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Authors:Zuheng, Xu, Moksh Jain, Ali Denton, Shawn Whitfield, Aniket Didolkar, Berton Earnshaw, Jason Hartford

Abstract:Pairwise interactions between perturbations to a system can provide evidence for the causal dependencies of the underlying underlying mechanisms of a system. When observations are low dimensional, hand crafted measurements, detecting interactions amounts to simple statistical tests, but it is not obvious how to detect interactions between perturbations affecting latent variables. We derive two interaction tests that are based on pairwise interventions, and show how these tests can be integrated into an active learning pipeline to efficiently discover pairwise interactions between perturbations. We illustrate the value of these tests in the context of biology, where pairwise perturbation experiments are frequently used to reveal interactions that are not observable from any single perturbation. Our tests can be run on unstructured data, such as the pixels in an image, which enables a more general notion of interaction than typical cell viability experiments, and can be run on cheaper experimental assays. We validate on several synthetic and real biological experiments that our tests are able to identify interacting pairs effectively. We evaluate our approach on a real biological experiment where we knocked out 50 pairs of genes and measured the effect with microscopy images. We show that we are able to recover significantly more known biological interactions than random search and standard active learning baselines.

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Abstract:Many causal systems such as biological processes in cells can only be observed indirectly via measurements, such as gene expression. Causal representation learning -- the task of correctly mapping low-level observations to latent causal variables -- could advance scientific understanding by enabling inference of latent variables such as pathway activation. In this paper, we develop methods for inferring latent variables from multiple related datasets (environments) and tasks. As a running example, we consider the task of predicting a phenotype from gene expression, where we often collect data from multiple cell types or organisms that are related in known ways. The key insight is that the mapping from latent variables driven by gene expression to the phenotype of interest changes sparsely across closely related environments. To model sparse changes, we introduce Tree-Based Regularization (TBR), an objective that minimizes both prediction error and regularizes closely related environments to learn similar predictors. We prove that under assumptions about the degree of sparse changes, TBR identifies the true latent variables up to some simple transformations. We evaluate the theory empirically with both simulations and ground-truth gene expression data. We find that TBR recovers the latent causal variables better than related methods across these settings, even under settings that violate some assumptions of the theory.

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Abstract:Scientific hypotheses typically concern specific aspects of complex, imperfectly understood or entirely unknown mechanisms, such as the effect of gene expression levels on phenotypes or how microbial communities influence environmental health. Such queries are inherently causal (rather than purely associational), but in many settings, experiments can not be conducted directly on the target variables of interest, but are indirect. Therefore, they perturb the target variable, but do not remove potential confounding factors. If, additionally, the resulting experimental measurements are multi-dimensional and the studied mechanisms nonlinear, the query of interest is generally not identified. We develop an adaptive strategy to design indirect experiments that optimally inform a targeted query about the ground truth mechanism in terms of sequentially narrowing the gap between an upper and lower bound on the query. While the general formulation consists of a bi-level optimization procedure, we derive an efficiently estimable analytical kernel-based estimator of the bounds for the causal effect, a query of key interest, and demonstrate the efficacy of our approach in confounded, multivariate, nonlinear synthetic settings.

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Abstract:Many causal systems such as biological processes in cells can only be observed indirectly via measurements, such as gene expression. Causal representation learning -- the task of correctly mapping low-level observations to latent causal variables -- could advance scientific understanding by enabling inference of latent variables such as pathway activation. In this paper, we develop methods for inferring latent variables from multiple related datasets (environments) and tasks. As a running example, we consider the task of predicting a phenotype from gene expression, where we often collect data from multiple cell types or organisms that are related in known ways. The key insight is that the mapping from latent variables driven by gene expression to the phenotype of interest changes sparsely across closely related environments. To model sparse changes, we introduce Tree-Based Regularization (TBR), an objective that minimizes both prediction error and regularizes closely related environments to learn similar predictors. We prove that under assumptions about the degree of sparse changes, TBR identifies the true latent variables up to some simple transformations. We evaluate the theory empirically with both simulations and ground-truth gene expression data. We find that TBR recovers the latent causal variables better than related methods across these settings, even under settings that violate some assumptions of the theory.

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Abstract:Multimodal representation learning techniques typically rely on paired samples to learn common representations, but paired samples are challenging to collect in fields such as biology where measurement devices often destroy the samples. This paper presents an approach to address the challenge of aligning unpaired samples across disparate modalities in multimodal representation learning. We draw an analogy between potential outcomes in causal inference and potential views in multimodal observations, which allows us to use Rubin's framework to estimate a common space in which to match samples. Our approach assumes we collect samples that are experimentally perturbed by treatments, and uses this to estimate a propensity score from each modality, which encapsulates all shared information between a latent state and treatment and can be used to define a distance between samples. We experiment with two alignment techniques that leverage this distance -- shared nearest neighbours (SNN) and optimal transport (OT) matching -- and find that OT matching results in significant improvements over state-of-the-art alignment approaches in both a synthetic multi-modal setting and in real-world data from NeurIPS Multimodal Single-Cell Integration Challenge.

