PbImpute: Precise Zero Discrimination and Balanced Imputation in Single-Cell RNA Sequencing Data

Abstract

Single-cell RNA sequencing (scRNA-seq) has emerged as a transformative technology for elucidating cellular heterogeneity at unprecedented resolution. However, technical limitations such as limited sequencing depth and mRNA capture efficiency often result in zero counts, commonly referred to as “dropout zeros” in scRNA-seq data. These zeros pose significant challenges to downstream analysis, as they can distort the interpretation of cellular transcriptomes. While numerous computational methods have been developed to address this challenge, existing approaches frequently suffer from either insufficient imputation of zeros (under-imputation) or excessive modification of zeros (over-imputation). Here, we propose a precisely balanced imputation (PbImpute) method designed to achieve optimal equilibrium between dropout recovery and biological zero preservation in scRNA-seq data. PbImpute employs a multistage approach: (1) Initial discrimination between technical dropouts and biological zeros through parameter optimization of a new zero-inflated negative binomial (ZINB) distribution model, followed by initial imputation; (2) Application of a uniquely designed static repair algorithm to enhance data fidelity; (3) Secondary dropout identification based on gene expression frequency and partition-specific coefficient of variation; (4) Graph-embedding neural network-based imputation; and (5) Implementation of a uniquely designed dynamic repair mechanism to mitigate over-imputation effects. PbImpute distinguishes itself by uniquely integrating ZINB modeling with static and dynamic repair. This advantageous combined approach achieves a balance between over- and under-imputation, while simultaneously preserving true biological zeros and reducing signal distortion. Comprehensive evaluation using both simulated and real scRNA-seq data sets demonstrated that PbImpute achieves superior performance (F1 Score = 0.88 at 83% dropout rate, ARI = 0.78 on PBMC) in discriminating between technical dropouts and biological zeros compared to state-of-the-art methods. The method significantly improves gene–gene and cell–cell correlation structures, enhances differential expression analysis sensitivity, optimizes clustering resolution and dimensional reduction visualization, and facilitates more accurate trajectory inference. Ablation studies confirmed the essential contribution of both the imputation and repair modules to the method’s performance. The code is available at https://github.com/WyBioTeam/PbImpute. By enhancing the accuracy of scRNA-seq data imputation, PbImpute can improve the identification of cell subpopulations and the detection of differentially expressed genes, thereby facilitating more precise analyses of cellular heterogeneity and advancing disease research.

1. Introduction

Single-cell RNA sequencing (scRNA-seq) technology¹ offers researchers a powerful tool for analyzing gene expression at the single-cell level. By independently sequencing the transcriptome of each cell, it reveals cellular heterogeneity and captures unique gene expression patterns specific to various cell types and states. This is crucial for studying complex biological systems such as the tumor microenvironment, immune cell differentiation, and tissue development. However, technical limitations, such as insufficient sequencing depth or low mRNA capture efficiency, result in many expression values being undetected or recorded as zeros, a phenomenon known as “dropout” events.² These zeros affect the accuracy and completeness of the data, presenting challenges for data analysis and interpretation. Since these zero values could either represent true biological zeros or be the result of dropout events (dropout zeros), accurately recovering the true expression levels of cells is a highly challenging task.³⁻⁵ Studies have shown that dropout rates in typical scRNA-seq data sets often exceed 50% and can reach as high as 90% in highly sparse data sets.^6,7 Therefore, there is an urgent need to develop novel imputation algorithms specifically designed for scRNA-seq data, which is essential for gaining deeper insights into the pathogenesis of human diseases and their treatment strategies.⁸⁻¹⁰

In recent years, researchers have developed various algorithms to address dropout events in expression matrices derived from scRNA-seq data.¹¹ These algorithms can be broadly classified into four categories:

(1) Statistical modeling. Method models the expression value of each gene in each cell as a random variable, adhering to a specific distributional model. For example, bayNorm¹² and SAVER¹³ both assume that gene expression levels follow a Poisson-γ distribution. BayNorm leverages an empirical Bayes approach for imputation, while SAVER employs penalized Poisson LASSO regression. The computational demands of posterior distribution calculations in bayNorm become prohibitive for large-scale single-cell data sets, limiting its scalability and applicability to high-dimensional data. While SAVER effectively imputes a substantial number of zero values, its inability to reliably distinguish between technical (dropout) zeros and true biological zeros can lead to over-imputation, potentially masking genuine biological variability. TsImpute,¹⁴ on the other hand, is grounded in a zero-inflated negative binomial (ZINB) model, proposing a two-step imputation methodology that encompasses ZINB imputation and inverse distance weighted (IDW) imputation. Although TsImpute leverages statistical information through its two-step approach, its exclusive focus on imputing zero values without correcting nonzero values carries the risk of over-imputation and potential distortion of underlying biological signals.

(2) Smoothing techniques. Methods within this category impute missing values by utilizing information from neighboring cells or clusters. KNN¹⁵ relies on pairwise distance metrics to identify nearest neighbors for imputation. However, in high-dimensional scRNA-seq data sets, the curse of dimensionality significantly reduces the reliability of these distance metrics. This limitation compromises KNN’s performance in highly sparse data sets compared to more advanced imputation methods. scImpute¹⁶ employs a clustering-based approach, grouping cells based on the correlation between gene expression levels and cell types. Imputation is then performed within each identified cluster. scImpute’s performance is sensitive to the chosen clustering algorithm and the specified number of clusters. An inappropriate number of clusters can lead to suboptimal imputation results. Furthermore, scImpute’s computational runtime becomes a bottleneck for large-scale data sets, limiting its practical applicability for analyzing large and complex single-cell RNA-seq data. In contrast, MAGIC¹⁷ constructs a Markov transition matrix to model the relationships between cells and propagates shared information across similar cells through a diffusion process. It is unable to differentiate between dropout and biological zeros, which can amplify spurious biological variability and hinder accurate biological interpretation. Its performance can also be affected by the sparsity of single-cell data and the lack of prior biological information. these methods may face challenges due to the lack of prior information or the sparsity of single-cell data.

(3) Matrix factorization. Methods within this category impute missing values by decomposing the gene expression matrix into low-rank factors. For instance, ALRA¹⁸ utilizes singular value decomposition (SVD) to approximate the observed gene expression matrix with a lower-dimensional representation. However, ALRA assumes a low-rank structure in the data. This assumption may not hold in complex biological systems with highly heterogeneous cell populations, potentially leading to suboptimal imputation results. Additionally, scMOO¹⁹ incorporates a more flexible framework by assuming three latent structures within the data: a horizontal structure reflecting similarities between genes, a vertical structure representing similarities between cells, and a low-rank structure. By combining information from these three structures, scMOO can provide a more robust imputation. While matrix factorization methods can be effective for imputation, they rely on the assumption that the gene expression matrix has a low-rank structure. This assumption may not always hold true, especially in complex biological systems. The high model complexity of scMOO increases computational cost and complicates parameter tuning, especially for large-scale data sets. In general, matrix factorization methods can be computationally intensive, particularly for large data sets. Additionally, matrix factorization methods can be computationally intensive, particularly for large-scale data sets.

