Symmetric game analysis shows Nash equilibria in three strategic states.
problem Analyzing Nash equilibria in a symmetric multi-player zero-sum game with two strategic variables.
method Using the minimax theorem by Sion to show equivalence of Nash equilibria.
result Nash equilibria are equivalent in three strategic states.
Study on diagonal and separating coordinates for symmetric spaces of rank 1.
problem Existence and nonexistence of diagonal and separating coordinates for symmetric spaces of rank 1.
method Generalization of results by Gauduchon and Moroianu, 2020, and analysis of constant sectional curvature and orthogonal separation of variables.
result Diagonal coordinates exist if and only if the symmetric space has constant sectional curvature.
Extended contraction inequality for Rademacher complexities to vector-valued functions.
problem Bounding Rademacher complexities for vector-valued functions.
method Extended contraction inequality for Lipschitz functions with vector-valued domains, using symmetric and sub-gaussian variables.
result Rademacher variables can be replaced by arbitrary symmetric and sub-gaussian variables in the bounding expression.
We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.
Bayesian networks are simplified for categorical variables using staged trees and asymmetry-labeled DAGs.
problem Representing non-symmetric conditional independences in Bayesian networks.
method Formalized relationship between Bayesian networks and staged trees, introduced asymmetry-labeled DAGs, and developed an algorithm to learn staged trees.
result A novel algorithm for learning staged trees that captures non-symmetric independences.
Motivated by the study of ribbon knots we explore symmetric unions, a beautiful construction introduced by Kinoshita and Terasaka in 1957. For symmetric diagrams we develop a two-variable refinement WD(s,t) of the Jones polynomial that is invariant under symmetric Reidemeister moves. Here the two variables s and $…
The paper finds determinantal expressions for certain symmetric space integrals.
problem Finding compact expressions for integrals on symmetric spaces.
method Expressing integrals as determinants or Pfaffians for K-invariant functions. result Determinantal expressions for specific symmetric space integrals.
Study provides explicit formula for complex 2D Kähler manifold quantization.
problem Quantization of complex 2D locally symmetric Kähler manifolds.
method Deformation quantization with separation of variables, solving recurrence relations.
result Explicit formula for star product on complex 2D locally symmetric Kähler manifolds.
Calculates moments of sectional curvature on Riemannian manifolds.
problem Understanding the distribution and moments of sectional curvature.
method Integrating local Riemannian invariants and analyzing sectional curvature on Grassmann bundles.
result Proves a weak version of the Hitchin-Thorpe Inequality.
Extends inequality for Rademacher complexities using p-stable variables.
problem Improving Rademacher complexity bounds using p-stable variables. method Extends contraction inequality to p-stable variables for 1<p<2. result New bounds for Rademacher complexities with p-stable variables. The study confirms a conjecture about polynomials related to symmetric spaces.
problem Understanding polynomials associated with isotropy orbits of symmetric spaces.
method Identified Reiswich's polynomials as special cases of Jacobi polynomials and proved their conjecture.
result The polynomials have pairwise different real roots in the interval [0,1].
We give a characterization for the Alexander Polynomials of closed orientable 3-manifolds M with first Betti number 1, as well as some partial results for the characterization problem for M having first Betti number > 1. We first prove an analogue of a theorem of Levine: that the product of an Alexander polynomial of M…
Researchers classify and describe Kα-translators in Euclidean space.
problem Classifying and describing Kα-translators in Euclidean space. method Rotationally symmetric and helicoidal motions.
result For each α, there is a Kα-translator intersecting orthogonally the rotation axis. Locally classifies 4D spherical symmetric Finsler spaces.
problem Classifying 4D spherical symmetric Finsler spaces.
method Local classification of pseudo-Finsler Berwald structures.
result Six classes of non-Riemannian SO(3)-symmetric pseudo-Finsler Berwald functions.
