Related papers: Theoretical Guarantees for Causal Discovery on Lar…

Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…

A $1$-factorization of a graph $G$ is a collection of edge-disjoint perfect matchings whose union is $E(G)$. A trivial necessary condition for $G$ to admit a $1$-factorization is that $|V(G)|$ is even and $G$ is regular; the converse is…

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first…

Determining whether deep neural network (DNN) models can reliably recover target functions at overparameterization is a critical yet complex issue in the theory of deep learning. To advance understanding in this area, we introduce a concept…

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their…

Recent advances in Neural Variational Inference allowed for a renaissance in latent variable models in a variety of domains involving high-dimensional data. While traditional variational methods derive an analytical approximation for the…

Though a belief network (a representation of the joint probability distribution, see [3]) and a causal network (a representation of causal relationships [14]) are intended to mean different things, they are closely related. Both assume an…

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…

Through recognizing causal subgraphs, causal graph learning (CGL) has risen to be a promising approach for improving the generalizability of graph neural networks under out-of-distribution (OOD) scenarios. However, the empirical successes…

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for…

We study the problem of robustly estimating the edge density of Erd\H{o}s-R\'enyi random graphs $G(n, d^\circ/n)$ when an adversary can arbitrarily add or remove edges incident to an $\eta$-fraction of the nodes. We develop the first…

Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features -- rationale -- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data…

Graph unlearning methods aim to efficiently remove the impact of sensitive data from trained GNNs without full retraining, assuming that deleted information cannot be recovered. In this work, we challenge this assumption by introducing the…

In this paper, assuming the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated Erd\H{o}s-R\'enyi graphs $\mathcal G(n,q;\rho)$ when the…

Let $F$ be a graph on $r$ vertices and let $G$ be a graph on $n$ vertices. Then an $F$-factor in $G$ is a subgraph of $G$ composed of $n/r$ vertex-disjoint copies of $F$, if $r$ divides $n$. In other words, an $F$-factor yields a partition…

This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based…

Stability and reproducibility are essential considerations in various applications of statistical methods. False Discovery Rate (FDR) control methods are able to control false signals in scientific discoveries. However, many FDR control…

Limiting distributions are derived for the sparse connected components that are present when a random graph on $n$ vertices has approximately $\half n$ edges. In particular, we show that such a graph consists entirely of trees, unicyclic…

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

Causal discovery aims to uncover cause-and-effect relationships encoded in causal graphs by leveraging observational, interventional data, or their combination. The majority of existing causal discovery methods are developed assuming…