training instability, with its performance scores fluctuating constantly throughout the training process, suggesting that the model had difficulty reaching a stable convergent state. Meanwhile, CpG Transformer and MambaCpG reached stable, high-performance plateaus at an early training stage (~10 epochs), with prolonged training yielding minimal additional gains in predictive performance. Despite these marked differences in training dynamics across models, the performance of most methods showed only limited changes after ~20 training epochs.

A dual-view strategy from model and data perspectives

BridgeCpG overcomes single-model limitations through adaptive ensemble learning

Overview of BridgeCpG

Our systematic benchmarking identified a critical trade-off inherent to single-model architectures: while GraphCpG utilizes topological learning to achieve superior sensitivity in highly heterogeneous populations (defined by elevated Shannon entropy, such as >1.5 in our earlier experiments, see “Intrinsic determinants of imputation performance” section for more details), it often suffers from volatility during transfer learning. Conversely, sequence-based models like CpG Transformer demonstrate robust generalization but may lack the specialized resolution for extreme sparsity. Meanwhile, state-space models like MambaCpG exhibit unique advantages in capturing long-range dependencies within highly heterogeneous datasets.

To synthesize these complementary strengths and overcome the limitations of standalone frameworks, we developed a model-view strategy, BridgeCpG, an ensemble strategy employing a meta-learner [37] to dynamically integrate diverse inductive biases. Specifically, BridgeCpG adaptively integrates three distinct architectures, CpG Transformer, GraphCpG, and MambaCpG, and machine-learning methods like CaMelia are excluded due to their restrictive scalability limits on datasets. To ensure strictly comparable inputs, we applied identical masking protocols to the training data for all base models, generating independent imputation matrices. Leveraging our prior analysis of data characteristics, we designed an interpretable LightGBM-based meta-learner. This design enables efficient modeling of nonlinear feature interactions while providing gain-based feature importance for interpretation. The meta-learner serves as a classifier that extracts multidimensional features encompassing statistical distributions to dynamically synthesize the final imputed values. To capture the fine-grained predictive confidence of each model, we retained the raw continuous probabilities (ranging from 0 to 1). Ultimately, these parallel cell-by-site probability distributions were fused into a comprehensive feature matrix, directly empowering the meta-learner to adaptively weigh the diverse inductive biases of the base models.

Dataset splitting and training strategy of BridgeCpG

In the BridgeCpG ensemble learning experiment, to eliminate data leakage between base model and meta-learner training, we implemented the following dataset partitioning rule for both mouse and human datasets. Specifically, the base model training set was the original benchmark training set with only chr11 excluded, chr11 served as the exclusive meta-learner training set, and chr10 remained the final held-out test set consistent with benchmark experiments. Following this adjustment, we designed a specialized training pipeline to ensure ensemble effectiveness leveraging stacked generalization principles [54–56], which follows three sequential steps. First, base models were trained on the adjusted training set; then, the LightGBM-based ensemble meta-learner was trained on chr11; and finally, the final performance was evaluated on chr10. This data splitting strategy is largely consistent with that used in the previous benchmark experiments (see “Dataset splitting and training strategy” section for more details). This design strictly prevented data leakage while maintaining identical evaluation conditions across all experiments, ensuring that the ensemble model was evaluated under strictly comparable conditions with the benchmark tests.

Result analysis

To validate this model-view strategy, we evaluated BridgeCpG on a targeted suite of challenging datasets, including mESC_2i, mESC_Ser, hMK, hPGC, and hCellLine (corresponding to the results in “Systematic benchmarking unveils a data-difficulty-dependent performance landscape and algorithmic bottlenecks” section). Furthermore, to rigorously assess the effectiveness of our meta-learning strategy, we introduced a naive average ensemble baseline for comparison (denoted as “Naive average ensemble” in Fig. 8a). This baseline simply calculates the arithmetic mean of probabilities from all base models, representing a standard unweighted integration approach.