In latent Dirichlet allocation (LDA), topics are multinomial distributions over the entire vocabulary. However, the vocabulary usually contains many words that are not relevant in forming the topics. We adopt a variable selection method widely used in statistical modeling as a dimension reduction tool and combine it wi…
We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natural 1-1 correspondence between simply connected hyper-Kaehler symmetric spaces of dimension 8m and orbits of the general linear group GL(m,H…
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for artificially included correlations in large random time series.The results are t…
We study a class of Poisson-Nijenhuis systems defined on compact hermitian symmetric spaces, where the Nijenhuis tensor is defined as the composition of Kirillov-Konstant-Souriau symplectic form with the so called Bruhat-Poisson structure. We determine its spectrum. In the case of Grassmannians the eigenvalues are the …
The paper introduces a valuation framework for variable selection in econometric models.
problem Optimizing variable selection in econometric models to balance gains and losses.
method Derives a valuation framework based on expected marginal gains and losses, introduces three unbiased solutions.
result New approaches significantly outperform existing methods in variable selection.
New random walk results on rank one symmetric spaces.
problem Analyzing random walks on noncompact rank one symmetric spaces.
method Unified algebraic framework using Möbius addition and harmonic analysis of spherical functions.
result Renormalized walk converges to heat kernel on Laplace-Beltrami operator.
New method identifies common cause in causal insufficiency, revealing complex phase transitions.
problem Identifying common cause in causal insufficiency with observed joint probability.
method Generalized maximum likelihood method, closely related to maximum entropy principle.
result Identifies consistent common cause that aligns with the common cause principle.
Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.
problem Future stability of solutions of the Einstein-Yang-Mills system with arbitrary dimension.
method Tensorial symmetric hyperbolic formulation and local well-posedness for Cauchy problem.
result Established local well-posedness for the Cauchy problem of EYM equations in the temporal gauge.
New algorithms learn simple staged trees from data, improving model fit.
problem Complex conditional independences in categorical data vectors.
method Structural learning algorithms for simple staged trees, coalescing the underlying tree.
result Data-learned simple staged trees often outperform Bayesian networks in model fit.
We consider an SO(4) Euler rigid body with two 'inertia momenta' coinciding. We study it from the point of view of bihamiltonian geometry. We show how to algebraically integrate it by means of the method of separation of variables.
New connections found on zero-mean multivariate normal distributions.
problem Characterizing statistical connections on zero-mean multivariate normal distributions.
method Investigating invariant conjugate symmetric statistical connections on the submanifold of zero-mean multivariate normal distributions.
result Invariant connections on zero-mean multivariate normal distributions are not uniquely characterized by invariance under the general linear group action.
New algorithms learn and interpret asymmetry-labeled DAGs for COVID-19 fear.
problem Bayesian networks' strict symmetric independence assumption limits their applicability in real-world scenarios.
method Developed novel structural learning algorithms for asymmetry-labeled DAGs.
result Efficient algorithms allow for straightforward interpretation of the underlying dependence structure.
The paper proposes noise-invariant distances and features for robust testing and learning.
problem Testing and learning on distributions with irrelevant noise.
method Kernel embeddings, Maximum Mean Discrepancy, distances invariant to additive symmetric noise.
result Noise-invariant distances and features for robust testing and learning.
A new asymmetric correntropy method improves robust adaptive filtering for asymmetric error distributions.
problem Inadequate handling of asymmetric error distributions in adaptive filtering.
method Proposes asymmetric correntropy using an asymmetric Gaussian kernel and develops a robust adaptive filtering algorithm.
result The proposed algorithm shows better steady-state convergence performance for asymmetric error distributions.
We introduce a new algorithm, called adaptive sparse backfitting algorithm, for solving high dimensional Sparse Additive Model (SpAM) utilizing symmetric, non-negative definite smoothers. Unlike the previous sparse backfitting algorithm, our method is essentially a block coordinate descent algorithm that guarantees to …
Deep neural networks with heavy-tailed weights converge to stable distributions.
problem Understanding the convergence of heavy-tailed weights in infinitely-wide neural networks.
method Analyzing infinitely-wide multi-layer perceptrons with i.i.d. symmetric α-stable weight distributions. result The vector of pre-activation values converges to i.i.d. symmetric α-stable distributions. Study recovers tree structure in noisy MRFs with support size 3 or more.
problem Learning tree-structured MRFs with symmetric noise.
method Characterized recoverability based on joint PMF, provided algorithm for recovery.
result Structure of leaf clusters can be partially or fully identifiable.
