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Caroline Uhler

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24 papers

2 author rows

ICLR Conference 2025 Conference Paper

An Information Criterion for Controlled Disentanglement of Multimodal Data

Chenyu Wang 0003
Sharut Gupta
Xinyi Zhang
Sana Tonekaboni
Stefanie Jegelka
Tommi S. Jaakkola
Caroline Uhler

Multimodal representation learning seeks to relate and decompose information inherent in multiple modalities. By disentangling modality-specific information from information that is shared across modalities, we can improve interpretability and robustness and enable downstream tasks such as the generation of counterfactual outcomes. Separating the two types of information is challenging since they are often deeply entangled in many real-world applications. We propose $\textbf{Disentangled}$ $\textbf{S}$elf-$\textbf{S}$upervised $\textbf{L}$earning (DisentangledSSL), a novel self-supervised approach for learning disentangled representations. We present a comprehensive analysis of the optimality of each disentangled representation, particularly focusing on the scenario not covered in prior work where the so-called $\textit{Minimum Necessary Information}$ (MNI) point is not attainable. We demonstrate that \algo successfully learns shared and modality-specific features on multiple synthetic and real-world datasets and consistently outperforms baselines on various downstream tasks, including prediction tasks for vision-language data, as well as molecule-phenotype retrieval tasks for biological data.

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ICML Conference 2025 Conference Paper

Probabilistic Factorial Experimental Design for Combinatorial Interventions

Divya Shyamal
Jiaqi Zhang
Caroline Uhler

A combinatorial intervention, consisting of multiple treatments applied to a single unit with potential interactive effects, has substantial applications in fields such as biomedicine, engineering, and beyond. Given $p$ possible treatments, conducting all possible $2^p$ combinatorial interventions can be laborious and quickly becomes infeasible as $p$ increases. Here we introduce the probabilistic factorial experimental design, formalized from how scientists perform lab experiments. In this framework, the experimenter selects a dosage for each possible treatment and applies it to a group of units. Each unit independently receives a random combination of treatments, sampled from a product Bernoulli distribution determined by the dosages. Additionally, the experimenter can carry out such experiments over multiple rounds, adapting the design in an active manner. We address the optimal experimental design problem within a novel intervention model that imposes bounded-degree interactions between treatments. In the passive setting, we provide a closed-form solution for the near-optimal design. Our results prove that a dosage of $\frac{1}{2}$ for each treatment is optimal up to a factor of $1+O(\frac{\ln(n)}{n})$ for estimating any $k$-way interaction model, regardless of $k$, and imply that $O\big(kp^{3k}\ln(p)\big)$ observations are required to accurately estimate this model. For the multi-round setting, we provide a near-optimal acquisition function that can be numerically optimized. We also explore several extensions of the design problem and finally validate our findings through simulations.

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ICML Conference 2024 Conference Paper

Causal Discovery with Fewer Conditional Independence Tests

Kirankumar Shiragur
Jiaqi Zhang
Caroline Uhler

Many questions in science center around the fundamental problem of understanding causal relationships. However, most constraint-based causal discovery algorithms, including the well-celebrated PC algorithm, often incur an exponential number of conditional independence (CI) tests, posing limitations in various applications. Addressing this, our work focuses on characterizing what can be learned about the underlying causal graph with a reduced number of CI tests. We show that it is possible to a learn a coarser representation of the hidden causal graph with a polynomial number of tests. This coarser representation, named Causal Consistent Partition Graph (CCPG), comprises of a partition of the vertices and a directed graph defined over its components. CCPG satisfies consistency of orientations and additional constraints which favor finer partitions. Furthermore, it reduces to the underlying causal graph when the causal graph is identifiable. As a consequence, our results offer the first efficient algorithm for recovering the true causal graph with a polynomial number of tests, in special cases where the causal graph is fully identifiable through observational data and potentially additional interventions.

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NeurIPS Conference 2024 Conference Paper

Identifiability Guarantees for Causal Disentanglement from Purely Observational Data

Ryan Welch
Jiaqi Zhang
Caroline Uhler

Causal disentanglement aims to learn about latent causal factors behind data, hold- ing the promise to augment existing representation learning methods in terms of interpretability and extrapolation. Recent advances establish identifiability results assuming that interventions on (single) latent factors are available; however, it re- mains debatable whether such assumptions are reasonable due to the inherent nature of intervening on latent variables. Accordingly, we reconsider the fundamentals and ask what can be learned using just observational data. We provide a precise characterization of latent factors that can be identified in nonlinear causal models with additive Gaussian noise and linear mixing, without any interventions or graphical restrictions. In particular, we show that the causal variables can be identified up to a layer -wise transformation and that further disen- tanglement is not possible. We transform these theoretical results into a practical algorithm consisting of solving a quadratic program over the score estimation of the observed data. We provide simulation results to support our theoretical guarantees and demonstrate that our algorithm can derive meaningful causal representations from purely observational data.

