Related papers: Learning directed acyclic graphs based on sparsest…

Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…

Causal Bayesian networks (CBN) are popular graphical probabilistic models that encode causal relations among variables. Learning their graphical structure from observational data has received a lot of attention in the literature. When there…

In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods…

New biological assays like Perturb-seq link highly parallel CRISPR interventions to a high-dimensional transcriptomic readout, providing insight into gene regulatory networks. Causal gene regulatory networks can be represented by directed…

We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a directed acyclic graph (DAG) model. The linear…

Several approaches to graphically representing context-specific relations among jointly distributed categorical variables have been proposed, along with structure learning algorithms. While existing optimization-based methods have limited…

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…

Stochastic Gradient Descent (SGD) is arguably the most important single algorithm in modern machine learning. Although SGD with unbiased gradient estimators has been studied extensively over at least half a century, SGD variants relying on…

We propose a novel adaptive empirical Bayesian method for sparse deep learning, where the sparsity is ensured via a class of self-adaptive spike-and-slab priors. The proposed method works by alternatively sampling from an adaptive…

Learning graphical conditional independence structures is an important machine learning problem and a cornerstone of causal discovery. However, the accuracy and execution time of learning algorithms generally struggle to scale to problems…

A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from…

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…

We prove that the true underlying directed acyclic graph (DAG) in Gaussian linear structural equation models is identifiable as the minimum-trace DAG when the error variances are weakly increasing with respect to the true causal ordering.…

We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…

Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…

In the algorithm Intersort, Chevalley et al. (2024) proposed a score-based method to discover the causal order of variables in a Directed Acyclic Graph (DAG) model, leveraging interventional data to outperform existing methods. However, as…

Causal structure learning from observational data remains a non-trivial task due to various factors such as finite sampling, unobserved confounding factors, and measurement errors. Constraint-based and score-based methods tend to suffer…

In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…

Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for…