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of…
A new method solves SymNMF problems faster and more efficiently.
problem Symmetric nonnegative matrix factorization (SymNMF) for data analytics.
method Nonconvex variable splitting method.
result The method converges to KKT points and has a global sublinear convergence rate.
Discriminative latent-variable models are typically learned using EM or gradient-based optimization, which suffer from local optima. In this paper, we develop a new computationally efficient and provably consistent estimator for a mixture of linear regressions, a simple instance of a discriminative latent-variable mode…
We study the stability of symmetric trajectories of a particle on the Lie group SO(3) whose motion is governed by an SO(3)×SO(2) invariant metric and an SO(2)×SO(2) invariant potential. Our method is to reduce the number of degrees of freedom at {\em singular} values of the SO(2)×SO(2) momentu…
A new method treats all variables equally in fitting data.
problem Fitting relationships to data with multiple variables, especially when dependent and independent variables are not clearly defined.
method A general method treating all variables impartially, using geometric mean functional relationships and correlation.
result The method provides coefficients that are easily calculated from covariances or correlations, making it scale-invariant and applicable to various units.
A new method computes link invariants from diagrams.
problem Computing link invariants efficiently.
method Single symmetric matrix from a link diagram.
result Multivariable Alexander polynomial computation.
Develops methods to construct harmonic and wave maps into variable-curvature surfaces.
problem Limited explicit constructions for harmonic and wave maps in variable-curvature settings.
method Reduction framework for pseudo-Riemannian surfaces, geometric ansatz, first-order ODEs.
result Constructs explicit harmonic and wave maps into ellipsoids, hyperboloids, and Schwarzschild exterior.
Bayesian test assesses conditional independence between variables.
problem Quantifying dependence or independence between variables given a third.
method Uses Polya tree priors on conditional probability densities.
result Provides a Bayesian measure of conditional dependence or independence.
Unified framework guarantees exactness of asymmetric low-rank SDP learning.
problem Exactness of asymmetric low-rank SDP learning with a quadratic penalty.
method Unified regularized asymmetric Burer-Monteiro factorization framework.
result Explicit lower bound on penalty parameter γ for exactness. We introduce and compare new variability measures based on risk quantiles.
problem Comparing variability measures in risk management.
method Developed a framework for one-parameter families of inter-Expected Shortfall differences and inter-expectile differences.
result Characterized symmetric and comonotonic variability measures as mixtures of inter-Expected Shortfall differences.
New algorithm selects relevant variables in high-dimensional graphical models.
problem Automatic selection of relevant variables in high-dimensional graphical models.
method Extends Chow and Liu's algorithm using mutual information and entropy coefficient of determination.
result Outperforms existing methods in selecting variables with explanatory power.
This paper improves sample complexity for tree-structured Ising model learning with noisy data.
problem Learning tree-structured Ising models with noisy data.
method High-probability sample complexity guarantees for structure recovery and predictive learning.
result Sample complexity remains logarithmic in the number of vertices, but depends on noise level.
Stabilizes cohomology of configuration spaces over complex varieties.
problem Stability of cohomology of configuration spaces.
method Probabilistic interpretation of stabilization as asymptotic independence of motivic random variables.
result Explicit formulas for limits in terms of motivic Euler product.
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank minrelation coefficient. We define a minrelation of X to Y (or equivalently a majrela…
Constructs Lepage equivalents for arbitrary-order Lagrangians.
problem Creating Lepage equivalents for complex Lagrangians.
method Uses variational bicomplex and symmetric linear connections to construct Lepage equivalents satisfying the closure property.
result Shows how to extend global Lepage equivalents to ones satisfying the closure property.
The consequences for Berezin's quantization on symmetric spaces of the identity of the set of coherent vectors orthogonal to a fixed one with the cut locus are stated precisely. It is shown that functions expressing the coherent states, the covariant symbols of operators, the diastasis function, the characteristic and …
A fast, approximate method for variable selection in GLMs tackles correlated data.
problem Variable selection in generalized linear models with correlated data.
method Replica method of statistical mechanics and vector approximate message passing.
result The proposed algorithm provides fast convergence and high approximation accuracy.