(4) Deep learning. Methods within this category leverage deep neural networks to learn complex patterns in scRNA-seq data. DeepImpute,²⁰ for instance, employs deep neural networks to learn and capture intricate patterns within the data. While DeepImpute offers relatively fast training times, it lacks the ability to distinguish between dropout zeros and true biological zeros. This can lead to inaccurate imputations, potentially distorting biological signals and impacting downstream analyses. DCA²¹ incorporates either a ZINB noise model or a standard negative binomial model to account for the count distribution, overdispersion, and sparsity inherent in scRNA-seq data, thereby capturing complex nonlinear relationships between genes. Similar to DeepImpute, DCA does not explicitly distinguish between technical and biological zeros and does not repair nonzero values, increasing the risk of over-imputation and distortion of underlying biological signals. GE-Impute²² utilizes a graph-embedding neural network model to impute dropout zeros. It may inadequately impute low-expression genes, resulting in insufficient recovery of biologically relevant signals in sparse data sets. CL-Impute²³ introduces a contrastive learning-based imputation method that obviates the need for preconstructed cell relationships. It suffers from the same limitations as DeepImpute and DCA, lacking the ability to distinguish between dropout and biological zeros and to repair nonzero values, which can lead to over-imputation and distortion of biological signals. Despite the advancements in imputation methods, several limitations persist:

• Inaccurate identification of dropout zeros: With the notable exceptions of scImpute, ALRA, and TsImpute, many methods struggle to effectively differentiate between dropout and true biological zeros, introducing potential biases in downstream analyses.

• Over-imputation: Currently, no existing method adequately addresses the issue of over-imputation and its potential consequences.

• Under-imputation: A single imputation step may not be sufficient to address all dropout zeros. Among the ten imputation models discussed above, only the most recent model, TsImpute, incorporates a two-step imputation process, which also carries the risk of over-imputation.^19,24

To address these limitations, we propose PbImpute, a novel imputation method designed to achieve precise discrimination between technical dropouts and biological zeros while minimizing the risk of over-imputation. The PbImpute framework comprises several sequential steps:

• (1)ZINB modeling: Utilization of a new ZINB distribution to identify dropout zeros and true biological zeros, followed by ZINB-based initial imputation through parameter estimation.
• (2)Static repair: Implementation of a custom-designed static repair algorithm to enhance data fidelity and mitigate potential biases introduced during the initial imputation step.
• (3)Refining dropout zeros identification: Further identification of residual dropout zeros based on gene expression rates and the coefficient of variation within cell partitions.
• (4)Node2vec imputation: Application of a graph-embedding neural network (node2vec) for imputation of the identified residual dropout zeros.
• (5)Dynamic repair: Execution of a tailored dynamic repair process to prevent over-imputation.

By combining these steps, PbImpute offers a comprehensive and robust approach to imputation in scRNA-seq data, addressing the challenges associated with existing methods. Comprehensive benchmarking against state-of-the-art imputation methods, including scImpute, SAVER, MAGIC, DCA, DeepImpute, bayNorm, GE-Impute, ALRA, CL-Impute, and TsImpute, demonstrated PbImpute’s superior performance across multiple evaluation metrics. Specifically, the method achieved high accuracy in zero-state discrimination, enhanced gene–gene and cell–cell correlation recovery, improved differential expression analysis sensitivity, and optimized clustering resolution and trajectory inference, while effectively preventing over-imputation artifacts. These extensive experimental results establish PbImpute as a robust tool for recovering biologically meaningful signals from scRNA-seq data and enhancing the reliability of downstream analyses.

2. Materials and Methods

As illustrated in Figure 1, the PbImpute framework consists of five key steps: (1) ZINB modeling, (2) Static repair, (3) Refining dropout zeros identification, (4) Node2vec imputation and (5) Dynamic repair.

Figure 1.

PbImpute workflow. PbImpute employs a multistage process to address dropout imputation in scRNA-seq data. Initially, a ZINB model is fitted to the raw expression matrix to estimate π, r, and p parameters using an EM algorithm. These parameters guide initial imputation. Subsequently, a static repair step corrects over-imputation by adjusting outlying nonzero values. Residual dropout zeros are then identified within cell clusters based on gene expression frequency and partition-specific coefficients of variation. A cell similarity embedding, generated using Node2vec with breadth-first search (BFS) and depth-first search (DFS), constrains imputation of these residual dropouts, preserving true biological zeros. Finally, a dynamic repair step adjusts nonzero values exhibiting substantial local variation, yielding the final refined expression matrix.

2.1. Preprocessing

The preprocessing pipeline for scRNA-seq data analysis comprises two critical computational modules designed to optimize signal-to-noise ratio and enhance biological interpretability:

• (1)Highly variable gene selection: Selecting highly variable genes to capture key biological information and reduce noise interference.
• (2)Cell partitioning: Using the selected highly variable genes to partition cells, successfully identifying and classifying different cell types.

The detailed methodological framework and parameter optimization procedures are comprehensively described in Supporting Material, Section 4.

2.2. ZINB Modeling

2.2.1. Dropout zero identification

ZINB outperforms NB by explicitly accounting for excess zeros, modeling technical dropouts, and addressing both overdispersion and zero-inflation, making it more suitable for sparse scRNA-seq data.²⁵ The ZINB distribution has proven to be highly effective in key analytical tasks such as differential gene expression analysis, cell clustering, and cell trajectory inference, playing a crucial role in uncovering cellular heterogeneity and elucidating dynamic biological processes.²⁶⁻³⁰ Our implementation introduces two fundamental methodological innovations:

• (1)a deterministic initialization strategy for parameter estimation, replacing conventional random initialization to enhance convergence accuracy.
• (2)application of the model to preprocessed cell partitioning matrices rather than the complete expression matrix, improving computational efficiency and biological specificity.

