New algorithm detects rare categories with few labels.
problem Detecting rare categories with limited labeled data.
method Dimension-driven statistics and kappa-profile.
result Algorithm performs well on separable and non-separable classes.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “dimension-driven statistics”
New statistic -profile helps monitor weather, soundscapes, and dynamical systems.
problem Monitoring intrinsic dimensionality of large data sets.
method Optimization problem to find -profile, which is the norm of the shortest projected secant.
result The -profile provides a useful statistic for understanding and monitoring large data sets.
We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature…
Study lightlike submanifolds in indefinite statistical manifolds, finding conditions and curvature expressions.
problem Characterize lightlike submanifolds in indefinite statistical manifolds.
method Analyze conditions for lightlike submanifolds to be lightlike statistical submanifolds, derive statistical sectional curvature, and investigate induced statistical Ricci tensor symmetry.
result Conditions for lightlike submanifolds to be lightlike statistical submanifolds and expressions for statistical sectional curvature and induced Ricci tensor symmetry.
Study on statistical properties of Kenmotsu statistical manifolds and inequalities.
problem Investigate statistical curvature properties and inequalities in Kenmotsu statistical manifolds.
method Optimization techniques on submanifolds to prove inequalities.
result Proved a Chen-Ricci inequality for statistical submanifolds in Kenmotsu statistical manifolds.
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.
Study on solitons in Kenmotsu statistical manifolds and submanifolds.
problem Investigating solitons in Kenmotsu statistical manifolds and their submanifolds.
method Examined statistical solitons and Yamabe solitons, studied curvature properties, and analyzed submanifolds with concircular and concurrent vector fields.
result Discussed the behavior of almost quasi-Yamabe solitons on submanifolds of Kenmotsu statistical manifolds.
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.
Almost product structures on statistical manifolds and para-Kähler-like statistical submersionsmath.DG
Study on statistical manifolds with product structures and their properties.
problem Investigating statistical manifolds with almost product structures.
method Proving properties of para-Kähler-like statistical manifolds and deriving properties of statistical submersions compatible with almost product structures.
result The statistical structure of a para-Kähler-like statistical manifold of constant curvature is a Hessian structure.
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.
Lightlike hypersurfaces in statistical manifolds have unique geometric properties.
problem Characterizing lightlike hypersurfaces in statistical manifolds.
method Analyzing geometric properties and induced structures of lightlike hypersurfaces.
result Lightlike hypersurfaces are not statistical manifolds but have a canonical screen distribution.
Optimization method yields geometric inequalities for submanifolds in statistical warped product manifolds.
problem Optimizing geometric inequalities for submanifolds in statistical warped product manifolds.
method Optimization techniques applied to statistical submanifolds in statistical warped product manifolds.
result Optimal Casorati inequalities and Chen-Ricci inequality derived for statistical submanifolds.
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.
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.
This paper simplifies computing higher-order -statistics efficiently.
problem The inefficiency of computing higher-order -statistics in practice.
method Decomposition, connection to Einstein summation, and treewidth-based complexity estimate.
result A new, more efficient algorithm to compute -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.
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.
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.
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.
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.
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.
Paper develops risk statistics for portfolios considering regulator-based risk.
problem Traditional risk statistics fail to describe regulator-based risk.
method Develop dual representation for regulator-based risk statistics.
result Derived dual representation for regulator-based risk statistics.
Active inference framework improves -statistic estimation efficiency.
problem Costly acquisition of labels for -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.
Introduces generalized almost statistical convergence and its properties.
problem Developing a new convergence concept for sequences.
method Introducing generalized almost statistical convergence and proving its properties.
result Existence of a GAS convergent sequence that is neither statistical nor almost convergent.
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.
One- and two-sample nonparametric tests for the signal-to-noise ratio based on record statisticsstat.ME
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 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.
Machine learning used in German official statistics.
problem Identifying areas and tasks where machine learning is applied in official statistics.
method Surveys conducted at statistical institutions and divisions of Destatis.
result Machine learning methods are used in various statistical areas and tasks.
Statistical Gamesmath.ST
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…
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.
New risk statistics for loss-based regulation.
problem Regulatory focus on losses over gains.
method Developed new risk statistics using scenario analysis.
result New risk statistics extend existing measures.
Basic inequality for statistical submanifolds of quaternion Kaehler-like statistical manifoldsmath.DG
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 , which enable 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.
Paper develops efficient statistical estimators for distributed data.
problem Communication and privacy issues in distributed statistical inference.
method Iterative algorithms for distributed optimization, adapting to loss function similarity.
result CEASE estimators achieve statistical efficiency in finite steps.
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.
Uniform bounds derived for nonlinear statistics.
problem Deriving uniform bounds for nonlinear statistics.
method Extended method to Gaussian and Rademacher complexities.
result Tight bounds for U-statistics and error functionals.
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…
Statistical Einstein manifolds of exponential families with group-invariant potential functionsmath-ph
The paper classifies statistical Einstein manifolds in exponential families.
problem Classifying statistical Einstein manifolds in exponential families.
method Deriving partial differential equations for potential functions, obtaining special and group-invariant solutions.
result Special and group-invariant solutions of the equations for potential functions of exponential families.
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 -statistics and variance estimation under varying kernel sizes.
problem Analyzing -statistics and variance estimation under varying kernel sizes.
method Develops a general framework for asymptotics of -statistics, reducing to -statistics and providing a unified variance estimation method.
result Demonstrates asymptotic normality of -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.