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The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum…
Motivated by recent developments in designing algorithms based on individual item scores for solving utility maximization problems, we study the framework of using test scores, defined as a statistic of observed individual item performance…
Constraint-based methods and noise-based methods are two distinct families of methods proposed for uncovering causal graphs from observational data. However, both operate under strong assumptions that may be challenging to validate or could…
Supported by the recent contributions in multiple branches, the first-order splitting algorithms became central for structured nonsmooth optimization. In the large-scale or noisy contexts, when only stochastic information on the smooth part…
A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
The abundance of fine-grained spatio-temporal data, such as traffic sensor networks, offers vast opportunities for scientific discovery. However, inferring causal relationships from such observational data remains challenging, particularly…
We revisit the classical problem of computing the \emph{contour tree} of a scalar field $f:\mathbb{M} \to \mathbb{R}$, where $\mathbb{M}$ is a triangulated simplicial mesh in $\mathbb{R}^d$. The contour tree is a fundamental topological…
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some…
It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal…
We study the arbitrary cost case of the unweighted Stochastic Score Classification (SSClass) problem. We show two constant approximation algorithms and both algorithms are 6-approximation non-adaptive algorithms with respect to the optimal…
The causal revolution has stimulated interest in understanding complex relationships in various fields. Most of the existing methods aim to discover causal relationships among all variables within a complex large-scale graph. However, in…
Linear structural causal models (SCMs) -- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources -- are pervasive in causal inference and casual discovery.…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the dataset and the training algorithm must be taken into account…
Unsupervised feature selection (UFS) has recently gained attention for its effectiveness in processing unlabeled high-dimensional data. However, existing methods overlook the intrinsic causal mechanisms within the data, resulting in the…
We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of…
In this paper we present a comprehensive view of prominent causal discovery algorithms, categorized into two main categories (1) assuming acyclic and no latent variables, and (2) allowing both cycles and latent variables, along with…