Global emission factor dataset for Scope 3 machine learning applications

Abstract

The accurate and transparent estimation of greenhouse gas emissions is essential for corporate sustainability reporting and machine learning applications. Existing emission-factor datasets have restrictive licenses, insufficient spatiotemporal granularity, or outdated information, limiting their reproducibility and utility across disciplines. We present ExioML, an open-source dataset derived from Exiobase 3.8.2. It integrates environmentally extended multi-regional input-output tables with a graphics processing unit (GPU)-accelerated computational toolkit, facilitating compatibility with and extensibility to other datasets. ExioML encompasses sector-level emission factor data for 49 regions and 28 years from 1995 to 2022, structured into two aggregation schemes: a product-by-product format covering 200 categories, and an industry-by-industry format covering 163 categories. To validate dataset usability and establish a reproducible baseline, we define a regression task for predicting sectoral greenhouse gas emissions. The task is evaluated using tree-based and neural-network-based models, with mean squared error as the evaluation metric. ExioML provides openly accessible emission-factor tables and a reproducible baseline intended to support reuse and benchmarking across sustainability and machine-learning studies.

Background & Summary

Accurate emission-factor data form the backbone of nearly all carbon accounting and sustainability assessments. They provide essential coefficients that map economic activities (e.g., purchases or outputs) to corresponding greenhouse gas (GHG) emissions. Recent reports suggest that up to 70% of companies rely on third-party emission-factor datasets when calculating Scope 3 value-chain emissions. However, many such datasets are inaccessible, outdated, or lack sufficient coverage^1–3.

This scarcity of open, high-resolution emission-factor data not only complicates corporate reporting but also hampers advanced data-driven methods. In practice, companies like IBM, Amazon, and Watershed have begun applying large language models (LLMs) and zero-shot text-matching techniques to automate carbon-footprinting tasks^1–4. Yet they consistently identify the paucity of high-quality, up-to-date emission factors as a common limitation.

At the same time, research in ecological economics (EE) increasingly seeks to leverage machine learning (ML) tools for analyzing how economic growth and climate actions interplay^5–9. However, such interdisciplinary work requires access to comprehensive eco-economic data. Environmentally Extended Multi-Regional Input-Output (EE-MRIO) is a framework that links inter-regional economic flows with environmental extensions and can serve as a rich source of emission factors and resource flows^10,11. However, these tables are rarely released in an ML-ready format and often impose licensing fees or restrictive terms. As a result, few public benchmarks exist for researchers to compare algorithms for GHG estimation, supply-chain sustainability, or real-time forecasting of emissions across multiple economic sectors^12–14.

Motivation for an Open Emission-Factor Dataset in EE–ML. Against this backdrop, a clear need emerges for an open, high-resolution dataset that unites machine learning practices with ecological economics principles. Existing ML-based studies classify financial transactions into emission categories^1,3 or match products to life-cycle emission factors^2,4. These studies underscore how crucial it is to have reliable numeric mappings from “economic sector” to “GHG intensity”. Yet most sector-level data remain locked in proprietary models, or they lack sufficient spatial/temporal resolution for advanced ML tasks. Consequently, the potential of ML—including deep learning for anomaly detection, time-series forecasting, or sector-based classification—is far from fully realized. Researchers face steep preprocessing hurdles, re-assembling partial data from disparate sources, and risk making inconsistent assumptions that limit reproducibility^13,14.

To succinctly highlight these gaps, Table 1 summarizes common limitations in existing EE-MRIO literature and datasets, directly contrasting them with ExioML. GPU acceleration is included as an additional dimension because handling large-scale MRIO tables is computationally demanding. These tables typically encompass hundreds of sectors and dozens of regions.

Table 1.

General Limitations in EE-MRIO Literature vs. ExioML’s Approach.

Aspect	Existing Limitations	ExioML’s Approach
Openness & Accessibility	Restricted licensing, costly paywalls, limited redistribution	Fully open-source, unrestricted redistribution and reuse
ML-readiness & Usability	Complex MRIO assumptions for ML researchers	Directly ingestible structure and ML-ready formats
Coverage & Granularity	Limited spatial coverage, outdated data, sparse updates	Detailed annual data, 49 regions, continuous coverage (1995-2022)
Format & Reproducibility	Inconsistent formats, fragmented data, limited reproducibility	Uniform, transparent schema, consistent format for reproducibility
Computational Efficiency	High computational complexity, no GPU acceleration, slow processing	Optimized MRIO computations, enhanced scalability

ExioML is constructed entirely from the openly licensed EXIOBASE 3.8.2 dataset and is released under an open licence compatible with EXIOBASE. We provide freely downloadable, preprocessed data in standard machine-readable formats without restrictions on reuse or redistribution. The inclusion of GPU acceleration supports computational workflows when handling large-scale MRIO tables.

