arXiv research

LMs inevitably generate hallucinations, but can be made statistically negligible.

We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite…

Kenmotsu geometry is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart of a Kenmotsu manifold, that is, Kenmotsu statistical manifold with some related examples. We investigate some statistical curvature properti…

Study anti-invariant submersions from holomorphic statistical manifolds.

Unified approach to private statistics from empirical to population data.

The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.

The Bonnet theorem is proven for statistical manifolds.

Enhances power of covariance matrix tests for high-dimensional data.

This paper simplifies computing higher-order $U$-statistics efficiently.

This paper studies the geometry of immersions into statistical manifolds. A necessary and sufficient condition is obtained for statistical manifold structures to be dual to each other for a non-degenerate equiaffine immersion. Then we obtain conditions for realizing an n-dimensional statistical manifold in an (n+1)-dim…

This work uses statistical mechanics to explain AI learning.

The differential geometry of Kenmotsu manifold is a valuable part of contact geometry with nice applications in other fields such as theoretical physics. In fact, its statistical counterpart, that is, Kenmotsu statistical manifold also has same importance as that of Kenmotsu manifold. Theoretical physicists have also b…

Author presents the second variational formula for statistical biharmonic maps.

Study CR-statistical submanifolds in holomorphic statistical spaces.

New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.

Lightlike hypersurfaces of a statistical manifold are studied. It is shown that a lightlike hypersurface of a statistical manifold is not a statistical manifold with respect to the induced connections, but the screen distribution has a canonical statistical structure. Some relations between induced geometric objects wi…

Proves Gerber statistic is always non-negative.

This paper deals with the applications of an optimization method on submanifolds, that is, geometric inequalities can be considered as optimization problems. In this regard, we obtain optimal Casorati inequalities and Chen-Ricci inequality for a statistical submanifold in a statistical warped product manifold of type $…

New statistical manifolds derived from identity map biharmonicity.

Active inference framework improves $U$-statistic estimation efficiency.

Sharp inequalities and solitons studied in statistical submersions.

Survey of statistical queries and their applications.

Paper discusses the Fisher metric and differentiability in statistical models.

Study on lightlike geometry in indefinite Sasakian statistical manifolds.

The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and…

The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-Kähler-like statistical manifold of constant curvature in the Kurose's sense is a Hessian structure. We also derive the main properties of statistical su…

Investigates transfer learning in spatial statistics.

Unified framework for Bayesian and Frequentist statistics.

Approximate Bayesian computation is an established and popular method for likelihood-free inference with applications in many disciplines. The effectiveness of the method depends critically on the availability of well performing summary statistics. Summary statistic selection relies heavily on domain knowledge and care…

The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given. We study the statistical hypersurfces of some types of the statistical manifolds $(M, \nabla, g )$, which enable $(M, \nabla^{(α)}, g ), \forallα\in\mathbf{R}$ to admit the structure of a constant curvature.

The φ-sectional curvature of statistical structures on almost contact metric manifolds is always non-positive.

Breiman discusses two statistical cultures, advocating for more research on 'before' and 'after' the black box.

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves. We a…

New statistical biharmonic maps derived from a variation problem.

Machine learning improves official statistics but needs rigorous validation.

GOE statistics emerge from surface moduli space averages.

Introduces statistical optimal transport for probabilistic lectures.

The objective of this paper is to introduce the notion of generalized almost statistical (briefly, GAS) convergence of bounded real sequences, which generalizes the notion of almost convergence as well as statistical convergence of bounded real sequences. As a special kind of Banach limit functional, we also introduce …

Develops theory of homogeneous statistical manifolds and classifies Lie groups.

Paper develops efficient incomplete U-statistics for degenerate cases.

Risk statistic is a critical factor not only for risk analysis but also for financial application. However, the traditional risk statistics may fail to describe the characteristics of regulator-based risk. In this paper, we consider the regulator-based risk statistics for portfolios. By further developing the propertie…

In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances…

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statis…

The paper optimizes private data sharing by selecting statistics and using MCMC for Bayesian inference.

Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of information. Thi…

In this note we prove certain necessary and sufficient conditions for the existence of an embedding of statistical manifolds. In particular, we prove that any compact smooth ($C^1$ resp.) statistical manifold can be embedded into the space of probability measures on a finite set. As a result, we get an answer to the La…

Symmetry helps VI recover certain statistics.