arXiv research

Study provides bounds for estimating intrinsic dimension using Gaussian kernels.

The paper provides concentration inequalities for Markov chain variance estimators.

Improved bounds for estimating discrete distributions in KL divergence.

The paper proves LOO CV is reliable under estimator stability.

Develops inequalities for high-dimensional linear processes with dependent innovations.

Improved estimation of concentration using half-spaces for adversarial vulnerability.

Study robust covariance estimation in large data with concentrated vectors.

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the light-tailed case, we use a classical CVaR estimator based on the empirical distributi…

New method improves missing mass concentration bounds.

Study Finsler metric measure manifolds' concentration properties.

This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.

We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequa…

We consider a priori generalization bounds developed in terms of cross-validation estimates and the stability of learners. In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general function of n independent random variables. Next, under some reasonable notion of s…

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estima…

Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.

The paper analyzes risk estimation methods and derives bounds for OCE risk.

Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and validate it. ID can be computed globally for the whole data point distribution, or comp…

Estimates barycenter in geodesic spaces with finite sample bounds.

The study characterizes heat flow and concentration on directed graphs with a lower Ricci curvature bound.

Study analyzes impact of concentrated liquidity on trading fees and provider returns.

The paper proves concentration inequalities for diffusion processes.

Paper shows how online betting algorithms' regret can be used to create tight confidence sequences.

We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the case when the underlyi…

Sharp Gaussian isoperimetry proven along Ricci flow.

In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional Value-at-Risk (CVaR) is a popular risk measure for modeling the aforementioned objec…

Sharp stability result for maps near infinitely concentrated minimisers.

We analyze a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the $d$-dimensional unit cube $[0,1]^d$ that lie in a $β$-Hölder s…

Tick-by-tick liquidity provision aims to maximize fees and reserves.

In this paper we study the local regularity of closed surfaces immersed in a Riemannian 3-manifold flowing by Willmore flow. We establish a pair of concentration-compactness alternatives for the flow, giving a lower bound on the maximal time of existence of the flow proportional to the concentration of the curvature an…

The study proves inequalities and curvature properties for Markov chains.

Study the averaging estimator on graphs with labeled nodes.

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a physics-informed deep neural networks (DNNs) machine lea…

Study on network-valued processes with asynchronous updates, proving consistency in community and changepoint estimation.

New model estimates indoor radon distribution with higher spatial resolution.

Many recent works have shown that adversarial examples that fool classifiers can be found by minimally perturbing a normal input. Recent theoretical results, starting with Gilmer et al. (2018b), show that if the inputs are drawn from a concentrated metric probability space, then adversarial examples with small perturba…

The problem of estimating a high-dimensional sparse vector $\boldsymbolθ \in \mathbb{R}^n$ from an observation in i.i.d. Gaussian noise is considered. The performance is measured using squared-error loss. An empirical Bayes shrinkage estimator, derived using a Bernoulli-Gaussian prior, is analyzed and compared with the…

This paper surveys the evolution of industrial concentration of the Brazilian automotive market as well as its positioning in the worldmarket. Data available by OICA (International Organization of Motor Vehicle Manufacturers) were used to better understand the characteristics of the Brazilian market on the world stage.…

Study on stock portfolio concentration among Finnish households and investors.

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $χ^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, …

Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.

Study on bending energy of surfaces with curvature concentration, deriving new lower bounds.

Improved privacy-preserving methods for convex optimization with heavy-tailed data.

This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as condition…

The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.

The paper develops concentration inequalities for structured random data, extending beyond independent terms.

Paper tackles offline preference-based RL with human feedback.

The paper offers a framework to analyze machine learning problems using concentration of measure.

Repelling random walks improve graph-based sampling efficiency.