Introducing ExioML. To help address these challenges, we propose ExioML, an open-source, ML-ready benchmark derived from the Exiobase 3.8.2 dataset¹⁵. ExioML is designed to address three challenges that have so far limited the use of EE-MRIO-based emission factors in global sustainability and machine-learning applications:

• Fragmented and sparse global emission-factor data. Existing emission-factor resources are dispersed across multiple EE-MRIO datasets, often with inconsistent formats, restrictive licences, and limited temporal or spatial coverage. ExioML reconstructs a coherent sector-level panel of emission factors for 49 regions and 28 years (1995-2022), harmonising units, sector codes, and environmental accounts so that high-resolution, globally comparable emission intensities can be queried from a single, unified source.

• Lack of scalable tools for analysing EE-MRIO data. Raw EE-MRIO tables are large, difficult to manipulate, and rarely shipped with modern analysis, visualisation, or machine-learning interfaces. Building on the open Exiobase release, ExioML provides a Python package with GPU-accelerated routines that automate core Leontief-based matrix operations, construct footprint-network representations, and export compact tabular and graph formats. This turns tens of gigabytes of MRIO data into manageable artefacts that can be inspected, visualised, and fed into ML pipelines with minimal manual preprocessing.

• High barriers for ML and ecological-economics communities to share benchmarks. To date, there has been no widely available benchmark that couples curated emission-factor data with standard prediction tasks and baseline models. ExioML offers preprocessed, “plug-and-play” factor tables and footprint networks together with a regression benchmark for sectoral GHG emissions and multiple baseline algorithms, enabling systematic model comparison and supporting benchmarking across ML and ecological-economics studies.

ExioML is released under an open license compatible with EXIOBASE and provides standardized factor and footprint tables for 49 regions (1995-2022).

Methods

In this section, we first introduce the core concepts of Environmentally Extended Multiregional Input-Output (EE-MRIO) analysis and explain why it underpins most emission-factor datasets in ecological economics research. We then compare five major EE-MRIO datasets—WIOD, GTAP, Eora, USEEIO, and Exiobase—highlighting their accessibility, coverage, time horizon, sector detail, and types of emission factors. Next, we demonstrate how ExioML was constructed as an open-source emission-factor dataset (EFDB) derived from ExioBase 3.8.2. We describe the construction workflow, the factor tables, the footprint networks, and the GPU-accelerated toolkit used to generate the released files.

EE-MRIO as a Foundation for Emission-Factor Datasets. Environmentally Extended Multiregional Input-Output (EE-MRIO) analysis frames the global economy as a network of interlinked sectors spanning multiple regions^16–20. It builds on classical work in interregional and international input-output modelling, which first formalised the idea of a space-economy in which regions are connected through trade and production linkages^21,22. Traditional input-output models focus on monetary flows among sectors, while their environmentally extended variants incorporate resource use and pollutant emissions^18,23–26. As Fig. 1 shows, an EE-MRIO dataset typically includes:

• A transaction matrix (Z) that records monetary flows between sectors and captures how industries purchase inputs from one another.

• A final demand matrix (Y) capturing non-intermediate consumption by households, government, and international markets (including exports).

• One or more factor accounts (F) specifying emissions and resource use by sector, containing environmental extensions such as GHG emissions, resource extraction, and pollutant releases.

Fig. 1.

Environmentally Extended Multi-Regional Input–Output (EE-MRIO) data are represented in a high-dimensional matrix format, tracking monetary transfers between international sectors via input–output and final-demand matrices. Additionally, it accounts for the environmental impacts of economic activities through the Factor Accounting table.

By combining Z, Y, and F, researchers can trace embodied emissions through complex supply chains, thereby calculating the total (direct + indirect) impact of any given sector. This approach underpins many studies of consumption-based accounting and trade-linked pollution, where emissions are allocated to the final consumers who drive production^27,28. It also informs structure-decomposition analysis²³ and sustainability evaluations in global trade^29,30. Methodological introductions such as Kitzes provide accessible overviews of how environmentally extended input-output analysis connects economic accounts with environmental extensions and footprint indicators²⁶.

Machine learning (ML) has recently entered the EE-MRIO arena for tasks such as automatically identifying high-emission hotspots and optimizing logistics³¹. Recent surveys show that machine learning can be a powerful tool for reducing greenhouse gas emissions and aiding society’s adaptation to climate change³². These works highlight how ML can complement EE-MRIO frameworks by automating hotspot detection, scenario forecasting, and anomaly identification. Embedding high-dimensional input-output data to discover latent patterns in supply chains^33,34, forecasting future emissions based on economic or technology scenarios^12,13, and clustering industrial sectors by environmental similarity for policy design^35,36 are all active research directions. Each of these tasks requires robust, well-documented EE-MRIO data.

