Causal Structure
================


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   <div class="table-container">
     <table id="methods-table" class="display" style="width:100%">
       <thead>
         <tr>
           <th></th><th>Method</th><th>Year</th><th>Task</th>
           <th>Model</th><th>Published</th><th>Code</th>
         </tr>
       </thead>
       <tbody>
         <tr data-description="AVICI proposes an amortized causal discovery approach, attempting to directly predict causal structures from observational or interventional data using variational inference rather than performing costly searches over possible structures. Since no ground truth is not available for real data, the mode is pre-trained using simulated data with known causal graphs and subsequently applied to real data.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/abs/2205.12934">AVICI</a></td>
           <td>2022</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Amortized pre-training</span><span class="badge model-badge">Variational Inference</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/larslorch/avici" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Bicycle addresses the challenge of robustly identifying cyclic causal graphs, particularly in domains like single-cell genomics, by leveraging perturbation data and explicitly replicating the perturbations on the graph. Following Dictys Bicycle assumes the perturbed cell states to be the steady-state solution of the Ornstein-Uhlenbeck process.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.mlr.press/v236/rohbeck24a.html">Bicycle</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Graph interventions</span><span class="badge model-badge">Ornstein-Uhlenbeck process</span><span class="badge model-badge">Steady-State ODE</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/PMBio/bicycle" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="CausCell integrates causal representation learning with diffusion-based generative modeling to generate counterfactual single-cell data. It disentangles observed and unobserved concepts using concept-specific adversarial discriminators and links the resulting latent representations through a structural causal model encoded as a directed acyclic graph.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41467-025-62008-1">CausCell</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Combinatorial Effect Prediction</span><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">Seen Perturbation Prediction</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Diffusion</span><span class="badge model-badge">Auxilary Classifiers</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/bm2-lab/CausCell" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="TODO">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s42256-023-00719-0">CIV</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Active Learning</span><span class="badge model-badge">Structural Causal Model</span><span class="badge model-badge">DAG-Bayesian linear regression</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td>✗</td>
         </tr>
         <tr data-description="DAG-GNN introduced a polynomial alternative for the acyclicity constraint of NOTEARS, and encodes the DAG in a Graph Neural Network. Experimental results on synthetic data sets indicate that DAG-GNN learns more accurate graphs for non-linearly generated samples. ">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/abs/1904.10098">DAG-GNN</a></td>
           <td>2019</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Continuous optimisation for acyclicity</span><span class="badge model-badge">GNN</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/fishmoon1234/DAG-GNN" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="DCD-FG leverages a Gaussian low-rank structural equation model to model factor directed acyclic graphs (f-DAGs). The f-DAG assumption posits that many nodes share a similar set of parents and children, reflecting the behavior of genes acting collectively in biological programs. This method restricts the search space to low-rank causal interactions to improve causal discovery accuracy and scalability for high-dimensional data. ">
           <td class="details-control"></td>
           <td><a href="https://proceedings.neurips.cc/paper_files/paper/2022/file/7a8fa1382ea068f3f402b72081df16be-Paper-Conference.pdf">DCD-FG</a></td>
           <td>2022</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Factor Model</span><span class="badge model-badge">DAGs</span><span class="badge model-badge">Latent DAGs</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/Genentech/dcdfg" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="DCDI advanced DAG learning by introducing a framework for causal discovery using interventional data. DCDI encoding interventions using a binary adjacency matrix, to replicate the interventional effects directly the DAG and uses neural networks to model the conditional densities. Further, the authors provided theoretical guarantees for DAG learning using interventional data and showed that the inferred graphs can scale to 100 nodes.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/pdf/2007.01754">DCDI</a></td>
           <td>2020</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Graph interventions</span><span class="badge model-badge">DNN</span><span class="badge model-badge">Normalizing-Flows</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/slachapelle/dcdi" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="DCI introduced a reformulated version of the PC algorithm. Rather than inferring the Causal Graph directly DCI attempts to identify causal differences between condition-dependent gene regulatory networks (GRNs) by focusing on edges that appear, disappear, or change between conditions. This significantly reduces the computational complexity in comparison to the original PC algorithm.">
