Paper introduces a new cost function to improve deep learning model generalization.
problem Overfitting and poor extrapolation of deep learning models.
method Introduces a 'whitening' cost function based on the Ljung-Box statistic.
result Significant improvement in generalization for RNNs and image autoencoders.
This work considers the problem of modified portmanteau tests for testing the adequacy of FARIMA models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak FARIMA). We first study the joint distribution of the least squares estimator and the noise empirical autocovariances. …
This paper examines autocorrelation in major crypto markets, finding persistent correlations on short time frames.
problem Assessing the efficiency of major cryptocurrency markets through autocorrelation analysis.
method Pearson's autocorrelation coefficient, Ljung-Box test, rolling window analysis.
result Persistent autocorrelation on 5m and 1H time frames, disagreement on 1D and 1W time frames.
K-ARMA models cluster time series data robustly.
problem Clustering time series data effectively.
method Model-based K-ARMA clustering algorithm with robust outlier detection.
result K-ARMA models outperform existing methods for time series clustering.
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.
problem Understanding submersions in statistical manifolds.
method Introduced and analyzed anti-invariant holomorphic statistical submersions.
result Supported results with examples.
Unified approach to private statistics from empirical to population data.
problem Divided focus on empirical vs population statistics in private statistics.
method Unified methods for both types of statistics.
result Methods for empirical statistics can be applied to population statistics.
The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.
problem Characterizing geometric properties of contact CR-submanifolds in Sasakian statistical manifolds.
method Characterization of integrability of invariant and anti-invariant distributions, development of results on specific types of contact CR submanifolds, introduction of statistical contact CR-product.
result Introduction of a statistical version of contact CR-product for Sasakian statistical manifolds.
The Bonnet theorem is proven for statistical manifolds.
problem Locally embeddable statistical manifolds in flat spaces.
method Using statistical embedding and the Gauss--Codazzi--Ricci equations.
result Statistical manifolds with specific tensor properties are locally embeddable to flat statistical manifolds.
Enhances power of covariance matrix tests for high-dimensional data.
problem Testing large covariance matrices in high-dimensional data.
method Proposes a new Fisher's combined probability test for quadratic form and maximum form statistics.
result Boosts power against more general alternatives.
This paper simplifies computing higher-order U-statistics efficiently.
problem The inefficiency of computing higher-order U-statistics in practice. method Decomposition, connection to Einstein summation, and treewidth-based complexity estimate.
result A new, more efficient algorithm to compute U-statistics. 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.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine 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.
problem Developing a formula for statistical biharmonic maps.
method Introduced the second variational formula for the statistical bi-energy functional.
result The second variational formula can be represented using Hessian curvature in Hessian manifolds.
Study CR-statistical submanifolds in holomorphic statistical spaces.
problem Characterize CR-statistical submanifolds and their properties.
method Optimization technique to relate Ricci curvature and mean curvature.
result Established relationship between Ricci curvature and mean curvature.
New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.
problem Maintaining the Fisher metric structure in statistical models.
method Characterizing statistics that maintain the Fisher metric structure bi-Lipschitz equivalently.
result Characterized statistics that preserve the Fisher metric structure closely.
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.
problem Verifying the positive semi-definiteness of Gerber statistic.
method Analytical proof of both forms of Gerber statistic.
result Gerber statistic is positive semi-definite.
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.
problem Deriving new statistical manifolds from identity map biharmonicity.
method Statistical biharmonicity of identity maps, semi-equiaffine condition, constant curvature.
result Determined statistical structures of new class of manifolds.
Active inference framework improves U-statistic estimation efficiency.
problem Costly acquisition of labels for U-statistics. method Active inference framework with optimal sampling rule.
result Substantial gains in estimation efficiency over baseline methods.
Sharp inequalities and solitons studied in statistical submersions.
problem Understanding geometric properties of statistical submersions.
method Proving sharp inequalities and establishing geometrical properties of statistical submersions.
result Characterization of fibers as Ricci-Bourguignon solitons with conformal vector field.
Survey of statistical queries and their applications.
problem Understanding statistical queries and their applications.
method Exploration of statistical queries model, definitions, and connections to learnability.
result Connections to learnability and applications in optimization, evolvability, and differential privacy.