However, these ML applications critically depend on open, granular, and up-to-date emission factors that map sector-level outputs to GHG intensities. In practice, many existing EE-MRIO datasets have restrictions or incomplete coverage, limiting reproducibility and cross-study benchmarking. Earlier work on building multi-year MRIO systems—for example the embedded carbon emissions indicator for the UK, constructed via an MRIO data optimisation system³⁷—demonstrates both the analytical value and the practical complexity of assembling time series of harmonised input-output tables. ExioML builds on these methodological strengths and formats the resulting emission factors for ML pipelines.

Comparison of Major EE-MRIO Datasets.Table 2 summarizes five commonly used EE-MRIO datasets and contrasts them with our proposed ExioML. Each dataset has distinctive strengths, yet also presents certain limitations when viewed from an ML perspective.

Table 2.

Comparison of major EE-MRIO datasets in terms of accessibility, geographical scope, temporal range, sectoral detail, and emission-factor breadth.

Dataset	Open	Regions	Time Span	Sector Detail
WIOD48	Yes	≈ 40 countries	1995–2016	35–56 sectors
GTAP49	No	≈ 140 regions	2004, 2007, 2011, 2014	57–65 sectors
Eora50	No	190 countries	1990–2023	15,909 sectors
USEEIO51	Yes	United States	2013, 2018	389 sectors
Exiobase52	Yes	49 regions	1995–2022	200 sectors
ExioML	Yes	49 regions	1995–2022	200 sectors

Accessibility and Licensing. While WIOD and Exiobase are nominally free, GTAP requires paid licenses, and Eora’s highest-resolution tables can also be costly to acquire. In contrast, ExioML retains Exiobase’s open-access basis and distributes ready-to-use factor tables in user-friendly formats.

Coverage & Updates. Eora is highly granular and frequently updated, but not fully open. GTAP covers a large set of regions but only releases discrete “snapshot” versions every few years, limiting time-series forecasting. WIOD’s coverage ends around 2016. ExioML extends Exiobase’s coverage to 2022, enabling more recent analyses of trends.

Sector Detail & Emissions Scope. Some datasets track only energy-related CO₂, whereas ExioML inherits thousands of environmental categories from Exiobase (417 emission types, 662 resource types). This breadth is vital for advanced ML tasks that go beyond carbon, e.g., analyzing air pollutants, water use, or material footprints.

Implications for ML. The standardized formats and coverage enable reuse in benchmarking and downstream analyses, subject to the constraints noted in the dataset description.

Machine-learning formulation. ExioML is organized to support machine-learning workflows in which sector attributes and network-derived features are used to estimate emission factors. The motivation for ML is practical: full EE-MRIO tables are high-dimensional and costly to recompute, while many applications require rapid estimation, imputation, or cross-year prediction on standardized features. The tabular and edge-list releases allow studies to operate without reconstructing full MRIO matrices.

Regression setting. We frame the primary tasks as supervised regression, with inputs drawn from the Factor Accounting tables (e.g., value added, employment, energy totals) and optional features derived from the Footprint Networks. The targets are continuous emissions or intensities (e.g., kg CO₂-eq), making regression a natural formulation; classification uses, when needed, thresholds or bins applied to these continuous targets. Region, sector, and year provide categorical or ordinal covariates alongside numeric attributes.

Input representation. The Factor Accounting tables provide numeric attributes and categorical identifiers that are directly usable in tabular pipelines. The Footprint Network edge lists can be consumed as graph inputs or aggregated into node-level summaries (e.g., inflow and outflow totals) before modeling. This separation supports both tabular and graph-based learning under a consistent schema.

Model families. We distinguish statistical machine-learning models, which rely on explicit features and comparatively shallow function classes (e.g., linear models, nearest neighbors, or tree ensembles), from deep learning models that learn hierarchical representations through multi-layer neural networks or attention mechanisms. This distinction captures differences in representation learning and capacity rather than data provenance. The Technical Validation section evaluates representative models from both families using the released ExioML tables.

Building ExioML as an Open Emission-Factor Dataset. The proposed ExioML dataset is an emission-factor dataset built by carefully restructuring the raw Exiobase 3.8.2 files. Figure 2 outlines the system architecture. We preserve the comprehensive environmental accounting of Exiobase but reformat it into two user-facing components:

• Factor Accounting (Tabular Data): Provides sector-level measures such as value added, employment, energy consumption, and total GHG emissions. These can be viewed as emission factors under different normalizations, e.g. per monetary unit or per unit of output.

• Footprint Networks (Graph Data): Graph-based representations of inter-sector trade flows annotated with embodied emissions capture the full trading network across 49 regions. Each edge denotes inter-sector flows and can store derived footprints of various pollutants.

Fig. 2.