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NeurIPS Conference 2024 Conference Paper

Learning Mixtures of Unknown Causal Interventions

Abhinav Kumar
Kirankumar Shiragur
Caroline Uhler

The ability to conduct interventions plays a pivotal role in learning causal relationships among variables, thus facilitating applications across diverse scientific disciplines such as genomics, economics, and machine learning. However, in many instances within these applications, the process of generating interventional data is subject to noise: rather than data being sampled directly from the intended interventional distribution, interventions often yield data sampled from a blend of both intended and unintended interventional distributions. We consider the fundamental challenge of disentangling mixed interventional and observational data within linear Structural Equation Models (SEMs) with Gaussian additive noise without the knowledge of the true causal graph. We demonstrate that conducting interventions, whether do or soft, yields distributions with sufficient diversity and properties conducive to efficiently recovering each component within the mixture. Furthermore, we establish that the sample complexity required to disentangle mixed data inversely correlates with the extent of change induced by an intervention in the equations governing the affected variable values. As a result, the causal graph can be identified up to its interventional Markov Equivalence Class, similar to scenarios where no noise influences the generation of interventional data. We further support our theoretical findings by conducting simulations wherein we perform causal discovery from such mixed data.

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ICLR Conference 2024 Conference Paper

Removing Biases from Molecular Representations via Information Maximization

Chenyu Wang 0003
Sharut Gupta
Caroline Uhler
Tommi S. Jaakkola

High-throughput drug screening -- using cell imaging or gene expression measurements as readouts of drug effect -- is a critical tool in biotechnology to assess and understand the relationship between the chemical structure and biological activity of a drug. Since large-scale screens have to be divided into multiple experiments, a key difficulty is dealing with batch effects, which can introduce systematic errors and non-biological associations in the data. We propose InfoCORE, an Information maximization approach for COnfounder REmoval, to effectively deal with batch effects and obtain refined molecular representations. InfoCORE establishes a variational lower bound on the conditional mutual information of the latent representations given a batch identifier. It adaptively reweights samples to equalize their implied batch distribution. Extensive experiments on drug screening data reveal InfoCORE's superior performance in a multitude of tasks including molecular property prediction and molecule-phenotype retrieval. Additionally, we show results for how InfoCORE offers a versatile framework and resolves general distribution shifts and issues of data fairness by minimizing correlation with spurious features or removing sensitive attributes.

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NeurIPS Conference 2023 Conference Paper

Identifiability Guarantees for Causal Disentanglement from Soft Interventions

Jiaqi Zhang
Kristjan Greenewald
Chandler Squires
Akash Srivastava
Karthikeyan Shanmugam
Caroline Uhler

Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.

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ICML Conference 2023 Conference Paper

Linear Causal Disentanglement via Interventions

Chandler Squires
Anna Seigal
Salil S. Bhate
Caroline Uhler

Causal disentanglement seeks a representation of data involving latent variables that are related via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement. We show that the method accurately recovers a latent causal model on synthetic and semi-synthetic data and we illustrate a use case on a dataset of single-cell RNA sequencing measurements.

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NeurIPS Conference 2023 Conference Paper

Meek Separators and Their Applications in Targeted Causal Discovery

Kirankumar Shiragur
Jiaqi Zhang
Caroline Uhler

Learning causal structures from interventional data is a fundamental problem with broad applications across various fields. While many previous works have focused on recovering the entire causal graph, in practice, there are scenarios where learning only part of the causal graph suffices. This is called \emph{targeted} causal discovery. In our work, we focus on two such well-motivated problems: subset search and causal matching. We aim to minimize the number of interventions in both cases. Towards this, we introduce the \emph{Meek separator}, which is a subset of vertices that, when intervened, decomposes the remaining unoriented edges into smaller connected components. We then present an efficient algorithm to find Meek separators that are of small sizes. Such a procedure is helpful in designing various divide-and-conquer-based approaches. In particular, we propose two randomized algorithms that achieve logarithmic approximation for subset search and causal matching, respectively. Our results provide the first known average-case provable guarantees for both problems. We believe that this opens up possibilities to design near-optimal methods for many other targeted causal structure learning problems arising from various applications.