Figure 8.

Performance and interpretability of the LightGBM-based ensemble model BridgeCpG. (a) Radar charts comparing the performance of BridgeCpG against individual models and the simple average ensemble across five datasets: hCellLine, mESC_Ser, mESC_2i, hMK, and hPGC (20 cells). (b) Performance comparison on the mESC_2i dataset (1–12 cells) between BridgeCpG, individual models (CpG Transformer, GraphCpG, MambaCpG), and the naive average ensemble. Line plots show ACC, MCC, and F1 results with increasing cell numbers. (c) Feature importance analysis for BridgeCpG on the hMK dataset. Left, contribution of different feature categories; right, top 20 specific features by importance score.

These datasets were specifically selected because baseline architectures exhibited poor performance or high result volatility on them. By leveraging the meta-learner to weigh model contributions adaptively, BridgeCpG achieved superior performance compared to all three individual base models and the naive averaging strategy (Fig. 8a). As visualized in the radar chart analysis, BridgeCpG consistently outperformed baseline models across multiple metrics (ACC, AUC, MCC, and F1), avoiding the trade-offs typical of single-architecture approaches. This robustness was particularly evident in extreme scenarios with high intrinsic data complexity, including severe sparsity and high biological variance.

Furthermore, in the settings with very few cells (1 to 12 cells, Fig. 8b, detailed statistical significance analysis is provided in Supplementary Table S7), we observed that while the naive average ensemble stabilized predictions compared to individual models, its performance hit a clear ceiling. Crucially, BridgeCpG showed improved overall performance relative to the baseline methods.

To clarify the decision-making process of the meta-learner and understand the driving forces behind BridgeCpG’s superior performance, we conducted a comprehensive feature importance analysis. By extracting the internal gain weights from the meta-learner, we systematically ranked the contributions of all input dimensions. As illustrated in Fig. 8c, this interpretable profiling reveals that the meta-learner identified predictions from GraphCpG as the most informative feature, closely followed by local relative-position features. This suggests that the ensemble does not merely average outputs; rather, it dynamically prioritizes the most reliable topological and spatial signals to compensate for the limitations of individual architectures in these complex scenarios.

Because BridgeCpG requires running multiple deep learning base models before meta-learner integration, its computational cost is primarily bounded by the most expensive base model. Detailed individual results of each model can be found in “Computational costs and training stability” section. Therefore, BridgeCpG is most suitable for small-to-moderate datasets where all base models can be trained within available GPU memory and runtime budgets. For large-scale datasets exceeding the feasible scale of base models, we recommend applying the adaptive divide-and-conquer (D&C) strategy (“Adaptive divide-and-conquer strategy resolves heterogeneity bottlenecks” section) before imputation and using BridgeCpG on partitioned subsets.

Adaptive divide-and-conquer strategy resolves heterogeneity bottlenecks

The design of the divide-and-conquer strategy

While BridgeCpG optimizes performance at the model view by integrating different architectural strengths, a fundamental challenge remains at the data view, particularly when processing large-scale and heterogeneous datasets. Global training on such highly heterogeneous populations introduces excessive complexity, making it difficult for models to capture consistent biological patterns. To overcome this intrinsic bottleneck, we implemented an adaptive D&C strategy. This approach shifts the paradigm from complex global modeling to subset-specific optimization.

Specifically, to evaluate the efficacy of heterogeneity resolution, we employed Ward’s linkage hierarchical clustering [57] to partition the global cell population according to overall methylation and coverage characteristics. This procedure grouped cells with relatively similar data profiles into multiple sub-clusters, reducing the conflicting signals encountered during global training. Imputation was then performed independently within each cluster before the results were aggregated, thereby transforming the global problem into a series of smaller and more homogeneous sub-tasks.