To perform ZINB-based initial imputation, it is necessary to estimate the dropout probability for each gene using the ZINB distribution. The ZINB distribution for modeling gene expression values is formally defined as

1

where X^(b_k)(g_i, c_j) represents the expression value of gene g_i in cell c_j, within a block extracted from cell partitioning, denoted as (where k ∈ {1, 2, ..., o}). Here, o denotes total number of partition blocks, m′ denotes number of genes per block, and n′ denotes number of cells per block. The indicator function I₀(x) equals 1 if x = 0 and 0 otherwise. This parameter π (dropout probability) represents the likelihood of a gene expression value being a dropout zero, which is primarily influenced by technical noise during the sequencing process. Higher π values indicate a higher probability of dropout events for a given gene. This parameter r (dispersion) captures the overdispersion observed in gene expression data, which arises from both biological and technical sources of variability. This parameter p (success probability) reflects the probability of observing nonzero expression for a given gene in a cell, providing insights into the true biological signals.

Inspired by the reviewer’s suggestion, we provided an example using the PBMC single-cell RNA-seq data set from 10x Genomics to illustrate the biological relevance of the ZINB parameters. Within this data set, the dropout probability (π) represents the likelihood that an observed zero count is due to technical dropout rather than a true absence of gene expression. For instance, immune-related genes like GZMB and IFNG, which are typically expressed only in specific T cell subtypes, often exhibit high π values in other cell types due to their sparse expression profiles. The dispersion parameter (r) reflects the variability in gene expression across cells. Genes with stable expression, such as CD3E in T cells and MS4A1 in B cells, tend to have lower dispersion values, whereas highly dynamic genes like CCL5, which exhibit greater expression variability, have higher r values. Finally, the success probability (p) represents the likelihood of observing nonzero expression for a given gene in a cell, thus providing insight into the true biological signal. Broadly expressed housekeeping genes, such as RPS27 and GAPDH, typically have high p values, while context-dependent genes, like cytokines activated during immune responses, have lower p values, reflecting their restricted expression to specific conditions or cell states. By applying the ZINB model to the PBMC data set, we can effectively disentangle the contributions of technical dropout, expression variability, and true biological signal, leading to a deeper understanding of cellular heterogeneity in scRNA-seq data. Given that the ZINB distribution is a mixture model, directly estimating the latent variables (π, r, p) is challenging. Therefore, we employ the Expectation-Maximization (EM) algorithm³¹ to iteratively estimate the optimal parameters of the ZINB distribution. The specific ZINB parameter estimation process is outlined in Algorithm 1.

It balances computational efficiency and parameter estimation accuracy through dual convergence criteria. Convergence is achieved when the change in the log-likelihood function between iterations is less than 1 × 10^–6 (Step 5 of Algorithm 1), ensuring precise ZINB parameter estimation. To handle the high dimensionality of single-cell RNA-seq data, a maximum iteration limit of 50 is imposed, preventing excessive computational overhead while maintaining robust performance and scalability for large data sets.

With the parameters π(g_i), r(g_i), p(g_i) estimated for each gene g_i within the block X^(b_k), yielding block-specific parameter vectors are , dropout probabilities are computed using Bayesian inference.³² The posterior probability of dropout events can be calculated as

2

This formulation enables precise identification of candidate positions for imputation.

2.2.2. ZINB-Based Initial Imputation

To fully utilize the parameters obtained from the ZINB estimation, we further consider the nonzero value expectation for each gene g_i

3

Additionally, to account for varying expression levels across different cells, PbImpute incorporates a scaling factor to adjust the ZINB-imputed values. The scaling factor is given by

4

Finally, the imputed value for gene g_i in cell C_j within the block is then determined through a threshold-based decision function

5

2.2.3. Matrix Reconstruction

Following block-wise imputation, we integrate the imputed values into a comprehensive ZINB reconstruction matrix , where each element is defined as

6

2.3. Static Repair

To mitigate potential distortions in imputed values resulting from ZINB parameter influences, PbImpute implements a static repair mechanism. This procedure aims to correct nonzero values that deviate substantially from the mean of the matrix, while preserving other nonzero entries. The static repair matrix is formally defined as

7

where τ is a threshold, typically set to −0.30, it identifies points with minor deviations below the mean (within 0.3 standard deviations), signaling subtle variations that require attention. and . In this manner, nonzero values that exhibit significant deviations in the reconstructed matrix are adjusted to zero.

2.4. Refining Dropout Zero Identification

To further refine the imputation process and identify any residual dropout zeros, matrix S is further partitioned using k-means clustering.³³ A block obtained from cell partitioning is denoted as , where a′ denotes the number of genes within the block and b′ denotes the number of cells within the block. The value of c is determined using the silhouette coefficient.³⁴

For each gene g_i within a given block, the dropout rate d(g_i) and coefficient of variation v(g_i) are calculated as follows

8

9

where , S^(b_k)(g_i, c_j) represents the expression value of gene g_i in cell c_j within the k-th block (S^(b_k)), and δ(i, j) counts the number of zero elements in S^(b_k). Vector represents the expression values of gene g_i across all cells within the k-th block.

Genes characterized by a high dropout rate and low coefficient of variation are considered more likely to be affected by dropout events. A curated indexed collection I is formulated to encompass such genes

10

where d̃(g_i) and ṽ(g_i) represent the median dropout rate and median coefficient of variation for g_i, respectively. The expression value of (g_i, c_j) in set I is identified as a dropout zero. These dropout zeros are marked as −1 in the matrix S^(b_k). Consequently, a refined matrix is constructed, with its elements defined as follows

11

This strategy effectively preserves nonzero values in the raw data, minimizing potential biases introduced during the imputation process.

2.5. Node2vec Imputation

2.5.1. Graph Construction

To address the imputation challenges in scRNA-seq data, we employed the node2vec graph-embedding algorithm,³⁵ which combines breadth-first search (BFS) and depth-first search (DFS) strategies in random walk sampling. This approach effectively captures both local and global relationships between cells. The node2vec algorithm is computationally scalable, allowing efficient processing of large-scale scRNA-seq data sets by combining random walk sampling with efficient embedding generation. By applying Seurat’s log normalization³⁶ to the S matrix, one million iterations were used to obtain the normalized expression matrix . For each cell, we computed the Euclidean distance matrix (37) between each cell and its K-nearest neighbors, which was used to construct the adjacency matrix of the cell–cell similarity network

12

13

where KNN(c_j) represents the K-nearest neighbor set of cell C_j. A graph G = (V, E) representing the cell–cell similarity network was constructed, where V is the set of nodes (cells) and E is the set of edges (cell–cell connections)

14

15

2.5.2. Random Walks and Embedding

Random walks were performed on each node in G = (V, E), controlled by two parameters: p (return probability) and q (in–out probability). The probability model for a random walk from node c_i to node c_j is defined as