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NeurIPS Conference 2023 Conference Paper

Unpaired Multi-Domain Causal Representation Learning

Nils Sturma
Chandler Squires
Mathias Drton
Caroline Uhler

The goal of causal representation learning is to find a representation of data that consists of causally related latent variables. We consider a setup where one has access to data from multiple domains that potentially share a causal representation. Crucially, observations in different domains are assumed to be unpaired, that is, we only observe the marginal distribution in each domain but not their joint distribution. In this paper, we give sufficient conditions for identifiability of the joint distribution and the shared causal graph in a linear setup. Identifiability holds if we can uniquely recover the joint distribution and the shared causal representation from the marginal distributions in each domain. We transform our results into a practical method to recover the shared latent causal graph.

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NeurIPS Conference 2023 Conference Paper

Unsupervised Protein-Ligand Binding Energy Prediction via Neural Euler's Rotation Equation

Wengong Jin
Siranush Sarkizova
Xun Chen
Nir HaCohen
Caroline Uhler

Protein-ligand binding prediction is a fundamental problem in AI-driven drug discovery. Previous work focused on supervised learning methods for small molecules where binding affinity data is abundant, but it is hard to apply the same strategy to other ligand classes like antibodies where labelled data is limited. In this paper, we explore unsupervised approaches and reformulate binding energy prediction as a generative modeling task. Specifically, we train an energy-based model on a set of unlabelled protein-ligand complexes using SE(3) denoising score matching (DSM) and interpret its log-likelihood as binding affinity. Our key contribution is a new equivariant rotation prediction network called Neural Euler's Rotation Equations (NERE) for SE(3) DSM. It predicts a rotation by modeling the force and torque between protein and ligand atoms, where the force is defined as the gradient of an energy function with respect to atom coordinates. Using two protein-ligand and antibody-antigen binding affinity prediction benchmarks, we show that NERE outperforms all unsupervised baselines (physics-based potentials and protein language models) in both cases and surpasses supervised baselines in the antibody case.

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CLeaR Conference 2022 Conference Paper

Causal Imputation via Synthetic Interventions

Chandler Squires
Dennis Shen
Anish Agarwal
Devavrat Shah
Caroline Uhler

Consider the problem of determining the effect of a compound on a specific cell type. To answer this question, researchers traditionally need to run an experiment applying the drug of interest to that cell type. This approach is not scalable: given a large number of different actions (compounds) and a large number of different contexts (cell types), it is infeasible to run an experiment for every action-context pair. In such cases, one would ideally like to predict the outcome for every pair while only needing outcome data for a small _subset_ of pairs. This task, which we label "causal imputation", is a generalization of the causal transportability problem. To address this challenge, we extend the recently introduced _synthetic interventions_ (SI) estimator to handle more general data sparsity patterns. We prove that, under a latent factor model, our estimator provides valid estimates for the causal imputation task. We motivate this model by establishing a connection to the linear structural causal model literature. Finally, we consider the prominent CMAP dataset in predicting the effects of compounds on gene expression across cell types. We find that our estimator outperforms standard baselines, thus confirming its utility in biological applications.

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CLeaR Conference 2022 Conference Paper

Causal Structure Discovery between Clusters of Nodes Induced by Latent Factors

Chandler Squires
Annie Yun
Eshaan Nichani
Raj Agrawal
Caroline Uhler

We consider the problem of learning the structure of a causal directed acyclic graph (DAG) model in the presence of latent variables. We define "latent factor causal models" (LFCMs) as a restriction on causal DAG models with latent variables, which are composed of clusters of observed variables that share the same latent parent and connections between these clusters given by edges pointing from the observed variables to latent variables. LFCMs are motivated by gene regulatory networks, where regulatory edges, corresponding to transcription factors, connect spatially clustered genes. We show identifiability results on this model and design a consistent three-stage algorithm that discovers clusters of observed nodes, a partial ordering over clusters, and finally, the entire structure over both observed and latent nodes. We evaluate our method in a synthetic setting, demonstrating its ability to almost perfectly recover the ground truth clustering even at relatively low sample sizes, as well as the ability to recover a significant number of the edges from observed variables to latent factors. Finally, we apply our method in a semi-synthetic setting to protein mass spectrometry data with a known ground truth network, and achieve almost perfect recovery of the ground truth variable clusters.