Paper discusses the Fisher metric and differentiability in statistical models.
problem Understanding the relationship between Fisher metric and differentiability in statistical models.
method Comparison of different concepts and models in Information Geometry, mathematical statistics, and measure theory.
result Discussion of various models and their differentiability properties.
Study on lightlike geometry in indefinite Sasakian statistical manifolds.
problem Exploring lightlike hypersurfaces and their properties in indefinite Sasakian statistical manifolds.
method Introducing indefinite Sasakian statistical manifolds and analyzing lightlike hypersurfaces with respect to dual connections.
result An invariant lightlike submanifold of an indefinite Sasakian statistical manifold is itself an indefinite Sasakian statistical manifold.
The paper derives Chen inequalities for statistical submanifolds in cosymplectic manifolds.
problem Deriving Chen inequalities for statistical submanifolds in cosymplectic manifolds.
method Analyzing statistical cosymplectic manifolds and Legendrian submanifolds to derive Chen inequalities.
result Chen inequalities for statistical submanifolds in cosymplectic manifolds and Legendrian submanifolds are derived.
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.
problem Applying transfer learning to spatial statistics.
method Simple MLP models for spatial data.
result Potential of transfer learning in spatial statistics.
Unified framework for Bayesian and Frequentist statistics.
problem Embedding Bayesian statistics within a broader decision-making framework.
method Game theory and statistical analysis.
result Statistical games unify 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 paper derives inequalities for submanifolds in quaternion Kaehler-like statistical manifolds.
problem Chen inequalities for submanifolds in quaternion Kaehler-like statistical manifolds.
method Derivation of Chen inequalities for submanifolds and discussion for Lagrangian submanifolds.
result Basic Chen inequalities for submanifolds of quaternion Kaehler-like statistical manifolds.
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,∇,g), which enable (M,∇(α),g),∀α∈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.
problem Analyzing the φ-sectional curvature of statistical structures on almost contact metric manifolds.
method Investigating the φ-sectional curvature induced by a statistical structure and deriving sufficient conditions.
result The φ-sectional curvature is always non-positive.
Breiman discusses two statistical cultures, advocating for more research on 'before' and 'after' the black box.
problem Statistical modeling lacks exploration of processes before and after the 'black box'.
method Analyzes Breiman's visual metaphor of two statistical cultures.
result Promotes the importance of studying the 'before' and 'after' of data transformations.
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.
problem Variation problem for mappings between statistical manifolds.
method Statistical biharmonic maps derived from the Euler-Lagrange equation.
result Improper affine hyperspheres induce examples of statistical biharmonic maps.
Machine learning improves official statistics but needs rigorous validation.
problem Lack of methodological robustness in machine learning for official statistics.
method Total Machine Learning Error (TMLE) framework to validate ML models.
result TMLE addresses representativeness and measurement errors in ML models.
The paper analyzes V-statistics and variance estimation under varying kernel sizes.
problem Analyzing V-statistics and variance estimation under varying kernel sizes. method Develops a general framework for asymptotics of V-statistics, reducing to U-statistics and providing a unified variance estimation method. result Demonstrates asymptotic normality of V-statistics when kernel size grows with sample size. GOE statistics emerge from surface moduli space averages.
problem Understanding spectral statistics on hyperbolic surfaces.
method Defined a smooth linear statistic, averaged over moduli space, and analyzed variance.
result GOE statistics are recovered in the large genus and high energy limits.
Introduces statistical optimal transport for probabilistic lectures.
problem No specific problem stated; focuses on introduction.
method Lecture-based introduction to statistical optimal transport.
result Provides an introduction to statistical optimal transport.
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.
problem Understanding statistical manifolds and Lie groups.
method Constructs examples and classifies Lie groups using information geometry.
result Explicit examples of homogeneous statistical manifolds of low dimension constructed.
Paper develops efficient incomplete U-statistics for degenerate cases.
problem High computational cost and non-standard asymptotic behavior in degenerate U-statistics.
method Characterizes dependence structure using hypergraph theory and combinatorial designs, bypassing traditional Hoeffding decomposition.
result Derives a Berry-Esseen bound for incomplete U-statistics of deterministic designs, enabling Gaussian limiting distributions in 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…