A novel functional estimator for Rényi's α-entropy and its multivariate extension was recently proposed in terms of the normalized eigenspectrum a Hermitian matrix projected data reproducing kernel Hilbert space (RKHS). However, utility possible applications these new estimators are rather mostly unknown to practitioners. In this brief, we first show that enables straightforward measurement information flow realistic convolutional neural networks (CNNs) without any approximation. Then,...

We propose causal recurrent variational autoencoder (CR-VAE), a novel generative model that is able to learn Granger graph from multivariate time series x and incorporates the underlying mechanism into its data generation process. Distinct classical VAEs, our CR-VAE uses multi-head decoder, in which p-th head responsible for generating dimension of (i.e., x^p). By imposing sparsity-inducing penalty on weights (of decoder) encouraging specific sets be zero, learns sparse adjacency matrix...

Converging evidence increasingly suggests that psychiatric disorders, such as major depressive disorder (MDD) and autism spectrum (ASD), are not unitary diseases, but rather heterogeneous syndromes involve diverse, co-occurring symptoms divergent responses to treatment. This clinical heterogeneity has hindered the progress of precision diagnosis treatment effectiveness in disorders. In this study, we propose BPI-GNN, a new interpretable graph neural network (GNN) framework for analyzing...

Developing new diagnostic models based on the underlying biological mechanisms rather than subjective symptoms for psychiatric disorders is an emerging consensus. Recently, machine learning (ML)-based classifiers using functional connectivity (FC) and healthy controls (HCs) are developed to identify brain markers. However, existing ML-based prone overfitting (due insufficient training samples) perform poorly in test environments. Furthermore, it difficult obtain explainable reliable...

The matrix-based Renyi's a-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix projected data in reproducing kernel Hilbert space (RKHS). However, current theory only defines single variable or mutual information between two random variables. In and machine learning communities, one is also frequently interested multivariate quantities, such as joint different interactive quantities among multiple this paper, we first define We then show...

Recent studies proposed the use of Total Correlation to describe functional connectivity among brain regions as a multivariate alternative conventional pairwise measures such correlation or mutual information. In this work, we build on idea infer large-scale (whole-brain) network based and show possibility using kind biomarkers alterations. particular, work uses Explanation (CorEx) estimate Correlation. First, prove that CorEx estimates clustering results are trustable compared ground truth...

Multiview learning has drawn widespread attention for its efficacy in leveraging cross-view consensus and complementarity information to achieve a comprehensive representation of data. While multi-view undergone vigorous development achieved remarkable success, the theoretical understanding generalization behavior remains elusive. This paper aims bridge this gap by developing information-theoretic bounds learning, with particular focus on reconstruction classification tasks. Our underscore...

This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the extensions of (CCA), D2PCCA captures latent dynamics and supports enhancements such as KL annealing for improved convergence normalizing flows more flexible posterior approximation. naturally extends multiple observed variables, making it versatile tool encoding prior knowledge about...

The Cauchy-Schwarz (CS) divergence was developed by Príncipe et al. in 2000. In this paper, we extend the classic CS to quantify closeness between two conditional distributions and show that can be elegantly estimated a kernel density estimator from given samples. We illustrate advantages (e.g., rigorous faithfulness guarantee, lower computational complexity, higher statistical power, much more flexibility wide range of applications) our over previous proposals, such as KL maximum mean...

Complex biological systems, like the brain, exhibit intricate multiway and multiscale interactions that drive emergent behaviors. In psychiatry, neural processes extend beyond pairwise connectivity, involving higher-order critical for understanding mental disorders. Conventional brain network studies focus on links, offering insights into basic connectivity but failing to capture complexity of dysfunction in psychiatric conditions. This study aims bridge this gap by applying a matrix-based...

Dynamic textures (DTs) that represent moving scenes such as flames, smoke, and waves, exhibit fixed dynamics within a period of time have been successfully modeled using linear dynamic systems (LDS). In this paper, we show the widely used LDS model can be approximated principal component regression (PCR) with main advantage simplicity. Furthermore, to capture nonlinearity training frames, extend traditional PCR its kernelized version introduce kernel (KPCR) synthesize DTs. To ensure...