To improve data suitability for stable training, cluster sizes were constrained to a predefined range, typically 10–100 cells. Clusters below the minimum size were individually reassigned to the nearest eligible-cluster centroid in the weighted feature space, whereas clusters above the maximum size were recursively subdivided until all resulting clusters satisfied the specified size limits. Independent imputation models (e.g. CpG Transformer or CaMelia) were then trained on each refined cluster, and final predictions were aggregated to reconstruct the complete dataset.

For comparative benchmarking, we established two baseline protocols: a random sampling approach where the dataset was split ignoring methylation and a stratified sampling approach where cells were sampled proportionally from identified clusters to train a single global model.

Result analysis

This strategy is grounded in the intrinsic topological structure of single-cell epigenomes. To visually validate the distinct epigenetic identities of these partitions, we employed t-SNE [58] to project the high-dimensional methylation profiles into a two-dimensional latent space. As shown in the hFC and mBrain_Atlas datasets (Fig. 9a), the resulting embeddings displayed distinguishable cell groups, indicating that the partitioning procedure can organize atlas-scale datasets into smaller subsets with relatively similar data characteristics. These results support the feasibility of applying the D&C partitioning workflow to large-scale datasets and provide a practical basis for subsequent cluster-wise imputation.

Figure 9.

Experimental validation of the adaptive divide-and-conquer strategy. (a) t-SNE embeddings visualizing the cellular manifolds of the massive biological atlases (mBrain_Atlas and hFC datasets). (b) Validation of the Ward-based clustering on the hEmbryo dataset. Left: t-SNE projection of the 11 identified cell sub-clusters. Right: methylation rate distributions of the sub-clusters compared to the global population. (c) Box plots comparing the imputation performance (MCC and F1) across 11 sub-clusters on the hEmbryo dataset against the global stratified sampling baseline. (d) Grouped bar plots demonstrating performance improvements of the divide-and-conquer strategy. The plots contrast the performance of CpG Transformer and GraphCpG using the D&C implementation (hatched bars) against standard global training (solid bars) on representative large-scale datasets. (e) Evaluation of the adaptive divide-and-conquer strategy on the highly heterogeneous mESC_2i dataset. Top left: dimensionality-reduction scatter plot of cells labeled according to their identified sub-clusters. Top right: methylation rate distributions of the three sub-clusters compared to the global population (all data). Bottom: box plots comparing the imputation performance (MCC and F1) of the cluster-based strategy against random and stratified sampling baselines.

To isolate the specific contribution of our Ward-based partition strategy, we established two control baselines: a random sampling strategy, which constructs training sets without regard for biological substructure, and a stratified sampling strategy (labeled as “Mixed”), which ensures proportional representation of cell types but still trains a single global model.

We first validated this strategy on the hEmbryo dataset (285 cells), which is characterized by significant developmental diversity (Fig. 9b). Our Ward-based clustering successfully partitioned the heterogeneous global population into 11 biologically consistent sub-clusters. Methylation rate analysis (Fig. 9b) confirms that this decomposition effectively resolves data complexity: while the global dataset exhibits high variance due to mixed cell states, each sub-cluster represents a distinct, low-variance developmental profile. Quantitative evaluation demonstrates that this reduction in heterogeneity directly translates to performance improvements. Notably, all 11 sub-clusters achieved imputation F1 scores and MCC superior to those of the stratified sampling strategy (Fig. 9c). This finding empirically validates a key finding of our research: the quality of the signal is more critical than the quantity of the sample size. Crucially, this result serves as the causal validation of our earlier benchmarking analysis regarding the impact of methylation rate complexity (corresponding to “Intrinsic determinants of imputation performance” section), where we observed that high-entropy distributions consistently degraded model performance regardless of data scale. By reducing this heterogeneity, we confirm that resolving complex biological signals is the key factor for high-fidelity imputation.