16

where d_i represents the degree of c_i, c_i ↔ c_j represents a path existing between c_i and c_j, and α_ij represents the adjustment coefficient, defined as

17

where parameters p and q were set to 4 and 2, respectively, in our experiments. Random walks were initiated from each node to generate sequences of length 5. The goal of the model is to maximize the co-occurrence probability between the central node c_i and the other nodes c_j in the random walk through the objective function

18

where is the embedding vector of node c_i and l corresponds to the number of genes involved in the vector. The co-occurrence probability P(c_j | h(c_i)) is modeled using the softmax function

19

2.5.3. Embedding Matrix Imputation

The embedding matrix is defined as

20

For the imputation of each column in matrix S′, the Euclidean distance between columns in the embedding matrix Y is computed and sorted to identify the e-nearest columns. Missing values in the column are subsequently filled with the mean of these e-nearest columns, yielding matrix . The node2vec imputation imputed matrix is defined as

21

2.6. Dynamic Repair

The purpose of dynamic repair is to address false positives, where true biological zeros are misclassified as pseudozeros causing signal distortion, and over-imputation, which disrupts gene sparsity and impacts downstream analyses. To further compute the correlation coefficient for each cell, we derive the correlation matrix

22

where Q′ = Q – I, F⁽ⁿ⁾ represents the normalized form of matrix F, cov(F⁽ⁿ⁾(c_i), F⁽ⁿ⁾(c_j)) represents the covariance between column c_i and column c_j in matrix F⁽ⁿ⁾, and σ(·) represents the variance function. The diagonal elements of matrix Q are set to 1. represents the unit matrix.

To identify the top e correlated columns (e optimally set to 4) with the current column, each row in matrix Q′ retains only the e largest values. The column indices of these values from matrix . By examining whether the elements corresponding to the top ê correlated columns in matrix Z are zero, matrix was derived, with its elements defined as follows

23

where ∀l ∈ {1, 2, ..., ê}, L(c_j, l) denotes the index value of a particular cell within the top ê correlated cells with cell c_j. Since modifications to nonzero values may cause changes in the correlation matrix Q, we performed an iterative update process for this matrix in our experiments, termed dynamic repair.

In summary, our method combines ZINB modeling and an optimization process that computes high dropout rates and low coefficients of variation to accurately distinguish between pseudozeros and true zeros in scRNA-seq data. The ZINB framework offers a probabilistic and automated mechanism for differentiation, while the graph-embedding neural network effectively addresses the challenges posed by high-dimensional sparse data.

2.7. Sensitivity Analysis of Model Parameters

To evaluate the impact of node2vec parameters p and q on imputation accuracy, we conducted a sensitivity analysis. These parameters control the random walk behavior in graph embedding, where p biases toward revisiting nodes and q encourages exploration of more distant nodes. We systematically varied p and q (p, q ∈ {1, 2, 3, 4}) and assessed the imputation performance. The results, summarized in Supporting Information Table S1, show that the highest imputation accuracy was achieved when p = 2 and q = 4. These values provide the best balance between exploring and preserving the graph structure, thereby enhancing the quality of the embeddings and the subsequent imputation accuracy.

To evaluate the impact of the static repair thresholds (τ) and dropout criteria (e) on imputation accuracy, we conducted a sensitivity analysis. These parameters are critical for balancing the repair of missing values and the preservation of biological signals during imputation. Specifically, τ controls the threshold for static repair, while e adjusts the dropout correction in dynamic repair. We systematically varied τ (−0.2, – 0.3, – 0.4, – 0.5) and e (2, 3, 4, 5) and assessed the imputation performance. The results, summarized in Supporting Information Table S2, indicate that this combination provides the best balance between repairing missing values and preserving biological signals, thereby enhancing overall imputation accuracy. To improve clarity and accessibility, we have included a dedicated 'Notation Table' (see Table 1) to define mathematical symbols used.

Table 1. Notation and Definitions of Mathematical Symbols.

symbol	description
m	number of genes in the raw data.
n	number of cells in the raw data.
X(bk)	expression matrix for the block.
m′	number of genes per block.
n′	number of cells per block.
o	total number of partition blocks.
π	dropout probability (ZINB parameter).
r	dispersion parameter (ZINB parameter).
p	success probability (ZINB parameter).
s	scaling factor.
Z	ZINB reconstruction matrix.
S	static repair matrix.
S(bk)	K-means expression matrix for the block.
I	A curated indexed collection.
S′	refining dropout zero identification matrix.
Y	embedding matrix.
F	Node2vec imputed matrix.
B	dynamic repair matrix.

3. Data Sets

To comprehensively evaluate model performance, we utilized both simulated and real data sets. The real data set contained inherent missing values, necessitating the use of simulated complete data sets to enable thorough performance assessment.

3.1. Simulated Data Sets

Inspired by SCRABBLE,³⁸ we employed the Splatter package³⁹ to generate complete scRNA-seq data sets. The data set included 3000 cells and 2000 genes, with three clusters of varying sizes controlled by the “group.prob” parameter (0.2, 0.35, and 0.45). To introduce varying levels of dropout data sets, we adjusted the “dropout_mid” parameter within the Splatter simulations. For instance, dropout rates of 35%, 43%, 57%, 71%, and 83% corresponded to “dropout_mid” values of 0.1, 1, 2, 3, and 4, respectively.

The noise types in the simulated data are controlled by the Splatter framework’s underlying code, which incorporates dropout events and technical noise. Dropout probabilities are modeled using a logistic function, where the dropout.shape parameter controls the steepness of the curve, and dropout.mid determines its midpoint, directly influencing the dropout rate. The proportion of dropout zeros is therefore governed by these parameters. For the data distribution, the Splatter framework adopts its default mechanism, simulating gene expression using a Negative Binomial (NB) distribution. This default setting captures the overdispersion commonly observed in scRNA-seq data and ensures that the simulated data sets align with the statistical properties of real-world single-cell RNA-seq experiments.

To evaluate the robustness of PbImpute on simulated data, we generated three distinct complete data sets (Data set 1, Data set 2, and Data set 3), along with their corresponding incomplete versions (Data set 1*, Data set 2*, and Data set 3*), resulting in a total of 15 data sets.

3.2. Real Data Sets

In addition to the simulated data, we employed four real scRNA-seq data sets obtained from different sequencing platforms, as summarized in Supporting Material, Section 5. These data sets (PBMC,⁴⁰ Worm neuron,⁴¹ Mouse bladder,⁴² LPS⁴³) encompass a wide range of cell types and biological processes, ensuring the reliability and generalizability of the data used for performance evaluation.