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JMLR Journal 2022 Journal Article

Joint Inference of Multiple Graphs from Matrix Polynomials

Madeline Navarro
Yuhao Wang
Antonio G. Marques
Caroline Uhler
Santiago Segarra

Inferring graph structure from observations on the nodes is an important and popular network science task. Departing from the more common inference of a single graph, we study the problem of jointly inferring multiple graphs from the observation of signals at their nodes (graph signals), which are assumed to be stationary in the sought graphs. Graph stationarity implies that the mapping between the covariance of the signals and the sparse matrix representing the underlying graph is given by a matrix polynomial. A prominent example is that of Markov random fields, where the inverse of the covariance yields the sparse matrix of interest. From a modeling perspective, stationary graph signals can be used to model linear network processes evolving on a set of (not necessarily known) networks. Leveraging that matrix polynomials commute, a convex optimization method along with sufficient conditions that guarantee the recovery of the true graphs are provided when perfect covariance information is available. Particularly important from an empirical viewpoint, we provide high-probability bounds on the recovery error as a function of the number of signals observed and other key problem parameters. Numerical experiments demonstrate the effectiveness of the proposed method with perfect covariance information as well as its robustness in the noisy regime. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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NeurIPS Conference 2021 Conference Paper

Matching a Desired Causal State via Shift Interventions

Jiaqi Zhang
Chandler Squires
Caroline Uhler

Transforming a causal system from a given initial state to a desired target state is an important task permeating multiple fields including control theory, biology, and materials science. In causal models, such transformations can be achieved by performing a set of interventions. In this paper, we consider the problem of identifying a shift intervention that matches the desired mean of a system through active learning. We define the Markov equivalence class that is identifiable from shift interventions and propose two active learning strategies that are guaranteed to exactly match a desired mean. We then derive a worst-case lower bound for the number of interventions required and show that these strategies are optimal for certain classes of graphs. In particular, we show that our strategies may require exponentially fewer interventions than the previously considered approaches, which optimize for structure learning in the underlying causal graph. In line with our theoretical results, we also demonstrate experimentally that our proposed active learning strategies require fewer interventions compared to several baselines.

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NeurIPS Conference 2021 Conference Paper

Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning

Scott Sussex
Caroline Uhler
Andreas Krause

Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest. We address the largely unexplored problem of designing a batch of experiments that each simultaneously intervene on multiple variables. While potentially more informative than the commonly considered single-variable interventions, selecting such interventions is algorithmically much more challenging, due to the doubly-exponential combinatorial search space over sets of composite interventions. In this paper, we develop efficient algorithms for optimizing different objective functions quantifying the informativeness of a budget-constrained batch of experiments. By establishing novel submodularity properties of these objectives, we provide approximation guarantees for our algorithms. Our algorithms empirically perform superior to both random interventions and algorithms that only select single-variable interventions.

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UAI Conference 2020 Conference Paper

Anchored Causal Inference in the Presence of Measurement Error

Basil Saeed
Anastasiya Belyaeva
Yuhao Wang 0005
Caroline Uhler

We consider the problem of learning a causal graph in the presence of measurement error. This setting is for example common in genomics, where gene expression is corrupted through the measurement process. We develop a provably consistent procedure for estimating the causal structure in a linear Gaussian structural equation model from corrupted observations on its nodes, under a variety of measurement error models. We provide an estimator based on the method-of-moments, which can be used in conjunction with constraint-based causal structure discovery algorithms. We prove asymptotic consistency of the procedure and also discuss finite-sample considerations. We demonstrate our method’s performance through simulations and on real data, where we recover the underlying gene regulatory network from zero-inflated single-cell RNA-seq data.

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ICML Conference 2020 Conference Paper

Causal Structure Discovery from Distributions Arising from Mixtures of DAGs

Basil Saeed
Snigdha Panigrahi
Caroline Uhler

We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a “union” of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.

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UAI Conference 2020 Conference Paper

Permutation-Based Causal Structure Learning with Unknown Intervention Targets

Chandler Squires
Yuhao Wang 0005
Caroline Uhler

We consider the problem of estimating causal DAG models from a mix of observational and interventional data, when the intervention targets are partially or completely unknown. This problem is highly relevant for example in genomics, since gene knockout technologies are known to have off-target effects. We characterize the interventional Markov equivalence class of DAGs that can be identified from interventional data with unknown intervention targets. In addition, we propose a provably consistent algorithm for learning the interventional Markov equivalence class from such data. The proposed algorithm greedily searches over the space of permutations to minimize a novel score function. The algorithm is nonparametric, which is particularly important for applications to genomics, where the relationships between variables are often non-linear and the distribution non-Gaussian. We demonstrate the performance of our algorithm on synthetic and biological datasets. Links to an implementation of our algorithm and to a reproducible code base for our experiments can be found at https: //uhlerlab. github. io/causaldag/utigsp.