Furthermore, we validated the broad applicability of the D&C strategy by extending our evaluation to additional deep learning architectures and large-scale datasets. As illustrated in Fig. 9d, both CpG Transformer and GraphCpG exhibited consistent performance improvements when integrated with the D&C strategy relative to their standard global training baselines. This advantage was robust across multiple metrics, including MCC and F1 (see Supplementary Fig. S5a and b for hPGC details), demonstrating that the D&C strategy functions as a data-view optimization framework that effectively enhances deep learning architectures in heterogeneous biological contexts.

Finally, to further evaluate the robustness of this approach, we extended the validation to high-complexity scenarios identified in our earlier benchmarking (“High Shannon entropy level” scenarios in “Intrinsic determinants of imputation performance” section), specifically mESC_2i and mESC_Ser datasets. Despite the limited cell counts and high noise inherent to these datasets, the D&C strategy generally achieved higher MCC and F1 than the random and stratified baselines (Fig. 9e; Supplementary Fig. S5c shows mESC_Ser details, and Supplementary Table S8 reports full results including significance analysis). In this robustness analysis, the predefined constraints on cluster cell numbers were not applied, allowing us to evaluate the effect of heterogeneity decomposition independently of cluster-size restrictions. This performance differential underscores a critical distinction: while the random and stratified strategies force the model to learn from a global distribution containing complex epigenetic patterns, the D&C strategy successfully decomposes the heterogeneous population into epigenetically homogeneous subsets. These results suggest that decomposing data heterogeneity is essential to recovering subset-specific signals masked by global modeling.

Establishment of a quantitative decision framework for data-fitness optimization

We present a global benchmark summary and multidimensional evaluation of all scDNAm imputation methods in Fig. 10a and Supplementary Table S9. The heatmap systematically summarizes the performance ranking of all methods across diverse evaluation dimensions, including imputation performance under simple, intermediate, and challenging data-difficulty levels, as well as scalability, robustness, generalization ability, fine-tuning impact, and computational costs. All methods were ranked according to their performance on each indicator, among which seven imputation methods (ranked 1–7) and three divide-and-conquer strategies (ranked 1–3) were evaluated and ranked separately. This comprehensive multidimensional assessment provides a holistic view of the strengths, limitations, and applicable scenarios of each method, laying a robust empirical foundation for rational imputation method selection.

Figure 10.

Global benchmark summary and practical guide for method selection. (a) Overall performance ranking and multidimensional evaluation. Heatmap summarizing the performance ranking of all methods across different evaluation dimensions. We ranked all the methods according to the performance of each indicator, among which seven imputation methods (ranked 1–7) and three divide-and-conquer strategies (ranked 1–3) were ranked separately. Gray cells with cross marks indicate unavailable results, while solid light gray cells indicate experiments not required. (b) A guided selection pipeline for scDNAm imputation methods.

Furthermore, building on our comprehensive benchmarking results, we established a quantitative decision framework [59] to guide imputation method selection based on model architectures and specific data characteristics, i.e. intrinsic biological complexity and dataset-scale settings. As delineated in the selection guide (Fig. 10b), the workflow begins with a quantitative profiling phase. In this step, we calculate data sparsity, Shannon entropy, and average methylation rate to provide a comprehensive quantitative characterization of the input data.

For small-scale settings containing 20 or fewer cells, our framework identifies CaMelia as the competitive option when compatible bulk information is available. This recommendation is driven by two key advantages: CaMelia efficiently circumvents the dependency on large-scale training data inherent to deep learning architectures and maintains high imputation fidelity even in data-scarce scenarios. However, this applicability is constrained by a computational bottleneck. As detailed in Supplementary Table S6, CaMelia encounters a memory limit at ~50 million unique loci. This genomic data volume matches the total sequencing data of ~20 cells from standard protocols, such as scBS-seq [6]. Datasets beyond this scale cause prohibitively high memory usage, requiring alternative strategies.