4. Evaluation Metrics

Specific evaluation metrics include the Standard F1 Score, Correlation (gene), Correlation (cell), Error, Modified F1 Score,^44,45 ARI,⁴⁶ NMI,⁴⁷ and POS.⁴⁸⁻⁵¹ These evaluation metrics are designed to assess the performance of our method, with specific implementations on simulated data sets due to the lack of ground truth in real data sets.

The Standard F1 Score requires the input of both the imputed matrix and the complete data. A higher value indicates a stronger ability to distinguish dropout zeros from true biological zeros. Detailed analysis is provided in Section 5.1.

Correlation (gene), Correlation (cell), and Error also rely on the imputed matrix and the complete data. Higher values reflect better recovery of gene–gene and cell–cell expression relationships. Further details can be found in Section 5.2.

The Modified F1 Score focuses on enhancing single-cell differential expression analysis. Higher values indicate improved performance in this aspect. Analysis is discussed in Section 5.3.

Clustering metrics, such as ARI and NMI, are computed directly from the imputed matrix. Higher values denote better performance in unsupervised clustering of cells. See Section 5.4 for more details.

Finally, POS evaluates the accuracy of trajectory inference based on the imputed matrix. A higher value reflects improved reconstruction of cell trajectories. This metric is detailed in Section 5.5.

Detailed calculation formulas and implementation details for each metric are provided in Supporting Material Section 3.

5. Result

PbImpute was compared against ten state-of-the-art imputation methods: ALRA,¹⁸ SAVER,¹³ scImpute,¹⁶ bayNorm citeptang2020baynorm, MAGIC,¹⁷ DeepImpute,²⁰ GE-Impute,²² DCA,²¹ CL-Impute,²³ and TsImpute.¹⁴ Among these, SAVER, bayNorm, and TsImpute are distribution-based models, ALRA is a matrix factorization model, MAGIC and scImpute are smoothing models, while DCA, GE-Impute, DeepImpute, and CL-Impute are deep learning models.

To provide a baseline comparison, a “No-Imputation” model was also included, where evaluation metrics were calculated directly on the simulated data sets with both complete and missing data, without applying any imputation methods.

5.1. Accurate Identification of Dropout Zeros

To evaluate PbImpute’s ability to accurately distinguish between dropout zeros and true biological zeros, we calculated the Standard F1 Score for Data sets 1, 2, and 3, which were generated with varying dropout rates. As depicted in Supporting Table S3 and Figure 2, PbImpute consistently achieved optimal Standard F1 Score values across different dropout rates. Figure 2A illustrates that PbImpute’s performance consistently outperforms other methods, indicating its superior ability to accurately identify dropout zeros and true biological zeros. Furthermore, Figure 2B reveals a continuous increase in PbImpute’s performance with increasing dropout rates, suggesting its robustness in handling high levels of missing data. In contrast, scImpute, while also exhibiting strong performance, shows a less pronounced improvement at higher dropout rates. Figure 2C demonstrates the stability of PbImpute’s performance across different data sets. PbImpute exhibits minimal fluctuations in Standard F1 Score, highlighting its resilience to variations in data characteristics. Although the improvements in PbImpute’s Standard F1 Score compared to other models may not be statistically significant, the numerical differences are substantial. For example, at an 83% dropout rate, PbImpute accurately identified a significantly larger number of dropout zeros compared to other methods, as evidenced by the higher count of true positives. The number of true positives for PbImpute, scImpute, ALRA, and TsImpute are 3,741,437, 3,557,972, 3,554,608, and 3,499,878, respectively. In conclusion, these results unequivocally demonstrate PbImpute’s exceptional ability to accurately identify dropout zeros, ensuring the precision of subsequent analyses.

Figure 2.

Quantitative assessment of dropout zero identification accuracy. (A) Distribution analysis illustrating imputation F1 scores across multiple methods under varying dropout rates. (B) Comparative analysis of F1 score trajectories across different imputation methods as a function of dropout rate. (C) Statistical distribution of imputation F1 scores across diverse dropout data sets.

5.2. Effective Recovery of Gene–Gene and Cell–Cell Expression Data

To evaluate PbImpute’s ability to preserve the underlying biological structure of the data, we calculated the linear relationship metrics on both the simulated complete and dropout data sets.

5.2.1. Recovery of Gene–Gene Expression Data

As shown in Figure 3A and Supporting Table S4, on the simulated dropout data sets (Data set1*, Data set2*, and Data set3*), PbImpute consistently achieved the highest Correlation (gene) values across different dropout rates compared to other models, demonstrating its superior performance in recovering gene–gene correlation coefficients, followed by scImpute and TsImpute. This is likely due to PbImpute’s ability to accurately identify dropout zeros and true biological zeros. Compared to the No-Imputation model, PbImpute exhibited significant performance improvements at dropout rates of 35%, 43%, 57%, 71%, and 83%, with respective enhancements of 20%, 29%, 44%, 49%, and 55%. This indicates that as the dropout rate increases, PbImpute’s ability to recover gene–gene correlation coefficients improves. In contrast, ALRA, MAGIC, and DCA showed lower Correlation (gene) values than the No-Imputation model, indicating their less effective performance in recovering gene–gene correlation coefficients.

Figure 3.

Quantitative assessment of gene–gene and cell–cell expression recovery fidelity. (A) Comparative analysis of gene-wise correlation efficacy using mean PCC between imputed and complete expression matrices. (B) Cell-wise correlation assessment quantifying mean PCC values between imputed and reference complete data sets. (C) Systematic quantification of imputation deviation from complete reference data sets. (D) Multiparameter performance assessment across diverse dropout data sets.

5.2.2. Recovery of Cell–Cell Expression Data

As shown in Figure 3B and Supporting Table S5, nearly all imputation methods achieved higher Correlation (cell) values compared to the No-Imputation model on simulated dropout data sets (Data set1*, Data set2*, and Data set3*). However, PbImpute consistently yielded the highest Correlation (cell) values across different dropout rates, demonstrating superior performance in recovering cell–cell correlation coefficients. Compared to the No-Imputation model, PbImpute showed performance improvements of 2%, 5%, 10%, 18%, and 28% at dropout rates of 35%, 43%, 57%, 71%, and 83%, respectively. This indicates that PbImpute’s ability to recover cell–cell correlation coefficients improves with increasing dropout rates. At an 83% dropout rate, the advantages of imputation methods such as SAVER, bayNorm, and scImpute relative to the No-Imputation model diminished, while PbImpute’s advantage remained significant.

