It is now possible to conduct large scale perturbation screens with complex readout modalities, such as different molecular profiles or high content cell images. While these open the way for systematic dissection of causal cell circuits, integrating such data across screens to maximize our ability to predict circuits poses substantial computational challenges, which have not been addressed. Here, we extend two Gromov-Wasserstein optimal transport methods to incorporate the perturbation label for cross-modality alignment. The obtained alignment is then employed to train a predictive model that estimates cellular responses to perturbations observed with only one measurement modality. We validate our method for the tasks of cross-modality alignment and cross-modality prediction in a recent multi-modal single-cell perturbation dataset. Our approach opens the way to unified causal models of cell biology.

Modeling the dynamics of complex real-world systems from temporal snapshot data is crucial for understanding phenomena such as gene regulation, climate change, and financial market fluctuations. Researchers have recently proposed a few methods based either on the Schroedinger Bridge or Flow Matching to tackle this problem, but these approaches remain limited in their ability to effectively combine data from multiple time points and different experimental settings. This integration is essential in real-world scenarios where observations from certain combinations of time points and experimental conditions are missing, either because of experimental costs or sensory failure. To address this challenge, we propose a novel method named Multi-Marginal Flow Matching (MMFM). MMFM first constructs a flow using smooth spline-based interpolation across time points and conditions and regresses it with a neural network using the classifier-free guided Flow Matching framework. This framework allows for the sharing of contextual information about the dynamics across multiple trajectories. We demonstrate the effectiveness of our method on both synthetic and real-world datasets, including a recent single-cell genomics data set with around a hundred chemical perturbations across time points. Our results show that MMFM significantly outperforms existing methods at imputing data at missing time points.

Editing biological sequences has extensive applications in synthetic biology and medicine, such as designing regulatory elements for nucleic-acid therapeutics and treating genetic disorders. The primary objective in biological-sequence editing is to determine the optimal modifications to a sequence which augment certain biological properties while adhering to a minimal number of alterations to ensure predictability and potentially support safety. In this paper, we propose GFNSeqEditor, a novel biological-sequence editing algorithm which builds on the recently proposed area of generative flow networks (GFlowNets). Our proposed GFNSeqEditor identifies elements within a starting seed sequence that may compromise a desired biological property. Then, using a learned stochastic policy, the algorithm makes edits at these identified locations, offering diverse modifications for each sequence to enhance the desired property. The number of edits can be regulated through specific hyperparameters. We conducted extensive experiments on a range of real-world datasets and biological applications, and our results underscore the superior performance of our proposed algorithm compared to existing state-of-the-art sequence editing methods.

The study of cells and their responses to genetic or chemical perturbations promises to accelerate the discovery of therapeutics targets. However, designing adequate and insightful models for such data is difficult because the response of a cell to perturbations essentially depends on contextual covariates (e.g., genetic background or type of the cell). There is therefore a need for models that can identify interactions between drugs and contextual covariates. This is crucial for discovering therapeutics targets, as such interactions may reveal drugs that affect certain cell types but not others. We tackle this problem with a novel Factorized Causal Representation (FCR) learning method, an identifiable deep generative model that reveals causal structure in single-cell perturbation data from several cell lines. FCR learns multiple cellular representations that are disentangled, comprised of covariate-specific (Z_x), treatment-specific (Z_t) and interaction-specific (Z_tx) representations. Based on recent advances of non-linear ICA theory, we prove the component-wise identifiability of Z_tx and block-wise identifiability of Z_t and Z_x. Then, we present our implementation of FCR, and empirically demonstrate that FCR outperforms state-of-the-art baselines in various tasks across four single-cell datasets.

Learning causal relationships between variables is a well-studied problem in statistics, with many important applications in science. However, modeling real-world systems remain challenging, as most existing algorithms assume that the underlying causal graph is acyclic. While this is a convenient framework for developing theoretical developments about causal reasoning and inference, the underlying modeling assumption is likely to be violated in real systems, because feedback loops are common (e.g., in biological systems). Although a few methods search for cyclic causal models, they usually rely on some form of linearity, which is also limiting, or lack a clear underlying probabilistic model. In this work, we propose a novel framework for learning nonlinear cyclic causal graphical models from interventional data, called NODAGS-Flow. We perform inference via direct likelihood optimization, employing techniques from residual normalizing flows for likelihood estimation. Through synthetic experiments and an application to single-cell high-content perturbation screening data, we show significant performance improvements with our approach compared to state-of-the-art methods with respect to structure recovery and predictive performance.