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ICML Conference 2018 Conference Paper

Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions

Karren D. Yang
Abigail Katoff
Caroline Uhler

We consider the problem of learning causal DAGs in the setting where both observational and interventional data is available. This setting is common in biology, where gene regulatory networks can be intervened on using chemical reagents or gene deletions. Hauser & Buhlmann (2012) previously characterized the identifiability of causal DAGs under perfect interventions, which eliminate dependencies between targeted variables and their direct causes. In this paper, we extend these identifiability results to general interventions, which may modify the dependencies between targeted variables and their causes without eliminating them. We define and characterize the interventional Markov equivalence class that can be identified from general (not necessarily perfect) intervention experiments. We also propose the first provably consistent algorithm for learning DAGs in this setting and evaluate our algorithm on simulated and biological datasets.

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NeurIPS Conference 2018 Conference Paper

Direct Estimation of Differences in Causal Graphs

Yuhao Wang
Chandler Squires
Anastasiya Belyaeva
Caroline Uhler

We consider the problem of estimating the differences between two causal directed acyclic graph (DAG) models with a shared topological order given i. i. d. samples from each model. This is of interest for example in genomics, where changes in the structure or edge weights of the underlying causal graphs reflect alterations in the gene regulatory networks. We here provide the first provably consistent method for directly estimating the differences in a pair of causal DAGs without separately learning two possibly large and dense DAG models and computing their difference. Our two-step algorithm first uses invariance tests between regression coefficients of the two data sets to estimate the skeleton of the difference graph and then orients some of the edges using invariance tests between regression residual variances. We demonstrate the properties of our method through a simulation study and apply it to the analysis of gene expression data from ovarian cancer and during T-cell activation.

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ICML Conference 2018 Conference Paper

Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Models

Raj Agrawal
Caroline Uhler
Tamara Broderick

Learning a Bayesian network (BN) from data can be useful for decision-making or discovering causal relationships. However, traditional methods often fail in modern applications, which exhibit a larger number of observed variables than data points. The resulting uncertainty about the underlying network as well as the desire to incorporate prior information recommend a Bayesian approach to learning the BN, but the highly combinatorial structure of BNs poses a striking challenge for inference. The current state-of-the-art methods such as order MCMC are faster than previous methods but prevent the use of many natural structural priors and still have running time exponential in the maximum indegree of the true directed acyclic graph (DAG) of the BN. We here propose an alternative posterior approximation based on the observation that, if we incorporate empirical conditional independence tests, we can focus on a high-probability DAG associated with each order of the vertices. We show that our method allows the desired flexibility in prior specification, removes timing dependence on the maximum indegree, and yields provably good posterior approximations; in addition, we show that it achieves superior accuracy, scalability, and sampler mixing on several datasets.

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UAI Conference 2017 Conference Paper

Counting Markov Equivalence Classes by Number of Immoralities

Adityanarayanan Radhakrishnan
Liam Solus
Caroline Uhler

Two directed acyclic graphs (DAGs) are called Markov equivalent if and only if they have the same underlying undirected graph (i. e. skeleton) and the same set of immoralities. When using observational data alone and typical identifiability assumptions, such as faithfulness, a DAG model can only be determined up to Markov equivalence. Therefore, it is desirable to understand the size and number of Markov equivalence classes (MECs) combinatorially. In this paper, we address this enumerative question using a pair of generating functions that encode the number and size of MECs on a skeleton G, and in doing so we connect this problem to classical problems in combinatorial optimization. The first generating function is a graph polynomial that counts the number of MECs on G by their number of immoralities. Using connections to the independent set problem, we show that computing a DAG on G with the maximum possible number of immoralities is NP-hard. The second generating function counts the MECs on G according to their size. Via computer enumeration, we show that this generating function is distinct for every connected graph on p nodes for all p ≤ 10.

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NeurIPS Conference 2017 Conference Paper

Permutation-based Causal Inference Algorithms with Interventions

Yuhao Wang
Liam Solus
Karren Yang
Caroline Uhler

Learning directed acyclic graphs using both observational and interventional data is now a fundamentally important problem due to recent technological developments in genomics that generate such single-cell gene expression data at a very large scale. In order to utilize this data for learning gene regulatory networks, efficient and reliable causal inference algorithms are needed that can make use of both observational and interventional data. In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption. These algorithms are interventional adaptations of the Greedy SP algorithm and are the first algorithms using both observational and interventional data with consistency guarantees. Moreover, these algorithms have the advantage that they are nonparametric, which makes them useful also for analyzing non-Gaussian data. In this paper, we present these two algorithms and their consistency guarantees, and we analyze their performance on simulated data, protein signaling data, and single-cell gene expression data.

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