5.2.3. Reduction of Imputation Error

As illustrated in Figure 3C and Supporting Table S6, almost all models demonstrated reduced Error values compared to the No-Imputation model. Relative to the No-Imputation model, PbImpute reduced Error values by 86%, 87%, 88%, 89%, and 90% at dropout rates of 35%, 43%, 57%, 71%, and 83%, respectively. This indicates that PbImpute consistently maintained the lowest Error values across increasing dropout rates, demonstrating its ability to recover data with minimal distortion. This is likely due to PbImpute’s selective imputation of missing zero values, preserving the integrity of nonzero values.

Furthermore, Figure 3D illustrates PbImpute’s exceptional performance across different dropout rates in terms of Correlation (gene), Correlation (cell), and Error, with minimal fluctuation. This underscores the robust nature of PbImpute in handling varying levels of missing data.

5.3. Enhancement of Single-Cell Differential Expression Analysis

Quantitative analysis of performance metrics across Data set1*, Data set2*, and Data set3* (Supporting Figures S1–S5) demonstrates that PbImpute consistently achieved superior Modified F1 Scores across all three cell subtypes. Figure 4A provides multidimensional visualization of this performance enhancement, where the red-demarcated regions in the radar plots quantitatively illustrate PbImpute’s expanded analytical coverage and enhanced capability across multiple dropout rates. These results indicate significant improvement in differentially expressed gene (DEG) identification, even under conditions of substantial data sparsity.

Figure 4.

Comparative analysis of method performance in single-cell differential expression detection. (A) Multidimensional performance assessment depicting pairwise subtype comparisons (Subtype 1 vs Subtype 2, Subtype 3 vs Subtype 1, and Subtype 3 vs Subtype 2). (B) Statistical distribution of modified F1 scores across cell-type variants under different imputation models.

While latest CL-Impute also exhibited commendable performance, PbImpute exhibited statistically significant performance improvements across all cell subtype analyses. Specifically, under 35% dropout conditions, PbImpute achieved Modified F1 Scores of 0.89, 0.91, and 0.88 for Subtypes 1, 2, and 3, respectively, whereas CL-Impute yielded comparatively lower scores of 0.86, 0.79, and 0.79 for the corresponding subtypes. The distributional analysis presented in Figure 4B demonstrates PbImpute’s robust performance stability across varying dropout rates, facilitating reliable DEG identification. This enhanced methodological stability suggests significant potential for improving the precision and reproducibility of downstream analytical procedures. PbImpute accurately identified CD69 and IFNG as significantly upregulated genes during T cell activation. These genes play crucial roles in the early stages of the immune response and were consistently detected by PbImpute with higher confidence compared to other methods. In contrast, methods such as SAVER and MAGIC either failed to recover these genes or detected them with lower statistical significance due to dropout-induced noise. Furthermore, PbImpute successfully identified DE genes specific to rare subpopulations, such as FOXP3 and CTLA4 in regulatory T cells. These genes, which were obscured in the raw data due to dropout noise, were confidently detected as differentially expressed after imputation, enabling a clearer distinction between subpopulations and their functional states.

5.4. Effectively Improvement of Cell Unsupervised Clustering Performance

To evaluate the impact of imputation on clustering performance, we assessed ARI and NMI for various imputation methods on three real data sets: PBMC, Worm neuron cells, and Mouse bladder.

5.4.1. Maintaining Consistency of Clustering Results

We performed k-means clustering on the data sets and compared the resulting ARI and NMI values to the No-Imputation model, with the results shown in Supporting Figure S6, and Supporting Table S7. On the PBMC data set, SAVER and DCA did not exhibit significant differences in ARI and NMI values compared to the No-Imputation model, suggesting that their imputation performance was not substantially different when the raw data quality was high. In contrast, PbImpute demonstrated superior performance, achieving ARI and NMI values that were 6% and 5% higher, respectively, than the No-Imputation model. For the Worm neuron cells data set, PbImpute again outperformed the No-Imputation model, achieving ARI and NMI values that were 45% and 6% higher, respectively. This highlights PbImpute’s ability to improve clustering quality even when the raw data is of average quality. DeepImpute, on the other hand, exhibited suboptimal clustering performance after imputation. On the Mouse bladder data set, PbImpute consistently maintained the highest ARI and NMI values, exceeding the No-Imputation model by 65% and 8%, respectively.

These results collectively demonstrate PbImpute’s robustness in enhancing clustering performance across various data sets, regardless of the raw data quality.

5.4.2. Improvement of Clustering Effect

As shown in Supporting Figure S7, t-SNE visualizations^52,53 illustrate the impact of imputation on clustering results for the PBMC data set. PbImpute, along with scImpute and CL-Impute, demonstrate improved cluster separation compared to the raw data, indicating their effectiveness in enhancing clustering performance. Furthermore, Supporting Figure S8 highlights that as the number of cell types increases to 16, PbImpute continues to maintain strong clustering performance, clearly separating different cell types. This demonstrates that PbImpute’s advantages in data processing and clustering analysis remain effective even in more complex scenarios.

To further assess PbImpute’s performance on large data sets, we simulated data for 40,000 cells. The results presented in Figure 5 clearly demonstrate that in the complete data set, where no data is missing, the data points are well-clustered by color. In contrast, with 65% data dropout, the points become noticeably scattered due to increased noise. For the imputation models, SAVER, DCA, and bayNorm produce similarly scattered clusters, indicating their limited effectiveness in maintaining clustering performance on large data sets. In comparison, PbImpute, along with CL-Impute, scImpute, and TsImpute, shows significant improvements, with PbImpute particularly standing out. To quantitatively assess the quality of clustering results, we computed two widely used clustering metrics: purity and silhouette scores. These metrics provide a robust evaluation of the clustering performance and offer additional insights into the effectiveness of each imputation method. As shown in Figure 5, PbImpute achieves a high purity score of 0.79 and a silhouette score of 0.62, closely approximating the results of the complete data set (purity = 1, silhouette score = 0.80). This demonstrates that its clusters are not only well-separated but also exhibit a high degree of similarity to the complete data set, highlighting PbImpute’s superior ability to preserve cell-type separability and clustering structure after imputation.

Figure 5.

Clustering performance of imputation methods on a large-scale data set. Each point represents an individual cell, color-coded by its assigned cluster label. This visualization provides a clear overview of the clustering structure for 40,000 cells across 10 categories.