Architecture of ExioML system derived from the open-source EE-MRIO dataset, ExioBase 3.8.2. Each color denotes an eco-economic factor: value added, employment, energy consumption, or GHG emission. The system contains Factor Accounting data describing heterogeneous sector features, and the Footprint Networks model the global trading network tracking resource transfers across sectors. The data are presented in two classifications: 200 products and 163 industries across 49 regions from 1995 to 2022 in the PxP and IxI datasets.

ExioBase 3.8.2 itself comprises over 40 GB of supply-use tables, satellite accounts, and emission categories^15,38. Users lacking deep input-output expertise often find it difficult to extract the relevant portion for machine learning tasks. To mitigate this challenge, we developed a GPU-accelerated toolkit that loads Exiobase, performs the required matrix operations, and outputs a compressed edge table or factor table for each year from 1995 to 2022. Data extraction and MRIO operations build on the open-source pymrio toolbox³⁸. It provides automated download and parsing routines for EXIOBASE and related EE-MRIO datasets. In constructing ExioML from over 40 GB of raw EE-MRIO files, we identify three main challenges that must be overcome to enable scalable machine-learning-ready emission-factor extraction:

1. Large-scale matrix computation: We implement the Leontief-based footprint calculation with CUDA or equivalent GPU libraries, accelerating (I−A)⁻¹y multiplications that would otherwise be prohibitively slow on standard CPUs.

2. Sparse representation of trade networks: Instead of storing a 200 × 200 adjacency for every region pair, we keep only the top million edges per year that exceed a threshold flow, reducing file size.

3. Standardized units and naming conventions: We unify currency units, sector codes, and emission categories to ensure direct comparability across all 49 regions and 28 time steps.

Openness and license compliance. ExioML is built solely from the openly available EXIOBASE 3.8.2 dataset, which is distributed under the Creative Commons Attribution–ShareAlike 4.0 International (CC BY-SA 4.0) license. This license permits reuse and redistribution with attribution and a share-alike obligation; ExioML follows these terms by releasing derived factor and footprint tables under a compatible open licence. No proprietary MRIO inputs (e.g., GTAP or full-resolution Eora tables) are incorporated; they are cited only for contextual comparison. EXIOBASE can be accessed via Zenodo and European Environment Agency portals, and we follow the data providers’ recommended citations^15,38.

The overall workflow is consistent with established practice in constructing multi-regional input-output systems and associated footprint indicators, such as the time-series MRIO for embedded carbon emissions developed for the UK³⁷ and subsequent global carbon-footprint studies based on trade-linked MRIO models²⁸.

Emission Factors in ExioML. The details of ExioML are summarised in Table 3. Four essential factors included in ExioML are identified by the EE research community: GHG emissions, population, gross domestic product (GDP), and total primary energy supply (TPES), the total energy available for use in an economy from all primary sources. The decomposition uses the Kaya Identity²⁴. This identity expresses emissions as the product of population, affluence, energy intensity, and carbon intensity, and was designed specifically for climate-change analysis. This method breaks down carbon emissions into four indicators, which are population (P), GDP per capita (G/P), energy intensity (E/G) and carbon intensity (F/E):

$$F=P\times \frac{G}{P}\times \frac{E}{G}\times \frac{F}{E}.$$

Table 3.

Summary of ExioML dataset details.

Characteristics	Description
Components	Factor accounting (Tabular data), Footprint Networks (Graph data)
Time frame	Covers 28 annual time steps from 1995 to 2022
Geographical coverage	49 regions (44 countries and 5 rest of the world)
Sector detail	200 products in PxP, 163 industries in IxI
Key factors	Value added, employment, energy consumption, and GHG emission

Beyond the Kaya identity, structural decomposition analysis (SDA) offers a general framework for attributing changes in environmental indicators to driving forces such as technology, demand, and structural effects. Prior work provides comprehensive discussions of alternative decomposition techniques for policymaking in energy and environmental applications³⁹ and highlights the trade-offs between different SDA formulations. A comparative review of SDA and index decomposition analysis outlines their respective strengths in input-output studies²³.

Technical Details of EE-MRIO Computations. Following standard EE-MRIO notation, let Z be the global transaction matrix (block-partitioned by region) and Y the final-demand matrix. Let x be the global output vector, such that

