arXiv research

Estimates barycenter in geodesic spaces with finite sample bounds.

This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.

Correspondence found between exponential families and affine Grassmannians.

Study non-parametric frequency-domain system identification from finite samples.

We show in this note that the Sobolev Discrepancy introduced in Mroueh et al in the context of generative adversarial networks, is actually the weighted negative Sobolev norm $||.||_{\dot{H}^{-1}(ν_q)}$, that is known to linearize the Wasserstein $W_2$ distance and plays a fundamental role in the dynamic formulation of…

This paper analyzes momentum Q-learning with finite-sample guarantees.

Moment polytope of toric exponential families is a projection of a simplex.

This paper finds a unique partition of a sample space for estimating continuous distributions.

MF-TRPO optimizes MFGs with finite sample guarantees.

This study approximates distances between Gaussian processes and covariance operators using RKHS.

The paper develops divergences for Gaussian processes and RKHS settings.

The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.

Study bounds variance modulation function for K-spider distributions.

It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same…

We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax sample complexity of estimation with respect to the operator infinity norm, while…

New method uncovers zero entropy in dependent observations after finite samples.

Kernelized convex clustering handles non-linear and non-convex data.

Proposes a method to create shorter, more accurate prediction intervals.

Bayesian algorithms improve online learning with adversaries over infinite action spaces.

Considering the creation of persistence landscape on a parametrized curve and structure of sampling, there exists a random process for which a finite mixture model of persistence landscape (FMMPL) can provide a better description for a given dataset. In this paper, a nonparametric approach for computing integrated mean…

Detect changes in noisy dynamical systems using empirical approximations and finite-sample bounds.

Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.

Study convergence and approximations of entropic regularized Wasserstein distances for Gaussian and RKHS measures.

Study learns convolution operators on compact Abelian groups using regularization.

The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We are motivated to study the optimal distribution of finite sampling points. Formul…

The paper extends Thompson Sampling to infinite action spaces using information theory.

This paper improves Thompson Sampling for complex decision-making problems.

New method predicts state evolution for non-first-order algorithms on nonconvex problems.

We tackle permutation in linear regression with a new inference framework.

Extends SGM to functional spaces for multimodal data.

RANDomized-exploration policy Optimization via Multiple Importance Sampling with Truncation (RANDOMIST) for PO with mediator feedback.

New framework improves EM algorithm convergence under log-Sobolev inequality.

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

Let F be a family of Borel measurable functions on a complete separable metric space. The gap (or fat-shattering) dimension of F is a combinatorial quantity that measures the extent to which functions f in F can separate finite sets of points at a predefined resolution gamma > 0. We establish a connection between the g…

The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.

The paper sets sample complexity bounds for identifying LTI systems from a finite set.

This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-co…

New learning rule for quantum measurement classes overcomes uniform convergence issues.

Optimizes data collection for ranking and selection problems.

New analysis shows actor-critic method converges efficiently in practical settings.

Learning rates for least-squares regression are typically expressed in terms of $L_2$-norms. In this paper we extend these rates to norms stronger than the $L_2$-norm without requiring the regression function to be contained in the hypothesis space. In the special case of Sobolev reproducing kernel Hilbert spaces used …

MAGT generates data efficiently by aligning to manifold structure.

The study establishes minimax bounds for estimating operators from noisy samples.

Develops robust MDPs for unknown disturbances with performance guarantees.

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group $G$ with a …

New RL method reduces sample complexity for large state-action spaces.

New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.

New bounds for private learning of high-dimensional Gaussian distributions.