           <td class="details-control"></td>
           <td><a href="https://academic.oup.com/bioinformatics/article/37/18/3067/6168117">DCI</a></td>
           <td>2021</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">PC Algorithm</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="http://uhlerlab.github.io/causaldag/dci" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Dictys integrates scRNA-seq and scATAC-seq data to infer gene regulatory networks (GRNs) and their changes across multiple conditions. By leveraging multiomic data, Dictys infers context-specific networks and dynamic GRNs using steady-state solutions of the Ornstein-Uhlenbeck process to model transcriptional kinetics and account for feedback loops. It reconstructs GRNs by detecting transcription factor (TF) binding sites and refining these networks with single-cell transcriptomic data, capturing regulatory shifts that reflect TF activity beyond expression levels.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41592-023-01971-3">Dictys</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">GRN Inference</span><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Ornstein–Uhlenbeck process</span><span class="badge model-badge">Steady-State ODE</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/pinellolab/dictys" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="A VAE that disentangles control and pertubed cells into a latent space organized by a causal DAG. The encoder produces a Gaussian latent code z, while an intervention encoder transforms intervention one-hot encodings into two embeddings - a soft assignment vector that targets specific latent dimensions and a scalar capturing the intervention’s magnitude. Multiplying and adding these embeddings to z yields a modified latent vector that simulates a soft intervention, whereas zeroing them recovers the control condition. A causal layer then processes the latent vectors using an upper-triangular matrix G, which enforces an acyclic causal structure and propagates intervention effects among the latent factors. The decoder is applied twice - once to the modified latent code to generate virtual counterfactual outputs that reconstruct interventional outcomes, and once to the unmodified code to recover control samples. This dual decoding forces the model to disentangle intervention-specific effects from the intrinsic data distribution. The training objective combines reconstruction error to reconstruct control samples, a discrepancy loss (e.g., MMD) to align virtual counterfactuals with observed interventional data, KL divergence on the latent space, and an L1 penalty on G to enforce sparsity.">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/forum?id=o16sYKHk3S&noteId=2EQ6cmfPHg">discrepancy-VAE</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Combinatorial Effect Prediction</span><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">Disentanglement via Virtual Counterfactuals</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/uhlerlab/discrepancy_vae" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="FLeCS models single-cell gene expression dynamics using coupled ordinary differential equations (ODEs) parameterized by a gene regulatory network. Cells are grouped into temporal bins either via pseudotime inference or experimental timestamps and aligned across time with optimal transport to form (pseudo)time series. To model interventions FLeCS replicates interventions in the learned graph.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/pdf/2503.20027">FLeCS</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">GRN Inference</span><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">ODE</span><span class="badge model-badge">Optimal Transport</span></div></td>


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/Bertinus/FLeCS" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="GSFA is a two-layer, guided Factor Analysis model that quantifies the effects of genetic perturbations on latent factors. The model first factorizes the expression matrix Y into a factor matrix Z (normal prior) and gene loadings W (normal-mixture prior). Then, it captures the effect (β) of perturbation on factors using multivariate linear regression. Spike-and-slab prior is used to enforce sparsity on β, which can also analogously be seen as a causal graph. The linearity of GSFA further enables perturbation-associated, differentially-expressed genes to be identified. GSFA uses Gibbs sampling for inference.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41592-023-02017-4">GSFA</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Linear Gene Programmes</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Factor Analysis</span><span class="badge model-badge">Probabilistic</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/xinhe-lab/GSFA" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="NODAGS-Flow utilizes contractive residual flows to model perturbational data as generated from the steady state of a dynamical system with explicit noise. Following DCDI, NODAGS-Flow replicates perturbations on the graph. Further, NODAGS-Flow drops the acyclicity constraint to model cyclic causal models and better explain the feedback loops inherent to biological data.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.mlr.press/v206/sethuraman23a/sethuraman23a.pdf">NODAGS-Flow</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Graph interventions</span><span class="badge model-badge">DNN</span><span class="badge model-badge">Residual Flow\nSteady-State ODE</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/Genentech/nodags-flows" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="NOTEARS-MLP  further generalized the continuous DAG objective introduced by NOTEARS to nonparametric and semi-parametric models, such as deep neural networks (DNNs), to better facilitate non-linear data.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/abs/1909.13189">NOTEARS-MLP</a></td>