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Abstract:Causal representation learning has showed a variety of settings in which we can disentangle latent variables with identifiability guarantees (up to some reasonable equivalence class). Common to all of these approaches is the assumption that (1) the latent variables are represented as $d$-dimensional vectors, and (2) that the observations are the output of some injective generative function of these latent variables. While these assumptions appear benign, we show that when the observations are of multiple objects, the generative function is no longer injective and disentanglement fails in practice. We can address this failure by combining recent developments in object-centric learning and causal representation learning. By modifying the Slot Attention architecture arXiv:2006.15055, we develop an object-centric architecture that leverages weak supervision from sparse perturbations to disentangle each object's properties. This approach is more data-efficient in the sense that it requires significantly fewer perturbations than a comparable approach that encodes to a Euclidean space and we show that this approach successfully disentangles the properties of a set of objects in a series of simple image-based disentanglement experiments.

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Abstract:Instrumental variable (IV) methods are used to estimate causal effects in settings with unobserved confounding, where we cannot directly experiment on the treatment variable. Instruments are variables which only affect the outcome indirectly via the treatment variable(s). Most IV applications focus on low-dimensional treatments and crucially require at least as many instruments as treatments. This assumption is restrictive: in the natural sciences we often seek to infer causal effects of high-dimensional treatments (e.g., the effect of gene expressions or microbiota on health and disease), but can only run few experiments with a limited number of instruments (e.g., drugs or antibiotics). In such underspecified problems, the full treatment effect is not identifiable in a single experiment even in the linear case. We show that one can still reliably recover the projection of the treatment effect onto the instrumented subspace and develop techniques to consistently combine such partial estimates from different sets of instruments. We then leverage our combined estimators in an algorithm that iteratively proposes the most informative instruments at each round of experimentation to maximize the overall information about the full causal effect.

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Abstract:Learning the causal structure of observable variables is a central focus for scientific discovery. Bayesian causal discovery methods tackle this problem by learning a posterior over the set of admissible graphs given our priors and observations. Existing methods primarily consider observations from static systems and assume the underlying causal structure takes the form of a directed acyclic graph (DAG). In settings with dynamic feedback mechanisms that regulate the trajectories of individual variables, this acyclicity assumption fails unless we account for time. We focus on learning Bayesian posteriors over cyclic graphs and treat causal discovery as a problem of sparse identification of a dynamical system. This imposes a natural temporal causal order between variables and captures cyclic feedback loops through time. Under this lens, we propose a new framework for Bayesian causal discovery for dynamical systems and present a novel generative flow network architecture (DynGFN) tailored for this task. Our results indicate that DynGFN learns posteriors that better encapsulate the distributions over admissible cyclic causal structures compared to counterpart state-of-the-art approaches.

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Authors:Moksh Jain, Tristan Deleu, Jason Hartford, Cheng-Hao Liu, Alex Hernandez-Garcia, Yoshua Bengio

Abstract:Tackling the most pressing problems for humanity, such as the climate crisis and the threat of global pandemics, requires accelerating the pace of scientific discovery. While science has traditionally relied on trial and error and even serendipity to a large extent, the last few decades have seen a surge of data-driven scientific discoveries. However, in order to truly leverage large-scale data sets and high-throughput experimental setups, machine learning methods will need to be further improved and better integrated in the scientific discovery pipeline. A key challenge for current machine learning methods in this context is the efficient exploration of very large search spaces, which requires techniques for estimating reducible (epistemic) uncertainty and generating sets of diverse and informative experiments to perform. This motivated a new probabilistic machine learning framework called GFlowNets, which can be applied in the modeling, hypotheses generation and experimental design stages of the experimental science loop. GFlowNets learn to sample from a distribution given indirectly by a reward function corresponding to an unnormalized probability, which enables sampling diverse, high-reward candidates. GFlowNets can also be used to form efficient and amortized Bayesian posterior estimators for causal models conditioned on the already acquired experimental data. Having such posterior models can then provide estimators of epistemic uncertainty and information gain that can drive an experimental design policy. Altogether, here we will argue that GFlowNets can become a valuable tool for AI-driven scientific discovery, especially in scenarios of very large candidate spaces where we have access to cheap but inaccurate measurements or to expensive but accurate measurements. This is a common setting in the context of drug and material discovery, which we use as examples throughout the paper.

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Authors:Chris Cameron, Jason Hartford, Taylor Lundy, Tuan Truong, Alan Milligan, Rex Chen, Kevin Leyton-Brown

Abstract:We introduce Monte Carlo Forest Search (MCFS), an offline algorithm for automatically synthesizing strong tree-search solvers for proving \emph{unsatisfiability} on given distributions, leveraging ideas from the Monte Carlo Tree Search (MCTS) algorithm that led to breakthroughs in AlphaGo. The crucial difference between proving unsatisfiability and existing applications of MCTS, is that policies produce trees rather than paths. Rather than finding a good path (solution) within a tree, the search problem becomes searching for a small proof tree within a forest of candidate proof trees. We introduce two key ideas to adapt to this setting. First, we estimate tree size with paths, via the unbiased approximation from Knuth (1975). Second, we query a strong solver at a user-defined depth rather than learning a policy across the whole tree, in order to focus our policy search on early decisions, which offer the greatest potential for reducing tree size. We then present MCFS-SAT, an implementation of MCFS for learning branching policies for solving the Boolean satisfiability (SAT) problem that required many modifications from AlphaGo. We matched or improved performance over a strong baseline on two well-known SAT distributions (\texttt{sgen}, \texttt{random}). Notably, we improved running time by 9\% on \texttt{sgen} over the \texttt{kcnfs} solver and even further over the strongest UNSAT solver from the 2021 SAT competition.

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