arXiv research

Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.

New insights into natural exponential families improve regret bounds for bandit problems.

New algorithms achieve high-probability parameter-free regret in online convex optimization with heavy-tailed data.

New algorithms improve stopping time for best arm identification.

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…

Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.

The paper introduces a new method for tail bounds of random vectors and matrices.

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

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…

The paper explores how benign overfitting occurs in heavy-tailed input distributions.

The paper provides a new uniform tail bound for empirical processes.

Study improves ERM for heavy-tailed data with dependent inputs.

There is accumulating evidence in the literature that stability of learning algorithms is a key characteristic that permits a learning algorithm to generalize. Despite various insightful results in this direction, there seems to be an overlooked dichotomy in the type of stability-based generalization bounds we have in …

Study differentially private linear regression with heavy-tailed data.

New model captures time-varying volatility with stochastic exponential tails.

New framework controls generalization for heavy-tailed data in RLHF and SGLD.

We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the dimens…

We study tilting subweibull distributions and their tail behavior.

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

In this paper a quantitative analysis of the ruin probability in finite time of discrete risk process with proportional reinsurance and investment of finance surplus is focused on. It is assumed that the total loss on a unit interval has a light-tailed distribution -- exponential distribution and a heavy-tailed distrib…

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

We improve bounds for stochastic processes, especially those with heavy tails.

Optimal algorithm for minimizing regret in heavy-tailed bandits.

Study Hilbert's projective metric for bounded growth functions leading to Sinkhorn's algorithm convergence.

New stability bounds for Sinkhorn's algorithm in entropic optimal transport.

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output c…

Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.

Sharp large deviations and Gibbs conditioning for portfolio credit risk models.

Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.

This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.

A robust conformal method for set estimation using non-conformity scores.

Novel LSE estimator improves off-policy learning and evaluation.

Stochastic approximation algorithms show exponential progress bounds.

Gradient descent implicitly follows regularization for general losses.

Nonlinear SGD achieves high-probability rates in non-convex optimization with heavy-tailed noise.

The paper improves PAC-Bayes bounds for losses with finite moments.

A simple log-transform fixes heavy-tailed data for generative models.

Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.

We study an equivalence of (i) deterministic pathwise statements appearing in the online learning literature (termed \emph{regret bounds}), (ii) high-probability tail bounds for the supremum of a collection of martingales (of a specific form arising from uniform laws of large numbers for martingales), and (iii) in-expe…

Study growth patterns in random networks using i.i.d. perturbations.

Estimate arrival times in random recursive trees using iterated Jordan centralities.

New ensemble method improves model stability exponentially.

Paper develops robust estimators and strategies for stochastic MABs with heavy-tailed rewards.

New bounds for non-convex estimators without Bernstein condition.

This paper extends the convergence analysis of Langevin Monte Carlo beyond Poincaré inequalities.

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…

We analyze systems of agents sharing light-tailed risky claims issued by different financial objects. Assuming exponentially distributed claims, we obtain that both agents' and system's losses follow generalized exponential mixture distributions. We show that this leads to qualitatively different results on individual …