$$\left(\begin{array}{c}\hfill x^1\hfill \\ \hfill x^2\hfill \\ \hfill ⋮\hfill \\ \hfill x^m\hfill \\ \hfill \hfill \end{array}\right)=\left(\begin{array}{cccc}\hfill Z^{11}\hfill & \hfill Z^{12}\hfill & \hfill \cdots \hfill & \hfill Z^{1m}\hfill \\ \hfill Z^{21}\hfill & \hfill Z^{22}\hfill & \hfill \cdots \hfill & \hfill Z^{2m}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \hfill Z^{m1}\hfill & \hfill Z^{m2}\hfill & \hfill \cdots \hfill & \hfill Z^{mm}\hfill \end{array}\right)e+\left(\begin{array}{cccc}\hfill Y^{11}\hfill & \hfill Y^{12}\hfill & \hfill \cdots \hfill & \hfill Y^{1m}\hfill \\ \hfill Y^{21}\hfill & \hfill Y^{22}\hfill & \hfill \cdots \hfill & \hfill Y^{2m}\hfill \\ \hfill ⋮\hfill & \hfill ⋮\hfill & \hfill \ddots \hfill & \hfill ⋮\hfill \\ \hfill Y^{m1}\hfill & \hfill Y^{m2}\hfill & \hfill \cdots \hfill & \hfill Y^{mm}\hfill \end{array}\right)e.$$

We compute the direct-requirement matrix $A=Z{\widehat{x}}^{-1}$, which shows how much input each sector requires from others per unit of output. From this, the Leontief inverse L = (I−A)⁻¹ is obtained, capturing the total direct and indirect production requirements across the entire supply chain. For a factor F (e.g., sector-level GHG emissions), we define the intensity vector $S=F{\widehat{x}}^{-1}$ to represent emissions or resource use per unit of economic output. The final footprint D, the total embodied emissions driven by final demand across all regions and sectors, is computed as

$$D=SLy,$$

where y collects final demand by region. This standard formulation underlies many MRIO-based footprint and consumption-based accounting studies, including national and global carbon-footprint analyses that link territorial emissions, trade, and final consumption^28,37.

PxP and IxI Variants. Exiobase 3.8.2 is distributed in two classifications. The product-by-product (PxP) version organises flows by 200 product categories, whereas the industry-by-industry (IxI) version describes flows between 163 industrial sectors. For maximum flexibility, ExioML retains both versions:

• PxP: Suitable for analyzing product-level footprints (e.g., food, textiles, chemicals) in more detail.

• IxI: Appropriate for policy or managerial studies focusing on industries (e.g., agriculture, manufacturing, retail).

Both follow the same data-structure pattern so that ML researchers can train on PxP and validate on IxI to test model generalization. Table 3 summarizes key details of the ExioML dataset. Toolkit Implementation and Availability. Our open-source ExioML development toolkit lowers technical barriers by:

• Performing heavy data preprocessing: discarding unnecessary satellite accounts, ensuring consistent units, labeling sector codes.

• Storing multi-dimensional networks in a single edge table with memory-efficient compression.

• Exposing a simple Python package to query any combination of the 417 emission categories and 662 resources available in Exiobase.

• Providing optional GPU-accelerated modules for matrix inversion and footprint calculations.

The data are available on Zenodo along with documentation and scripts to recreate the factor tables⁴⁰. This standardization supports reproducibility and provides a basis for future updates to ExioML.

Data Records

The dataset is hosted on Zenodo⁴⁰. The release contains four CSV files at the repository root: ExioML_factor_accounting_PxP.csv, ExioML_factor_accounting_IxI.csv, ExioML_footprint_network_PxP.csv, and ExioML_footprint_network_IxI.csv. ExioML ships two coordinated components: a Factor Accounting Table and a Footprint Network Table. The Factor Accounting Table lists sector attributes in tabular form, while the Footprint Network Table records inter-sector links as an edge list. Both cover 49 regions from 1995 to 2022 and are distributed in product-by-product (PxP) and industry-by-industry (IxI) variants. Below we outline their structure, file formats, and the range of carbon-intensity patterns they capture.

Factor Accounting Table.Table 4 summarizes the main fields included in each record. In both PxP and IxI datasets, each row refers to a single (Region, Sector, Year) triple with economic and environmental indicators. Combining the GHG emission column with Energy carrier net total or value added yields intensity measures such as kg CO₂/EUR. Files are released in CSV, and the full time series occupies roughly 20–30 MB.

Table 4.

Key attributes in the ExioML Factor Accounting Table (PxP and IxI).

Attribute name	Type	Description
Region	Categorical	Region code (e.g. AU, US, CN)
Sector	Categorical	Product or industry (e.g. biogasoline, construction)
Year	Numerical	Timestep (e.g. 1995, 2022)
Value added	Numerical	GDP expressed in millions of Euros
Employment	Numerical	Employment (thousand persons)
Energy carrier net total	Numerical	Sum of all energy carriers in Terajoules
GHG emission	Numerical	GHG emissions in kilograms of CO2 equivalent

Footprint Network Table. The companion component is a high-dimensional edge list that encodes trade flows and their footprints between sectors. Each row gives a directed link from a (Region_src, Sector_src) to a (Region_tgt, Sector_tgt) in a given year. The edge stores derived indicators such as:

• Monetary value of the transaction,

• Embodied emissions (e.g., total kg CO₂-eq flowing along this link),

• Embodied energy usage,

and other possible expansions. Because the full adjacency can be exceedingly large, we retain only the top 1,000,000 edges per year by transaction magnitude and then merge with the selected factor attributes. This sparse representation cuts storage dramatically: the PxP and IxI Footprint Networks each total about 1.3–1.4 GB in CSV form, compared to tens of gigabytes in the raw adjacency.

