arXiv research

This paper solves the normalizability crisis in sequential inference by introducing bounded information geometry.

This work tightens generalization error bounds using Wasserstein distance.

Proper holomorphic isometries between Bergman domains are biholomorphisms.

The Fisher-Rao geometry is applied to elliptical distributions for optimization and classification.

Upper bound on CRN reaction rates derived using information geometry.

The paper connects Bergman geometry with information geometry.

This paper solves the intractability barrier in non-parametric information geometry by introducing a novel framework.

The paper generalizes Bayesian Cramér-Rao inequality using information geometry of relative α-entropy.

GeoIB uses information geometry to control compression in deep learning models.

New information-theoretic bounds improve machine learning generalization.

Study reveals limits of detecting local geometry in random graphs.

Researchers use information geometry to analyze and improve DRWs for node classification.

Machine learning approximates phase transitions using Fisher information.

The cost of belief changes with precision and is a hyperbolic geometry.

New method improves counterfactual distribution learning for high-dimensional outcomes.

In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain must be strongly pseudoconvex. One consequence of our general result is the followi…

New framework explains data augmentation's role in machine learning.

Enhanced 3D shape analysis using information geometry.

UMAP connects to Information Geometry principles.

Symplectic and Poisson structures proved for information geometry's Frobenius manifold.

Information geometry offers new tools for statistical analysis.

Study submanifolds in spheres with Ricci curvature bounds.

A benchmarking framework for studying data geometry.

Develops information geometry for Lévy processes in finance.

Survey of linking information geometry and optimal transport.

Hyperbolic space outperforms Euclidean in learning hierarchical data.

The paper explores geometry of probability measures and barycenter maps.

Bi-forms extend contrast functions to handle torsion in information geometry.

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary con…

Estimates for geodesics on hyperbolic tori improve previous bounds.

GS-B$^3$SE improves label shift estimation by smoothing priors on a graph.

We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, $α$-connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic statistical inference.

Geometric approach to thermodynamics of chemical reaction networks.

Information geometry applies concepts in differential geometry to probability and statistics and is especially useful for parameter estimation in exponential families where parameters are known to lie on a Riemannian manifold. Connections between the geometric properties of the induced manifold and statistical properti…

We consider globally hyperbolic flat spacetimes in 2+1 and 3+1 dimensions, in which a uniform light signal is emitted on the $r$-level surface of the cosmological time for $r\to 0$. We show that the frequency of this signal, as perceived by a fixed observer, is a well-defined, bounded function which is generally not co…

Study information geometry of warped product spaces, finding special connections.

This work proves generalization bounds for neural networks without Lipschitz assumptions.

New bounds derived for machine learning algorithms using convex functions.

Warped product affects divergences in information geometry.

Optimizes quadratic bandits with tight Hessian-dependent sample complexity bounds.

Cone structures in quantum field theory linked to information geometry.

Study compares geometric approaches for shape and deformation statistics.

We study the relationship between geometry and capacity measures for deep neural networks from an invariance viewpoint. We introduce a new notion of capacity --- the Fisher-Rao norm --- that possesses desirable invariance properties and is motivated by Information Geometry. We discover an analytical characterization of…

We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. W…

The paper uses geometric methods to classify medical data histograms.

For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geomet…

The paper explores how AI systems use information geometry to encode semantic structure.

New method uses entropy dissipation to prove isoperimetric inequalities.