New Advances in Optimization Algorithms for Causal Discovery

Soham Jana Chair
University of Notre Dame
 
Abhishek Roy Organizer
Texas A&M University
 
Sunday, Aug 3: 4:00 PM - 5:50 PM
0305 
Invited Paper Session 
Music City Center 
Room: CC-104A 

Applied

No

Main Sponsor

Section on Statistical Computing

Co Sponsors

IMS
Section on Statistical Learning and Data Science

Presentations

Bridging causality and deep learning with causal generative models

Generative models for vision and language have shown remarkable capacities to emulate creative processes but still lack fundamental skills that have long been recognized as essential for genuinely autonomous intelligence. Difficulties with causal reasoning and concept abstraction highlight critical gaps in current models, despite their nascent capacities for reasoning and planning. Bridging this gap requires a synthesis of deep learning's expressiveness with the powerful framework of statistical causality.

We will discuss our recent efforts towards building generative models that extract causal knowledge from data while retaining the flexibility and expressivity of deep learning. Unlike traditional causal methods that rely on predefined causal structures, we tackle the more complex problem of learning causal structure directly from data—even when the causal variables themselves are not explicitly observed. This introduces significant challenges, including ill-posedness, nonconvexity, and the exponential complexity of combinatorial search. We will outline statistical aspects of these problems and present progress towards resolving these challenges with differentiable approaches to causal discovery and representation learning.
 

Keywords

Greedy optimization

Misspecified Nonparametric Model Selection

Laplace approximation

Nonparametric Graphical Models 

Speaker

Bryon Aragam, The University of Chicago

Likelihood-based differentiable structure learning

Existing approaches to differentiable structure learning of directed acyclic graphs (DAGs) rely on strong identifiability assumptions in order to guarantee that global minimizers of the acyclicity-constrained optimization problem identifies the true DAG. Moreover, it has been observed empirically that the optimizer may exploit undesirable artifacts in the loss function. We explain and remedy these issues by studying the behavior of differentiable acyclicity-constrained programs under general likelihoods with multiple global minimizers. By carefully regularizing the likelihood, it is possible to identify the sparsest model in the Markov equivalence class, even in the absence of an identifiable parametrization. We first study the Gaussian case in detail, showing how proper regularization of the likelihood defines a score that identifies the sparsest model. Assuming faithfulness, it also recovers the Markov equivalence class. These results are then generalized to general models and likelihoods, where the same claims hold. These theoretical results are validated empirically, showing how this can be done using standard gradient-based optimizers, thus paving the way for differentiable structure learning under general models and losses. 

Keywords

DAG Learning

Identifiability

Sparsest model

Regularization 

Speaker

Pradeep Ravikumar, Carnegie Mellon University

Enhancing Causal Effect Estimation with Diffusion-Generated Data

Estimating causal effects from observational data is inherently challenging due to the lack of observable counterfactual outcomes and even the presence of unmeasured confounding. Traditional methods often rely on restrictive, untestable assumptions or necessitate valid instrumental variables, significantly limiting their applicability and robustness. In this paper, we introduce Augmented Causal Effect Estimation (ACEE), an innovative approach that utilizes synthetic data generated by a diffusion model to enhance causal effect estimation. By fine-tuning pre-trained generative models, ACEE simulates counterfactual scenarios that are otherwise unobservable, facilitating accurate estimation of individual and average treatment effects even under unmeasured confounding. Unlike conventional methods, ACEE relaxes the stringent unconfoundedness assumption, relying instead on an empirically checkable condition. Additionally, a bias-correction mechanism is introduced to mitigate synthetic data inaccuracies. We provide theoretical guarantees demonstrating the consistency and efficiency of the ACEE estimator, alongside comprehensive empirical validation through simulation studies and benchmark datasets. Results confirm that ACEE significantly improves causal estimation accuracy, particularly in complex settings characterized by nonlinear relationships and heteroscedastic noise. 

Keywords

Causal effect estimation

Data augmentation

Unmeasured confounding

Generative models

Transfer learning 

Co-Author(s)

Xiaotong Shen, University of Minnesota
Wei Pan, University of Minnesota

Speaker

LI Chen

Stochastic Optimization Algorithms for Instrumental Variable Regression with Streaming Data

We develop and analyze algorithms for instrumental variable regression by viewing the problem as a conditional stochastic optimization problem. In the context of least-squares instrumental variable regression, our algorithms neither require matrix inversions nor mini-batches and provides a fully online approach for performing instrumental variable regression with streaming data. When the true model is linear, we derive rates of convergence in expectation, that are of order O(log T/T) and O(T^{ι-1}) for any ι>0, respectively under the availability of two-sample and one-sample oracles, respectively, where T is the number of iterations. Importantly, under the availability of the two-sample oracle, our procedure avoids explicitly modeling and estimating the relationship between confounder and the instrumental variables, demonstrating the benefit of the proposed approach over recent works based on reformulating the problem as minimax optimization problems. Numerical experiments are provided to corroborate the theoretical results. 

Keywords

Online Instrumental Variable Regression

Conditional Stochastic Optimization

Stochastic approximation

Causal Inference

Streaming Data 

Speaker

Abhishek Roy, Texas A&M University

Advancing Causal Structure Learning: Addressing Challenges with Latent Confounders

Recently, causality has garnered significant interest within the research communities of statistics, machine learning, and computer science. A central challenge in this field is uncovering the underlying causal structures and models. Traditional methods for causal structure learning often assume the absence of latent confounders. In this talk, I will highlight recent advances in causal structure learning that specifically address the challenges posed by latent confounders. I will focus on three key techniques and their associated structural or distributional constraints, which enable us to identify latent variables, determine their cardinalities, and map out the structure involving both latent and observed variables.
 

Keywords

Casual Discovery

Latent Confounders 

Speaker

Biwei Huang, Halicioğlu Data Science Institute (HDSI), UC San Diego (UCSD)