Technical Validation

Problem Formation

Quantifying sector-level GHG emissions is challenging because emissions must be inferred from production efficiency and material inputs rather than measured directly^41,42. This uncertainty complicates transparency and policy evaluation, especially when sectors differ substantially in technology⁴³. To illustrate how ExioML can support estimation tasks, we frame a regression problem that uses mixed categorical and numerical predictors to estimate sectoral GHG emissions.

We cast the task as supervised regression, learning f_θ: X ↦ Y on $\mathcal{D}=\left\{\left(x_1,y_1\right),...,\left(x_n,y_n\right)\right\}$. After removing missing entries, the PxP and IxI Factor Accounting tables provide 221,307 and 179,185 samples, respectively. Each feature vector contains value-added, employment, and energy consumption, and the target Y is the GHG emission.

We benchmark representative tabular learners spanning statistical machine learning and deep learning families^44,45. Statistical machine learning refers to classical models with explicit feature engineering and non-neural estimators, whereas deep learning refers to neural architectures that learn representations from inputs. Statistical machine learning baselines apply leave-one-out target encoding to categorical inputs because they cannot ingest raw categories⁴⁶, while neural models learn embeddings directly. Deep implementations rely on the PyTorch Tabular package⁴⁷. Table 5 summarizes the evaluated models.

Table 5.

Evaluated models, types, and brief descriptions.

Model	Type	Description
K-Nearest Neighbour (KNN)	Statistical learning	Predicts labels from the closest neighbours in feature space53.
Ridge Regression (Ridge)	Statistical learning	Linear regression with ℓ2 regularization to control overfitting54.
Decision Tree (DT)	Statistical learning	Recursively splits features into a tree structure for decisions55.
Random Forest (RF)	Statistical learning	Ensemble of bootstrapped decision trees for robust predictions56.
Gradient Boosted Decision Tree (GBDT)	Statistical learning	Sequentially boosts weak trees to reduce residual error57.
Multi-Layer Perceptron (MLP)	Deep learning	Feedforward neural network trained via backpropagation58.
Gated Adaptive Network (GANDALF)	Deep learning	Employs Gated Feature Learning Units (GFLU) for automated feature selection59.
Feature-Tokenizer Transformer (FTT)	Deep learning	Transformer architecture with tokenization tailored to tabular inputs44.

Experimental Setting

Effective preprocessing and rigorous evaluation are necessary for unbiased performance assessment. We therefore combined data normalization, categorical encoding, and careful dataset partitioning to avoid leakage.

Features were selected using the Kaya Identity, a structural decomposition method widely adopted in eco-economic modeling. Four numerical predictors were retained: population, GDP per capita, energy intensity, and carbon intensity. Two categorical predictors, region and sector, were also included.

Numerical features were min-max scaled to the [0, 1] range. While tree-based models are less sensitive to scaling, normalizing all numerical inputs keeps training stable for deep models and improves comparability across algorithms.

Categorical handling differed by model family. Neural models (MLP, GANDALF, FTT) learn embeddings directly, whereas statistical machine learning models require explicit encoding. We used Leave-One-Out encoding for the latter, computing category-wise target means while excluding the current sample to limit leakage and overfitting to rare categories.

To prevent data leakage, the dataset was split before tuning into training (64%), validation (16%), and testing (20%) subsets. Hyperparameter search and model fitting used only the training and validation sets; the test set remained untouched until final evaluation to reflect genuine generalization capability.

A 30-trial random search explored a compact parameter grid (Table 6). Parameter ranges were chosen heuristically from prior studies. Ensemble models required about 10–20 minutes per dataset to tune, while deep models trained for roughly 2–3 hours.

Table 6.

Parameter grid for tuning and best parameters found for PxP and IxI.

