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Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…

The loss and the norm of its gradient separate the healthy and the pathological regimes of neural-network training only weakly, whilst the curvature of the empirical risk differs qualitatively between them but is inaccessible explicitly at…

We present the first neural network that has learned to compactly represent and can efficiently reconstruct the statistical dependencies between the values of physical variables at different spatial locations in large 3D simulation…

Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…

We propose a novel kernel based post selection inference (PSI) algorithm, which can not only handle non-linearity in data but also structured output such as multi-dimensional and multi-label outputs. Specifically, we develop a PSI algorithm…

The connectivity of networked systems is often dependent on a small portion of critical nodes. Network dismantling studies the strategy to identify a subset of nodes the removal of which will maximally destroy the connectivity of a network…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…

We apply a new technique, the mutual information (MI) from information theory, to time-distance helioseismology, and demonstrate that it can successfully reproduce several classic results based on the widely used cross-covariance method. MI…

Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the…

In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…

Fault intensity diagnosis (FID) plays a pivotal role in monitoring and maintaining mechanical devices within complex industrial systems. As current FID methods are based on chain of thought without considering dependencies among target…

Graph structured data has wide applicability in various domains such as physics, chemistry, biology, computer vision, and social networks, to name a few. Recently, graph neural networks (GNN) were shown to be successful in effectively…

Developing interpretable models for neurodevelopmental disorders (NDDs) diagnosis presents significant challenges in effectively encoding, decoding, and integrating multimodal neuroimaging data. While many existing machine learning…

Deviations from the center within a robust neighborhood of a parametric model distribution may naturally be considered an infinite dimensional nuisance parameter. Thus, the semiparametric method may be tried, which is to compute the scores…

We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…

In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While powerful probabilistic models such as Gaussian Processes…

We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…

Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…

The Information Bottleneck method is a learning technique that seeks a right balance between accuracy and generalization capability through a suitable tradeoff between compression complexity, measured by minimum description length, and…

We propose a new way to measure inequalities such as the glass ceiling effect in attributed networks. Existing measures typically rely solely on node degree distribution or degree assortativity, but our approach goes beyond these measures…