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arXiv Machine Learning

A computational approach to maximum likelihood thresholds for colored Gaussian graphical models

The paper presents a computational framework for determining the maximum likelihood threshold (MLT) in colored Gaussian graphical models (CGGMs). It focuses on a geometric approach that seeks the minimal rank of a sample covariance matrix whose projection lies within the interior of the cone of sufficient statistics. The authors extend theoretical results from uncolored to colored models, introduce new symbolic algorithms, and demonstrate how topological data analysis (TDA) can alleviate computational challenges associated with traditional symbolic algebraic methods.

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arXiv Machine Learning
Aug 20

Learning Random Geometric Graphs Drawn in Probabilistic Metric Spaces

The paper introduces a data‑driven method for learning Random Geometric Graphs (RGGs) in probabilistic metric spaces. It defines a distance function based on the cumulative distribution of a disparity variable that captures differences in vertex connectivity and correlation of attached random variables, enabling edges to exist with a specified probability. The approach includes a rejection‑sampling technique for edge probability estimation and a closed‑form posterior for learning the inter‑observable correlation matrix, and it is demonstrated on highly multivariate real datasets.

By Dalia Chakrabarty, Kangrui Wang, Chuqiao Zhang, Ye Liu
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arXiv Machine Learning
Sep 25

Common Covariance Geometry and Certification for Brownian Kernel Ladders

The paper introduces a new representation‑adaptive kernel class that, on a fixed sample, yields a union of reproducing‑kernel Hilbert‑space ellipsoids instead of a single ellipsoid. It defines a minimum‑trace common covariance dominating the empirical union generated by Brownian kernel ladders, and derives exact formulations, statistical and computational consequences, and a universal Gaussian‑complexity bound. The work further develops geometric reductions, deterministic depth laws, and exact empirical Kolmogorov‑width formulas, providing both lower and upper certificates for covariance certification and illustrating the distinction between successful covariance certification and predictive selection.

By Mahdi Mohammadigohari
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