Model	Parameter range	Best PxP	Best IxI
KNN
# Neighbours	Range(1, 50, 2)	5	3
Weights	Uniform, Distance	Distance	Distance
Metric	Euclidean, Manhattan	Manhattan	Manhattan
Ridge
Alpha	0, 0.001, 0.01, 0.1, 1, 10, 100	0	100
DT
Max depth	Range(1, 50, 2)	46	46
Min samples leaf	1, 2, 3	3	1
Min samples split	2, 4, 6, 8	4	6
Max features	Sqrt, Log2	Sqrt	Log2
RF
Max depth	Range(1, 50, 2)	26	26
Min samples leaf	1, 2, 3	1	1
Min samples split	2, 4, 6, 8	2	2
Max features	Sqrt, Log2	Sqrt	Log2
# Estimators	50, 100, 150	100	100
GBDT
Max depth	Range(1, 50, 2)	16	31
Min samples leaf	1, 2, 3	3	3
Min samples split	2, 4, 6, 8	8	2
Max features	Sqrt, Log2	Log2	Log2
# Estimators	50, 100, 150	100	100
Learning rate	0.01, 0.1, 1	0.1	0.1
MLP
Layers	256-128-64, 128-64-32, 64-32-16	256-128-64	256-128-64
Dropout	0, 0.05, 0.1	0	0
Learning rate	0.001, 0.01	0.01	0.01
GANDALF
GFLU stages	1,2,3,4,5	4	4
GFLU dropout	0, 0.05, 0.1	0	0
Feature sparsity	0, 0.05, 0.1	0	0
Learning rate	0.001, 0.01	0.01	0.01
FTT
# Heads	4, 8	8	8
# Attention blocks	1, 2, 3, 4	2	3
# Multiplier	1, 2, 3, 4	4	1
Learning rate	0.001, 0.01	0.01	0.01

We assessed each model on mean squared error and training time. After the 30-trial search, each tuned configuration was run 10 times and evaluated on the held-out test set. Implementation notes appear in Table 7. Deep models were trained with Apple’s Metal Performance Shaders (MPS) backend on an M3 Pro GPU; normalization mainly stabilized training rather than materially improving accuracy.

Table 7.

Implementation details.

Data	Description	Setting	Description
# Train	141,635 (PxP), 114,678 (IxI)	Epoch	30
# Validation	35,409 (PxP), 28,670 (IxI)	Batch size	512
# Test	44,262 (PxP), 35,837 (IxI)	Statistical ML	Scikit-learn
Encoding	Statistical ML models only	Deep	PyTorch Tabular
Normalization	DL models only	Version	Python 3.11.7
Scaling	Log-transformation	GPU	Apple M3 Pro 18 GB

Result Analysis

Table 8 summarizes the mean performance and standard deviation of all evaluated models. Overall, the performance gap between tree-based ensemble methods and deep learning architectures is not substantial. This can be explained by the relatively moderate feature dimensionality in the ExioML Factor Accounting dataset. Deep learning methods typically demonstrate advantages in high-dimensional or unstructured feature spaces, where complex nonlinear dependencies can be captured through large parameter networks. However, when the number of features is limited–as in this case–ensemble models can achieve comparable accuracy while being computationally more efficient.

Table 8.

Result for models with standard deviation for 10 runs and the top results are in bold.

Model	PxP		IxI
	MSE	Time (s)	MSE	Time (s)
KNN	1.071  ±  0.010	0.035  ±  0.001	1.151  ±  0.018	0.026  ±  0.001
Ridge	2.265  ±  0.000	0.005  ±  0.002	2.514  ±  0.000	0.004  ±  0.002
DT	0.926  ±  0.051	0.316  ±  0.017	0.848  ±  0.070	0.254  ±  0.019
RF	0.356  ±  0.004	21.521  ±  0.157	0.302  ±  0.004	16.511  ±  0.060
GBDT	0.234  ±  0.006	30.276  ±  0.224	0.219  ±  0.007	32.847  ±  0.388
MLP	0.226  ±  0.007	219.218  ±  0.904	0.250  ±  0.092	205.051  ±  24.309
GANDALF	0.204  ±  0.010	352.756  ±  7.036	0.189  ±  0.007	383.119  ±  3.664
FTT	0.330  ±  0.007	330.578  ±  1.527	0.302  ±  0.023	468.911  ±  7.329

From the bias-variance perspective, deep neural networks usually have lower bias but higher variance, while ensemble methods such as Random Forest (RF) and Gradient Boosting Decision Trees (GBDT) achieve a better trade-off between bias and variance through aggregation. Consequently, the GBDT and MLP models perform at a similar mean squared error (MSE) level, with GBDT offering faster convergence and lower computational cost.

The results also reveal several important characteristics of the eco-economic dataset and its modeling behavior:

• Nonlinear relationships dominate the data. Linear models such as Ridge Regression perform the weakest, suggesting that sectoral GHG emissions are governed by nonlinear interactions between economic value-added, employment, and energy consumption. This highlights the importance of adopting nonlinear learners for eco-economic data modeling.

• KNN is sensitive to feature weighting. Since the dataset contains encoded categorical features (representing sector information), different dimensions vary greatly in importance. KNN applies uniform distance metrics, which makes it overly influenced by the most dominant features while neglecting subtle but informative ones. This explains its relatively poor generalization.

