Related papers: Information Geometric Approach to Bayesian Lower E…

We introduce an information theoretic criterion for Bayesian network structure learning which we call quotient normalized maximum likelihood (qNML). In contrast to the closely related factorized normalized maximum likelihood criterion, qNML…

The theoretical foundation of quantum sensing is rooted in the Cram\'er-Rao formalism, which establishes quantitative precision bounds for a given quantum probe. In many practical scenarios, where more than one parameter is unknown, the…

Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…

Computing posterior distributions in large-scale Bayesian linear inverse problems is challenging due to the high dimensionality of the parameter space. In this work, we develop a data-informed framework that shifts the computational focus…

We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve…

This work focuses on assessing the information-theoretic limits of scene parameter estimation in plenoptic imaging systems. A general framework to compute lower bounds on the parameter estimation error from noisy plenoptic observations is…

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…

In some estimation problems, not all the parameters can be identified, which results in singularity of the Fisher Information Matrix (FIM). The Cram\'er-Rao Bound (CRB), which is the inverse of the FIM, is then not defined. To regularize…

In robotic networks relying on noisy range measurements between agents for cooperative localization, the achievable positioning accuracy strongly strongly depends on the network geometry. This motivates the problem of planning robot…

We consider the problem of aggregating pairwise comparisons to obtain a consensus ranking order over a collection of objects. We use the popular Bradley-Terry-Luce (BTL) model which allows us to probabilistically describe pairwise…

Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…

We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a…

We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…

In this note we present a fully information theoretic approach to renormalization inspired by Bayesian statistical inference, which we refer to as Bayesian Renormalization. The main insight of Bayesian Renormalization is that the Fisher…

Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…

To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…

We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…

In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…

I define a natural measure of the complexity of a parametric distribution relative to a given true distribution called the {\it razor} of a model family. The Minimum Description Length principle (MDL) and Bayesian inference are shown to…