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We consider the problem of predicting perturbation effects via causal models. In many applications, it is a priori unknown which mechanisms of a system are modified by an external perturbation, even though the features of the perturbation…

Influence maximization (IM) aims to select a small number of nodes that are able to maximize their influence in a network and covers a wide range of applications. Despite numerous attempts to provide effective solutions in ordinary…

This article provides an overview of our joint work on binary polynomial optimization over the past decade. We define the multilinear polytope as the convex hull of the feasible region of a linearized binary polynomial optimization problem.…

An intersection digraph is a digraph where every vertex $v$ is represented by an ordered pair $(S_v, T_v)$ of sets such that there is an edge from $v$ to $w$ if and only if $S_v$ and $T_w$ intersect. An intersection digraph is reflexive if…

Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed…

Archetypes are typical population representatives in an extremal sense, where typicality is understood as the most extreme manifestation of a trait or feature. In linear feature space, archetypes approximate the data convex hull allowing…

Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning…

Inferring the causal relationships among a set of variables in the form of a directed acyclic graph (DAG) is an important but notoriously challenging problem. Recently, advancements in high-throughput genomic perturbation screens have…

A fundamental challenge in artificial intelligence is learning useful representations of data that yield good performance on a downstream task, without overfitting to spurious input features. Extracting such task-relevant predictive…

We address the problem of representing context-specific causal models based on both observational and experimental data collected under general (e.g. hard or soft) interventions by introducing a new family of context-specific conditional…

Masked Image Modeling (MIM) has emerged as a promising method for deriving visual representations from unlabeled image data by predicting missing pixels from masked portions of images. It excels in region-aware learning and provides strong…

Causal discovery is a fundamental problem with applications spanning various areas in science and engineering. It is well understood that solely using observational data, one can only orient the causal graph up to its Markov equivalence…

We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely upon sampling large numbers of training…

The Influence Maximization (IM) problem is a well-known NP-hard combinatorial problem over graphs whose goal is to find the set of nodes in a network that spreads influence at most. Among the various methods for solving the IM problem,…

Most neural models of causality assume static causal graphs, failing to capture the dynamic and sparse nature of physical interactions where causal relationships emerge and dissolve over time. We introduce the Causal Process Framework and…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

One of the grand challenges of utilizing machine learning for the discovery of innovative new polymers lies in the difficulty of accurately representing the complex structures of polymeric materials. Although a wide array of hand-designed…

Given a tree $T$, its path polytope is the convex hull of the edge indicator vectors for the paths between any two distinct leaves in $T$. These polytopes arise naturally in polyhedral geometry and applications, such as phylogenetics,…

We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at…

Causal DAGs(Directed Acyclic Graphs) are usually considered in a 2D plane. Edges indicate causal effects' directions and imply their corresponding time-passings. Due to the natural restriction of statistical models, effect estimation is…