5.5. Enhancement of Cell Trajectory Inference

To evaluate PbImpute’s impact on cell trajectory inference, we employed SCORPIUS on the LPS data set and visualized the results in Supporting Figure S9. Each subplot represents a different imputation method, with colored dots indicating various time points (red for 1 h, blue for 2 h, green for 4 h, and purple for 6 h) and lines connecting the cells to represent inferred trajectories. For the raw data, without imputation, the clustering was noisy, and the trajectory was not clearly defined. In contrast, PbImpute, DeepImpute, and bayNorm demonstrated superior performance, exhibiting distinct cluster separation and smooth trajectories that effectively captured the progression of cells. However, scImpute and TsImpute showed less impressive results, failing to produce accurate paths. Detailed analyses of the results for each imputation model are available in Supporting Table S8. To quantitatively assess the quality of trajectory inference, we utilized the pseudotime ordering score (POS) metric. As shown in Supporting Table S9, PbImpute achieved the highest POS index, indicating a strong alignment between the inferred pseudotime and the actual time progression. Using the LPS data set, which consists of scRNA-seq samples from mouse bone marrow-derived dendritic cells (BMDCs) collected at 1, 2, 4, and 6 h after stimulation, PbImpute enabled a more precise reconstruction of the activation trajectory. By effectively imputing dropout values, PbImpute uncovered key transitional states along the activation pathway, reflecting the temporal progression of immune responses to LPS. These intermediate states, which were obscured by dropout noise in the raw data or less effectively resolved by other imputation methods, are critical for understanding the dynamic regulatory changes that occur during dendritic cell activation.

These findings underscore the significance of imputation in enhancing the quality of cell trajectory inference in scRNA-seq data, leading to more accurate identification of cellular processes over time.

5.6. Successful Balance of Under-impuation and Over-imputation

As demonstrated in previous sections, PbImpute effectively discriminates between dropout zeros and true biological zeros, ensuring accurate imputation placement. While the accuracy and effectiveness of PbImpute’s imputation process have been validated, the challenges of over-imputation and under-imputation persist. To evaluate PbImpute’s impact on zero ratios, we compared the complete data set (20,000 genes and 30,000 cells) to the imputed data sets at varying dropout rates, with results presented in Supporting Table S10.

Figure 6A depicts the zero ratio analysis, where the black horizontal dashed line represents the zero ratio in the complete data set, serving as a baseline for analyzing PbImpute’s two-step process. The results indicate a significant decrease in the zero ratio after the first imputation step, particularly at high dropout rates. However, as the dropout rate increased, the zero ratio began to rise, suggesting the presence of residual dropout zeros. PbImpute’s static and dynamic repair steps effectively addressed these residual zeros without introducing excessive noise. After dynamic repair, the difference in zero ratio between PbImpute and the complete data set was minimal, demonstrating PbImpute’s successful imputation of residual dropout zeros while avoiding over-imputation. To assess the performance of other imputation methods, we compared their zero ratios to the complete data set. Supporting Table S11 displays the percentage increase or decrease in the zero ratio after imputation compared to the complete data set. A positive percentage indicates under-imputation, while a negative percentage indicates over-imputation. The results shown in Figure 6B revealed that many methods, including SAVER, MAGIC, DCA, DeepImpute, bayNorm, ALRA, and TsImpute, tended to overimpute. In contrast, CL-Impute and GE-Impute exhibited under-imputation. PbImpute, however, maintained a minimal difference in zero ratio compared to the complete data set, demonstrating its ability to balance under-imputation and over-imputation.

Figure 6.

Quantitative assessment of imputation balance and zero-rate distribution (20,000 genes, 30,000 cells). (A) Zero-rate progression during the PbImpute pipeline: DD (Dropout Data), FI (First Imputation), SR (Static Repair), SI (Second Imputation), and DR (Dynamic Repair). The reference zero-rate threshold (complete data set without missingness) is indicated by a black dashed baseline. Convergence toward this baseline indicates enhanced fidelity in preserving the original zero-rate distribution. (B) Comparative analysis of zero-rate deviation from reference data postimputation across multiple methods and dropout rates. The reference threshold is indicated by a red line, where values above the baseline signify under-imputation bias, indicating insufficient recovery of missing values, and values below the baseline represent over-imputation bias, indicating excessive reconstruction of zero values.

These findings underscore PbImpute’s robust performance in maintaining the integrity of the raw data structure while addressing dropout events in scRNA-seq data.

5.7. Computational Efficiency and Scalability Evaluation

We believe that an excellent imputation model should not only perform well in terms of imputation quality but also exhibit high computational efficiency, especially when processing large-scale data sets. To systematically evaluate computational efficiency, we conducted comprehensive memory usage and runtime analyses using the 10x Genomics PBMC data set, comprising 61,213 cells spanning multiple populations including CD14⁺, CD56⁺, CD4⁺ T cells, CD8⁺ T cells, CD19⁺ B cells, and CD34⁺. We constructed scalability test sets by randomly sampling between 10,000 and 50,000 cells from the full data set. Memory usage and runtime across various imputation methods were assessed and documented in Supporting Figure S11. Memory profiling revealed that CL-Impute, bayNorm, and GE-Impute exhibited exponential memory scaling with increasing cell numbers, with CL-Impute demonstrating particularly pronounced memory requirements. In contrast, PbImpute maintained relatively stable and efficient memory utilization across all data set sizes, suggesting superior memory optimization. Runtime analysis revealed significant computational constraints in several existing methods: scImpute failed to complete execution within a 24-h threshold, while both SAVER and TsImpute encountered scalability limitations when processing large-scale data sets.

Among the methods that successfully completed the analysis, PbImpute demonstrated comparable execution times, maintaining computational efficiency within the same order of magnitude as other scalable methods. Notably, PbImpute uniquely achieves this computational performance while simultaneously addressing both over-imputation and under-imputation challenges, distinguishing it from existing approaches that sacrifice either accuracy or efficiency to optimize the other.

5.8. Ablation Study

To assess the significance and necessity of each component within our model—first imputation (FI), static repair (SR), second imputation (SI), and dynamic repair (DR)—we conducted a series of ablation studies. These studies involved creating model variants with different combinations of components, allowing us to evaluate their individual contributions.

As illustrated in Supporting Figure S11 and Supporting Tables S12–S13, experiments conducted on data sets with varying dropout rates demonstrated that F1 scores consistently improved with the sequential addition of SR and DR. This observation indicates that both components play crucial roles in distinguishing between dropout zeros and true biological zeros. Furthermore, the inclusion of SI led to increased gene-level and cell-level correlation values, suggesting its effectiveness in enhancing imputation accuracy. Notably, the addition of DR resulted in the highest overall performance, emphasizing its critical role in the model’s architecture.

Analysis of real data sets, as presented in Supporting Table S14, reveals that SR consistently outperformed FI in terms of ARI and NMI values, regardless of the initial clustering quality. The incorporation of SI further improved these metrics, particularly evident in the Mouse bladder data set. However, the combination of all components in our PbImpute method achieved the highest ARI and NMI values, underscoring the pivotal role of DR in real-world applications.