• Tree-based ensemble models fit moderate feature complexity effectively. A single Decision Tree (DT) lacks expressive capacity and is prone to overfitting. However, ensemble variants such as RF and GBDT significantly improve prediction accuracy by combining multiple weak learners. RF reduces variance through averaging, while GBDT sequentially minimizes residual errors, leading to improved robustness and performance.

• Deep learning models show marginal but stable improvement. The MLP and GANDALF models achieve the lowest overall MSEs, with GANDALF performing best across both PxP and IxI datasets. This is attributed to its Gated Feature Learning Unit (GFLU), which adaptively adjusts feature relevance. Nevertheless, the advantage of deep architectures over GBDT remains small, indicating that model complexity yields diminishing returns in relatively low-dimensional, structured data.

While deep learning models exhibit marginal improvements in predictive performance, practical considerations such as computational efficiency and ease of parameter tuning significantly influence model selection. As shown in Table 9, deep learning methods (e.g., MLP, GANDALF, FTT) have training times approximately an order of magnitude longer than tree-based ensemble models (RF, GBDT), primarily due to their higher complexity and extensive hyperparameter tuning requirements. Additionally, despite achieving the best accuracy, deep learning approaches often suffer from higher variance, making them less straightforward to implement effectively in practical eco-economic contexts. Thus, considering the balanced trade-off between predictive accuracy, computational efficiency, and ease of deployment, we recommend tree-based ensemble models, particularly GBDT, as more practical baseline choices for modeling similar eco-economic datasets in future research.

Table 9.

Comparative summary of evaluated models in terms of performance, computational efficiency, and key characteristics.

Model	MSE	Time	Advantages	Limitations
KNN	High	Fast	Simple, Interpretable	Sensitive to Features
Ridge	High	Fastest	Interpretable, Robust	Linear Only
DT	Medium	Moderate	Interpretable, Simple	Overfitting
RF	Low	Moderate	Robust, Nonlinear	Moderate Complexity
GBDT	Low	Moderate	High Accuracy	Computational Cost
MLP	Low	Slow	Nonlinear, Flexible	High Complexity
GANDALF	Lowest	Slowest	Best Accuracy	Computational Cost
FTT	Medium	Slow	Feature Interaction	High Complexity

In summary, these findings illustrate that ExioML reflects the intrinsic nonlinear and hierarchical structure of eco-economic data. While deep learning methods can capture more nuanced feature interactions, ensemble approaches remain competitive and computationally efficient, making them practical baselines for sustainability-related machine learning research.

Usage Notes

This section provides practical notes for reuse. The Zenodo record and the versioned PyPI package distribute identical PxP/IxI factor tables with stable column aliases, schema/region/year selectors, and recorded checksums; each deposition is tagged to the manuscript version so that retrieved artefacts can be traced directly to the published analyses. The PyPI distribution is intended as a foundational utility layer that simplifies downstream development for both machine-learning practitioners and domain specialists without extensive software tooling.

Reproducing the reported outputs requires selecting the relevant schema, regions, and years to obtain the factor tables and, where needed, the associated footprint derivatives. The package provides direct loaders for these assets and ships default train/validation/test partitions with accompanying evaluation metadata, allowing the baseline regression figures and metrics to be regenerated deterministically on standard CPU environments. GPU-enabled training routines and scikit-learn wrappers are included for users who wish to rerun or extend the published experiments with minimal configuration; example workflows are documented in the public GitHub repository to demonstrate end-to-end replication.

Portability is maintained through an all-open-source dependency chain and avoidance of platform-specific binaries. Local caching with hash validation prevents silent drift between runs, and per-table metadata describing units, provenance, and feature definitions supports consistent interpretation across independent studies.

Author contributions

Y. Guo designed the study and produced the dataset, visualisations, and regression models for technical validation. J. Ma supervised the project. C. Guan participated in the project design discussion and helped improve the paper draft. All authors contributed to the manuscript.

Data availability

The ExioML dataset⁴⁰, including the Factor Accounting and Footprint Network tables, is publicly available on the Zenodo repository (10.5281/zenodo.10604610). The repository provides four CSV files: ExioML_factor_accounting_PxP.csv, ExioML_factor_accounting_IxI.csv, ExioML_footprint_network_PxP.csv, and ExioML_footprint_network_IxI.csv, covering 49 regions from 1995 to 2022. The PxP/IxI suffixes distinguish product-by-product and industry-by-industry variants, and the two components correspond to the tabular factor tables and footprint edge lists described in Data Records. ExioML redistributes only derived emission factors and footprint summaries computed from the openly licensed EXIOBASE 3.8.2 dataset (CC BY-SA 4.0)¹⁵; no proprietary MRIO inputs are included.

Code availability

The code for constructing ExioML can be found on GitHub (https://github.com/Yvnminc/ExioML).

Competing interests

The authors declare no competing interests.