A common theme in causal inference is learning causal relationships between observed variables, also known as causal discovery. This is usually a daunting task, given the large number of candidate causal graphs and the combinatorial nature of the search space. Perhaps for this reason, most research has so far focused on relatively small causal graphs, with up to hundreds of nodes. However, recent advances in fields like biology enable generating experimental data sets with thousands of interventions followed by rich profiling of thousands of variables, raising the opportunity and urgent need for large causal graph models. Here, we introduce the notion of factor directed acyclic graphs ($f$-DAGs) as a way to restrict the search space to non-linear low-rank causal interaction models. Combining this novel structural assumption with recent advances that bridge the gap between causal discovery and continuous optimization, we achieve causal discovery on thousands of variables. Additionally, as a model for the impact of statistical noise on this estimation procedure, we study a model of edge perturbations of the $f$-DAG skeleton based on random graphs and quantify the effect of such perturbations on the $f$-DAG rank. This theoretical analysis suggests that the set of candidate $f$-DAGs is much smaller than the whole DAG space and thus may be more suitable as a search space in the high-dimensional regime where the underlying skeleton is hard to assess. We propose Differentiable Causal Discovery of Factor Graphs (DCD-FG), a scalable implementation of $f$-DAG constrained causal discovery for high-dimensional interventional data. DCD-FG uses a Gaussian non-linear low-rank structural equation model and shows significant improvements compared to state-of-the-art methods in both simulations as well as a recent large-scale single-cell RNA sequencing data set with hundreds of genetic interventions.

We study the problem of batch learning from bandit feedback in the setting of extremely large action spaces. Learning from extreme bandit feedback is ubiquitous in recommendation systems, in which billions of decisions are made over sets consisting of millions of choices in a single day, yielding massive observational data. In these large-scale real-world applications, supervised learning frameworks such as eXtreme Multi-label Classification (XMC) are widely used despite the fact that they incur significant biases due to the mismatch between bandit feedback and supervised labels. Such biases can be mitigated by importance sampling techniques, but these techniques suffer from impractical variance when dealing with a large number of actions. In this paper, we introduce a selective importance sampling estimator (sIS) that operates in a significantly more favorable bias-variance regime. The sIS estimator is obtained by performing importance sampling on the conditional expectation of the reward with respect to a small subset of actions for each instance (a form of Rao-Blackwellization). We employ this estimator in a novel algorithmic procedure---named Policy Optimization for eXtreme Models (POXM)---for learning from bandit feedback on XMC tasks. In POXM, the selected actions for the sIS estimator are the top-p actions of the logging policy, where p is adjusted from the data and is significantly smaller than the size of the action space. We use a supervised-to-bandit conversion on three XMC datasets to benchmark our POXM method against three competing methods: BanditNet, a previously applied partial matching pruning strategy, and a supervised learning baseline. Whereas BanditNet sometimes improves marginally over the logging policy, our experiments show that POXM systematically and significantly improves over all baselines.

We address a practical problem ubiquitous in modern marketing campaigns, in which a central agent tries to learn a policy for allocating strategic financial incentives to customers and observes only bandit feedback. In contrast to traditional policy optimization frameworks, we take into account the additional reward structure and budget constraints common in this setting, and develop a new two-step method for solving this constrained counterfactual policy optimization problem. Our method first casts the reward estimation problem as a domain adaptation problem with supplementary structure, and then subsequently uses the estimators for optimizing the policy with constraints. We also establish theoretical error bounds for our estimation procedure and we empirically show that the approach leads to significant improvement on both synthetic and real datasets.

To make decisions based on a model fit with auto-encoding variational Bayes (AEVB), practitioners often let the variational distribution serve as a surrogate for the posterior distribution. This approach yields biased estimates of the expected risk, and therefore leads to poor decisions for two reasons. First, the model fit with AEVB may not equal the underlying data distribution. Second, the variational distribution may not equal the posterior distribution under the fitted model. We explore how fitting the variational distribution based on several objective functions other than the ELBO, while continuing to fit the generative model based on the ELBO, affects the quality of downstream decisions. For the probabilistic principal component analysis model, we investigate how importance sampling error, as well as the bias of the model parameter estimates, varies across several approximate posteriors when used as proposal distributions. Our theoretical results suggest that a posterior approximation distinct from the variational distribution should be used for making decisions. Motivated by these theoretical results, we propose learning several approximate proposals for the best model and combining them using multiple importance sampling for decision-making. In addition to toy examples, we present a full-fledged case study of single-cell RNA sequencing. In this challenging instance of multiple hypothesis testing, our proposed approach surpasses the current state of the art.

Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research. While providing appealing flexibility, this approach makes it difficult to impose or assess structural constraints such as conditional independence. We propose a framework for learning representations that relies on Auto-Encoding Variational Bayes and whose search space is constrained via kernel-based measures of independence. In particular, our method employs the $d$-variable Hilbert-Schmidt Independence Criterion (dHSIC) to enforce independence between the latent representations and arbitrary nuisance factors. We show how to apply this method to a range of problems, including the problems of learning invariant representations and the learning of interpretable representations. We also present a full-fledged application to single-cell RNA sequencing (scRNA-seq). In this setting the biological signal in mixed in complex ways with sequencing errors and sampling effects. We show that our method out-performs the state-of-the-art in this domain.