Related papers: Theoretical Guarantees for Causal Discovery on Lar…

Let $\mathcal{G}(N,\frac 1Nt_N)$ be the Erd\H{o}s-R\'enyi graph with connection probability $\frac 1Nt_N\sim t/N$ as $N\to\infty$ for a fixed $t\in(0,\infty)$. We derive a large-deviations principle for the empirical measure of the sizes of…

We prove that the treewidth of an Erd\"{o}s-R\'{e}nyi random graph $\rg{n, m}$ is, with high probability, greater than $\beta n$ for some constant $\beta > 0$ if the edge/vertex ratio $\frac{m}{n}$ is greater than 1.073. Our lower bound…

Graph Neural Networks (GNNs) often perform better for high-degree nodes than low-degree nodes on node classification tasks. This degree bias can reinforce social marginalization by, e.g., privileging celebrities and other high-degree actors…

Graph Neural Networks (GNNs) have achieved promising results in tasks such as node classification and graph classification. However, recent studies reveal that GNNs are vulnerable to backdoor attacks, posing a significant threat to their…

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or…

Out-of-distribution (OOD) detection is crucial to safety-critical machine learning applications and has been extensively studied. While recent studies have predominantly focused on classifier-based methods, research on deep generative model…

Wireless vehicular communication will increase the safety of road users. The reliability of vehicular communication links is of high importance as links with low reliability may diminish the advantage of having situational traffic…

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged,…

Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…

We study the problem of detecting the edge correlation between two random graphs with $n$ unlabeled nodes. This is formalized as a hypothesis testing problem, where under the null hypothesis, the two graphs are independently generated;…

Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges)…

Graph data often contain noisy and spurious correlations that mask the true causal relationships, which are essential for enabling graph models to make predictions based on the underlying causal structure of the data. Dependence on spurious…

The correlated Erd\"os-R\'enyi random graph ensemble is a probability law on pairs of graphs with $n$ vertices, parametrized by their average degree $\lambda$ and their correlation coefficient $s$. It can be used as a benchmark for the…

We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…

The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…

Large deviation behavior of the largest eigenvalue $\lambda_1$ of Gaussian networks (Erd\H{o}s-R\'enyi random graphs $\mathcal{G}_{n,p}$ with i.i.d. Gaussian weights on the edges) has been the topic of considerable interest. Recently in…

It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well. An attempt of understanding this puzzle is to discover implicit biases underlying the training process of DNNs, such as the…

False discovery rates (FDR) are typically estimated from a mixture of a null and an alternative distribution. Here, we study a complementary approach proposed by Rice and Spiegelhalter (2008) that uses as primary quantities the null model…

We develop a flexible feature selection framework based on deep neural networks that approximately controls the false discovery rate (FDR), a measure of Type-I error. The method applies to architectures whose first layer is fully connected.…

For random $d$-regular graphs on $N$ vertices with $1 \ll d \ll N^{2/3}$, we develop a $d^{-1/2}$ expansion of the local eigenvalue distribution about the Kesten-McKay law up to order $d^{-3}$. This result is valid up to the edge of the…