Conversely, for large-scale, high-complexity scDNAm datasets exceeding 500 cells, the framework directs the analytical workflow toward the D&C strategy. By utilizing Ward-based clustering, this approach decomposes the extensive global dataset into multiple computationally tractable subsets. This partitioning allows for the independent processing of each subgroup, effectively circumventing the prohibitive memory and computational bottlenecks associated with training a single monolithic model, thereby ensuring robust scalability for atlas-level data.

For moderate-scale datasets, typically comprising hundreds of cells, method selection is guided by the specific data attributes quantified during the initial profiling. Specifically, MambaCpG is prioritized for highly heterogeneous populations, where its sequence modeling capabilities effectively capture complex intercellular variations. Alternatively, GraphCpG is recommended for scenarios with significant class imbalance (characterized by exceptionally high or low average methylation rates in “Intrinsic determinants of imputation performance” section), as its graph-based learning framework effectively preserves signals from minority classes. In the absence of these pronounced distributional challenges, CpG Transformer serves as the robust standard, while BridgeCpG is identified as the superior candidate when computational resources allow for the deployment of ensemble learning to achieve maximum fidelity.

Conclusions

In this study, we conducted a benchmark analysis of five imputation methods using scDNAm data from diverse tissues and sources of human and mouse. We evaluated these methods on the basis of accuracy, sensitivity to data characteristics, sensitivity to scalability, robustness to data splitting strategies, inter-dataset generalizability, convergence behavior, and computational efficiency, providing a comprehensive framework for the evaluation of methylation data imputation that can assist researchers in selecting the optimal imputation tool for their scDNAm data. Our results indicate that no single method is universally effective across all datasets and metrics, and the selection of the optimal method is highly dependent on the intrinsic characteristics of the data, such as sparsity and data entropy. This comprehensive evaluation benchmark we established not only provides a guideline for researchers to select the optimal imputation tool, but also reveals the limitations of current methods in handling complex heterogeneous data. Regarding the identified limitations, we proposed the BridgeCpG framework and demonstrated that integrating ensemble models with adaptive data strategies can break the performance bottleneck of single models, establishing a new gold standard for data recovery under high sparsity. Meanwhile, with the increasing requirements for memory and computational resources of scDNAm data, greater scalability is desirable to meet these demands. In parallel, the adaptive divide-and-conquer strategy demonstrates that benchmark-derived insights can guide scalable data-view optimization for large and heterogeneous scDNAm datasets.

Notably, we observed a negative transfer phenomenon in the generalizability evaluation. Although integrating more data is generally considered beneficial for improving model robustness, our experiments show that the predictive performance of the model decreases significantly when low-entropy datasets are mixed with high-entropy datasets. This finding alerts the research community that in large-scale scDNAm data imputation, the priority of data quality control should be higher than the blind expansion of data volume. The noise introduced by high-entropy data not only fails to provide valid information, but also contaminates the general biological features learned by the model. Therefore, future multi-dataset integration studies should establish stricter data admission criteria.

Beyond data quality control, the severe TPR–TNR imbalance observed in high-entropy datasets reveals an inherent algorithmic limitation of existing scDNAm imputation models. Optimizing solely for global accuracy may bias models toward dominant methylation states, resulting in asymmetric recognition of methylated and unmethylated signals. Thus, future scDNAm imputation methods may benefit from entropy-aware or class-balanced learning objectives to explicitly penalize asymmetric errors between positive and negative methylation states. For instance, focal loss functions [60] or class-balanced loss functions [61] can mitigate the dominance of easily classified majority methylation states while enhancing the contribution of hard-to-classify minority states during training. This provides a promising path for next-generation imputation models with balanced performance in highly heterogeneous methylomes.

Emerging spatial DNA methylation technologies, such as spatial-DMT [62] and SmC-seq [63], further raise new requirements for methylation imputation. Spatial DNA methylation data share core characteristics with scDNAm data, including sparse methylation observations and cell-by-locus or spot-by-locus representations, suggesting that scDNAm imputation models may be adapted to this emerging modality. However, spatial methylation data may exhibit stronger sparsity and additional spatially structured heterogeneity [64]. The adaptive D&C strategy proposed here is potentially extensible to this setting by partitioning spatially or epigenetically heterogeneous regions into more homogeneous subsets before imputation [65].

