Related papers: A U-statistic Approach to Hypothesis Testing for S…
Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised…
Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…
Though Gaussian graphical models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses…
Hypothesis testing is a statistical method used to draw conclusions about populations from sample data, typically represented in tables. With the prevalence of graph representations in real-life applications, hypothesis testing in graphs is…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of…
The chain graph model admits both undirected and directed edges in one graph, where symmetric conditional dependencies are encoded via undirected edges and asymmetric causal relations are encoded via directed edges. Though frequently…
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the…
In reliable decision-making systems based on machine learning, models have to be robust to distributional shifts or provide the uncertainty of their predictions. In node-level problems of graph learning, distributional shifts can be…
The use of data-random graphs in statistical testing of spatial patterns is introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the points from various classes.…
A vast amount of expert and domain knowledge is captured by causal structural priors, yet there has been little research on testing such priors for generalization and data synthesis purposes. We propose a novel model architecture, Causal…
The G-Wishart distribution is an essential component for the Bayesian analysis of Gaussian graphical models as the conjugate prior for the precision matrix. Evaluating the marginal likelihood of such models usually requires computing…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
We study the general problem of testing whether an unknown distribution belongs to a specified family of distributions. More specifically, given a distribution family $\mathcal{P}$ and sample access to an unknown discrete distribution…
Probabilistic graphs are an abstraction that allow us to study randomized propagation in graphs. In a probabilistic graph, each edge is "active" with a certain probability, independent of the other edges. For two vertices $u,v$, a classic…
We study random graphs with latent geometric structure, where the probability of each edge depends on the underlying random positions corresponding to the two endpoints. We focus on the setting where this conditional probability is a…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In…
U-statistics are a fundamental class of estimators that generalize the sample mean and underpin much of nonparametric statistics. Although extensively studied in both statistics and probability, key challenges remain: their high…
We propose a novel method to test the existence of community structure of undirected real-valued edge-weighted graph. The method is based on Wigner semicircular law on the asymptotic behavior of the random distribution for eigenvalues of a…