           <td>2020</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Continuous optimisation for acyclicity</span><span class="badge model-badge">DNN</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/xunzheng/notears" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="NOTEARS replaced traditional statistical DAG learning techniques for observational data with a continuous optimisation problem, by reformulating the acyclicity constraint. This reduces the computational complexity and facilitated first small scale biological applications. ">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/abs/1803.01422">NOTEARS</a></td>
           <td>2018</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Continuous optimisation for acyclicity</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/xunzheng/notears" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="RENGE attempts to infer gene regulatory networks from time-series single-cell CRISPR knockout data. It models changes in gene expression following a knockout by propagating the effects through direct and higher-order (indirect) regulatory paths, where the gene network is represented as a matrix of regulatory strengths between gene pairs.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s42003-023-05594-4">RENGE</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">GRN Inference</span><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Regression model</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/masastat/RENGE" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="RiTINI employs graph ordinary differential equations (graph-ODEs) to infer time-varying interaction graphs from multivariate time series data. RiTINI integrates dual attention mechanisms to enhance dynamic modeling and defines interaction graph inference as identifying a directed graph. Further, RiTINI utilizes prior knowledge to initialise the causal graph and by penalizing deviations the prior. Additionally, RiTINI simulates perturbations in silico to further refine the graph structure.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.mlr.press/v231/bhaskar24a.html">RiTINI</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">GRN Inference</span><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Context Transfer</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Graph interventions</span><span class="badge model-badge">Graph-ODE</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/KrishnaswamyLab/RiTINI" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="A VAE that encodes input data into background latent variables and learns sparse, global (salient) embeddings representing the effects of perturbations. These sparse salient embeddings are modeled using a joint relaxed straight-through (Beta-)Bernoulli distribution (mask) and a normally distributed latent space. This method captures perturbation-specific effects as an additive shift to the background representation, analogous to additive shift methods, but it can also be thought as a multi-condition extention to the contrastive framework (limited to two latent variables (case vs. control), to a more general setup capable of learning global embeddings for each perturbation. As in some contrastive methods, for perturbation samples, the perturbation (global) embeddings are added to the background latent variables to reconstruct the data, while for control samples, the perturbation embeddings are effectively set to zero. ">
           <td class="details-control"></td>
           <td><a href="https://proceedings.neurips.cc/paper_files/paper/2023/hash/0001ca33ba34ce0351e4612b744b3936-Abstract-Conference.html">SAMS-VAE</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Combinatorial Effect Prediction</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">NB likelihood</span><span class="badge model-badge">Conditional Latent Embeddings</span><span class="badge model-badge">Addative Shift</span><span class="badge model-badge">Sparse Mechanism Shift</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/insitro/sams-vae" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="scCausalVI is a causality-aware generative model that disentangles inherent cellular heterogeneity from treatment-induced effects in perturbational single-cell RNA-seq data. It encodes structural causal model (SCM) principles into a deep variational inference framework, learning two distinct but interrelated latent factor sets: background factors capturing intrinsic cellular states and treatment effect factors encoding condition-specific transcriptional changes. A Squeeze-and-Excitation Networks (SENet) attention mechanism adaptively scales treatment effects per cell, enabling cell-state-specific response modeling at single-cell resolution. When batch information is available, scCausalVI simultaneously disentangles batch effects, treatment effects, and baseline cellular states in multi-source data integration. Through cross-condition in silico prediction, scCausalVI predicts gene expression profiles under hypothetical scenarios by intervening on condition assignments within the SCM. This enables identification of treatment-responsive cells via permutation-based significance testing, as well as identification of susceptible versus resistant subpopulations by computationally projecting treated cells back to untreated states. Downstream differential expression and pathway analyses on these virtual cells identified subpopulations reveal molecular signatures and regulatory mechanisms underlying differential cellular responses, facilitating the discovery of therapeutic targets and mechanistic drivers of disease susceptibility. ">