Although this study provides a comprehensive evaluation, it still has certain limitations. First, the absence of a gold standard for real data is always an inherent challenge in evaluation. Although we investigated the impact of some data characteristics on imputation performance, this cannot fully replace the complex features in real data. Second, this study did not explore the impact of imputation performance on downstream analyses. The influence of data characteristics on downstream analyses is complex and requires extensive future investigation for validation, which is beyond the scope of the present study. Third, our evaluation focused exclusively on scDNAm-specific methods. We did not evaluate methods developed for other modalities, such as scRNA-seq [66] or scATAC-seq [67], because the extreme dimensionality and binary distribution of methylomes render direct cross-application architecturally incompatible. However, benchmarking studies of these omics modalities [68–70] have provided critical methodological references for our evaluation framework, and established standardized evaluation paradigms while sorting out the similarities and differences in data characteristics and modeling logic across single-cell omics. Combined with our scDNAm-specific benchmarking analyses, these collective efforts further highlight the promise of multi-omics integration. Therefore, with the popularization of multi-omics technologies, utilizing cross-modality information to assist scDNAm imputation represents a critical breakthrough for next-generation methods.

Key Points

• This study develops the first systematic benchmarking framework for single-cell DNA methylation (scDNAm) data imputation, addressing the critical gap that the performance boundaries, use cases, and strengths and limitations of existing imputation methods remain poorly characterized.

• We conducted comprehensive evaluation of five state-of-the-art imputation methods across seven biologically critical dimensions, with validations conducted across 13 diverse published experimental scDNAm datasets spanning multiple species, tissues, sequencing technologies, and cell scales.

• We developed BridgeCpG, a model-view strategy, to resolve the rigid trade-offs of single method, establishing a new paradigm for robust signal recovery under extreme sparsity.

• We proposed an adaptive divide-and-conquer strategy at the data view, which circumvents GPU memory bottlenecks and achieves high-fidelity imputation for massive heterogeneous datasets.

• We distilled our findings into a method-selection roadmap, empowering researchers to select the optimal imputation strategy tailored to their specific biological scenarios.

Author contributions

S.C. conceived and supervised the project. H.L. conducted the experiments and analyzed the results. H.L. and H.H. designed the dual-view strategy and method-selection guidance. H.L., H.H., S.L. and S.C. contributed to the experiment design. S.L. helped in the data analysis. H.L. and H.H. wrote the manuscript. All authors read and approved the final manuscript.

Conflicts of interest

None declared.

Funding

This work was supported by the National Natural Science Foundation of China [62473212 (S.C.) and 62203236 (S.C.)] and the Fundamental Research Funds for the Central Universities [050-63253077 (S.C.)].

Data availability

The scDNAm datasets analyzed in this study are publicly available in the NCBI Gene Expression Omnibus repository (https://www.ncbi.nlm.nih.gov/geo/). The specific accession codes are GSE56879 (covering mESC_2i, mESC_Ser, and mOocyte) [6], GSE87197 (covering hCLP, hCMP, hGMP, hMK, hHSC, and hMLP) [38], GSE65364 (hHCC) [39], GSE83882 (hCellLine) [40], GSE89545(mHSC) [44], GSE97179 (hFC) [8], GSE107714 (hPGC) [42], and GSE132489 (mBrain_Atlas) [43]. Additionally, the dataset hEmbryo can be downloaded from the scMethBank database (https://ngdc.cncb.ac.cn/methbank/scm/) with the accession number GSE100272 [41].

Code availability

The source code of all the methods, our benchmark, and the two strategies are available on GitHub at https://github.com/BioX-NKU/scMethyImputeBenchmarks.