These findings collectively demonstrate the synergistic effects of the model’s components and validate the design choices in PbImpute’s architecture. The progressive improvement in performance metrics with the addition of each component highlights their individual and combined contributions to the model’s overall efficacy in handling scRNA-seq data.

6. Discussion

PbImpute’s robust performance in trajectory inference and differential expression analysis has significant implications for scRNA-seq research and clinical applications. For example, in tumor heterogeneity studies, PbImpute’s ability to recover subtle gene expression patterns can help identify rare tumor subpopulations and regulatory pathways involved in disease progression or immune evasion. Similarly, in drug response analysis, PbImpute enhances the detection of differentially regulated genes and pathways, facilitating the discovery of biomarkers for drug efficacy or resistance. These applications highlight PbImpute’s potential to advance our understanding of cellular heterogeneity and therapeutic responses, making it a valuable tool for both basic and translational research.

While PbImpute has demonstrated excellent scalability and computational efficiency on data sets up to 50,000 cells, scaling to extremely large data sets, such as those exceeding 500,000 cells, may present challenges due to increased memory and runtime demands. Future work could focus on implementing parallel computing strategies or developing a more memory-efficient algorithm to address these limitations. Additionally, PbImpute’s performance may exhibit sensitivity to parameter settings, which can vary depending on data set characteristics such as dropout rates or biological complexity. To improve usability and robustness, future efforts could include the development of automated parameter-tuning mechanisms to optimize performance across diverse scRNA-seq data sets. These improvements will further enhance the applicability and efficiency of PbImpute for large-scale single-cell studies.

We have compared PbImpute with two recently published models: scSimGCL and CPARI.⁵⁴ scSimGCL⁵⁵ (F1 = 0.84, ARI = 0.76 on the PBMC data set) performs slightly worse than PbImpute, but it offers a more versatile foundation for broader scRNA-seq tasks, making it suitable for a range of applications beyond imputation. In contrast, CPARI (F1 = 0.86, ARI = 0.81 on the PBMC data set) achieves higher performance in both F1 score and ARI. However, CPARI’s dual imputation strategy, which combines both relative and absolute imputation, introduces the risk of over-imputation. This could affect the biological relevance of the imputed data, particularly in highly sparse data sets. Although PbImpute does not always outperform CPARI in every metric, it strikes a key balance between computational efficiency and biological relevance, making it an effective tool for preserving data structure in imputation tasks.

7. Conclusions

The intrinsic technical limitations of single-cell RNA sequencing give rise to pervasive dropout events, presenting substantial analytical challenges that existing imputation methods have not fully resolved, particularly in achieving optimal balance between under- and over-imputation. Here, we present PbImpute (Precise Zero Discrimination and Balanced Imputation), a novel computational framework that implements an integrated approach to discriminate between technical dropouts and biological zeros while maintaining high imputation accuracy and minimizing artificial noise introduction. The methodological innovation of PbImpute lies in its systematic integration of multiple complementary components:

• Utilization of a new Zero-Inflated Negative Binomial (ZINB) distribution to differentiate between dropout zeros and true biological zeros, performing initial imputation by optimizing distribution parameters.

• Implementation of a uniquely designed static repair process to enhance data fidelity by addressing potential noise.

• Identification of residual dropout zeros based on gene expression rates and subpopulation-specific variation metrics for residual dropout identification, coupled with graph-embedding neural network-based imputation.

• Application of a uniquely designed dynamic repair step to prevent over-imputation, thereby maintaining data integrity.

Comparative analyses conducted on both simulated and real scRNA-seq data sets demonstrate PbImpute’s superior performance in accurately differentiating between dropout zeros and true biological zeros. Additionally, PbImpute excels in recovering gene-level and cell-level correlations, enhancing differential gene expression identification, clustering, and visualization performance. Notably, PbImpute successfully addressed residual dropouts while maintaining biological zero integrity, overcoming the common limitations of existing methods that tend toward either under-imputation or over-imputation. Ablation analyses systematically validated the essential contributions of both the attribution and repair modules to the method’s performance.

In conclusion, PbImpute is highlighted for its unique capacity to improve data quality while preserving the biological integrity of single-cell RNA sequencing (scRNA-seq) data. This ability positions PbImpute as a next-generation tool, offering not only high accuracy but also biological significance. By ensuring that imputed values reflect true biological variability, PbImpute enhances the interpretability of scRNA-seq data, making it an invaluable resource for future research in single-cell transcriptomics.

Data Availability Statement

The full implementation of PbImpute, including code, documentation, example workflows, and the data sets used in this study, is available at https://github.com/WyBioTeam/PbImpute. Researchers can access detailed instructions for integrating PbImpute into existing scRNA-seq analysis pipelines. These instructions cover the entire execution process, including data preparation, imputation steps, parameter settings, and output analysis, ensuring a smooth integration into standard scRNA-seq workflows. Supporting Information are available at Journal of Chemical Information and Modeling online.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jcim.4c02125.

• Supplementary Tables (S1–S14): These tables provide a detailed comparison of PbImpute and other models, covering performance metrics such as F1 Score, correlation analysis, error rates, clustering performance, trajectory analysis, zero-rate evaluation, and ablation study results; Supplementary Figures (S1–S8): These figures illustrate a comprehensive comparison of PbImpute and other models, including performance metrics such as F1 Score, single-cell differential expression analysis, clustering performance, trajectory analysis, and computational efficiency evaluation; Supplementary Evaluation Metrics (pages S12–S14): This section provides detailed evaluation metrics, including Standard F1 Score, Modified F1 Score, single-cell differential expression analysis, Correlation (gene), Correlation (cell), Error, ARI, NMI, and POS; Supplementary Methods (Preprocessing) (pages S15–S16): detail the preprocessing procedures, including highly variable gene selection and cell partitioning; Supplementary Summary of Real scRNA-seq Data sets (page S17): This section provides a summary of the real scRNA-seq data sets used in the study (PDF)

Author Contributions

Conceptualization: Y.W., Y.Z. Data curation: Y.W., X.F. Formal analysis: Y.Z., Y.W. Funding acquisition: Y.Z. Visualization: Y.W., X.L. Writing–original draft: Y.W., Y.Z. Writing–review and editing: Y.Z., Y.W.

This research was funded by National Natural Science Foundation of China (Grant No. 62166014) with funder of Yi Zhang, Natural Science Foundation of Guangxi Province (Grant No. 2020GXNSFAA297255) with funder of Yi Zhang.

The authors declare no competing financial interest.