           <td class="details-control"></td>
           <td><a href="https://doi.org/10.1016/j.cels.2025.101443">scCausalVI</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Unsupervised Disentanglement</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Perturbation Responsiveness</span><span class="badge task-badge">Differential Analysis</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Variational Autoencoder</span><span class="badge model-badge">Structural Causal Model</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/ShaokunAn/scCausalVI" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="SCCVAE combines mechanistic causal modeling with variational deep learning to predict single-cell transcriptomic responses to perturbations. It features an expression encoder that converts gene expression data from control cells into exogenous variables, a shift encoder that processes perturbation labels, a structural causal model (SCM) to represent perturbations as shift interventions, and an expression decoder.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2025.06.05.657988v1.full.pdf">SCCVAE</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unseen Perturbation Prediction</span><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">Variational Inference</span><span class="badge model-badge">Latent Causal Structure</span></div></td>


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/uhlerlab/sccvae" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="SEA predicts large causal graphs by leveraging small graphs generated from subsets of variables using standard causal discovery algorithms like FCI or GIES. To tackle the challenges of causal discovery with large variable sets, SEA employs an amortized learning approach and utilizes a complex architecture, including transformer modules and diverse embeddings, to aggregate the subgraphs. SEA is pre-trained on synthetic data with known causal structures and encodes interventions by replicating the effects on the encoded graph.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/abs/2402.01929">SEA</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Amortized pre-training</span><span class="badge model-badge">Transfomer</span><span class="badge model-badge">Graph Attention</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/rmwu/sea" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="SENA replaces discrepancy‑VAE&#39;s encoder by using a gene-to-pathway mask that applies a soft weighting, via the pathway activity scores α, to the gene expression inputs. In this design, each weight in the encoder is elementwise multiplied by a mask M that assigns full weight to genes known to belong to a pathway and a tunable, lower weight (λ) to genes outside the pathway. This allows the model to primarily capture the signal of annotated genes while still letting unannotated genes contribute, thereby forming interpretable latent factors as linear combinations of pathway activities. ">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/forum?id=NjlafBAahz">SENA</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Combinatorial Effect Prediction</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Discrepancy-VAE architecture</span><span class="badge model-badge">VAE</span><span class="badge model-badge">PK Representations</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/ML4BM-Lab/SENA" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="A VAE  that combines the sparse mechanism shift from SVAE+ with learning a probabilistic pairing between cells and unobserved auxiliary variables. These auxilary variables correspond to the observed perturbation labels in SVAE+, but here they are learned in a data-driven way (rather than passed as static labels) which in turn enables counterfactual context-transfer scenarios.">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/pdf?id=8hptqO7sfG">svae-ligr</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">NB likelihood</span><span class="badge model-badge">Sparse Mechanism Shift</span><span class="badge model-badge">Generative/Experience Replay</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/theislab/svaeligr" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="A VAE that integrates recent advances in sparse mechanism shift modeling for single-cell data, inferring a causal structure where perturbation labels identify the latent variables affected by each perturbation. The method constructs a graph identifying which latent variables are influenced by specific perturbations, promoting disentaglement and enabling biological interpretability, such as uncovering perturbations affecting shared processes. A key modelling contribution is its probabilistic sparsity approach (relaxed straight-through Beta-Bernoulli) on the global sparse embeddings (graph),  improving upon its predecessor, SVAE. As such, the latent space can be seen as being modelled from a Spike-and-Slab prior.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.mlr.press/v213/lopez23a/lopez23a.pdf">sVAE+</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Nonlinear Gene Programmes</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">NB likelihood</span><span class="badge model-badge">Sparse Mechanism Shift</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/Genentech/sVAE" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
       </tbody>
     </table>
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