arXiv research

Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.

The study establishes risk bounds for distributional regression estimators.

Paper finds how many neurons are needed to approximate histogram distributions.

Improved bounds for estimating discrete distributions in KL divergence.

Study error bounds in evaluating distributional computational graphs.

New method improves understanding of machine learning model performance.

This paper explains why distributional reinforcement learning is better than vanilla RL using small-loss bounds.

Paper develops a new generalization bound using PAC-Bayes theory and Gibbs distributions.

Study improves generalization bounds for linear regression across tasks.

Proves equivalence of two types of Ricci curvature bounds.

The distributional category bounds manifold invariants and imposes constraints.

Optimal SQ bounds for learning binary product distributions and Ising models.

New trade-off found in bandit problems with unknown range.

Study compares synthetic and distributional Ricci curvature bounds.

Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this makes them widely applicable, a drawback is that the bounds can be too loose in so…

Study large deviations in life insurance portfolios without identical distributions.

The study optimizes bounds for comparing training and population loss.

In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation ineq…

We consider the stochastic multi-armed bandit problem with a prior distribution on the reward distributions. We are interested in studying prior-free and prior-dependent regret bounds, very much in the same spirit as the usual distribution-free and distribution-dependent bounds for the non-Bayesian stochastic bandit. B…

Whereas subriemannian geometry usually deals with smooth horizontal distributions, partially hyperbolic dynamical systems provide many examples of subriemannian geometries defined by non-smooth (namely, Hölder continuous) distributions. These distributions are of great significance for the behavior of the parent dynami…

We consider $K$-armed stochastic bandits and consider cumulative regret bounds up to time $T$. We are interested in strategies achieving simultaneously a distribution-free regret bound of optimal order $\sqrt{KT}$ and a distribution-dependent regret that is asymptotically optimal, that is, matching the $κ\ln T$ lower b…

The Probably Approximately Correct (PAC) Bayes framework (McAllester, 1999) can incorporate knowledge about the learning algorithm and (data) distribution through the use of distribution-dependent priors, yielding tighter generalization bounds on data-dependent posteriors. Using this flexibility, however, is difficult,…

A new framework tightens risk measure confidence bounds.

Study learns optimal auctions from corrupted or perturbed bidder valuation samples.

Flow matching KL divergence bound derived for smooth distributions.

Sharp error bounds derived for bidirectional GANs without restrictive assumptions.

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on…

High-probability bound for distributed stochastic approximation tracking error.

Proposes a general method to derive regret bounds for multi-armed bandit algorithms.

Exact bounds derived for neural network outputs with noisy inputs.

New bounds on generalization error for distributed learning using rate-distortion theory.

Valid p-value for bounded random variables without distributional assumptions.

The paper improves SMC algorithm for multi-modal distributions by proving variance bounds.

We study distributed estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.

Unified framework for distributional regret in bandits and reinforcement learning.

Unified learning bound for covariate and concept shifts.

We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a stochastically independent uniformly distributed unit vector. When the set of unit vectors …

Study shows data heterogeneity affects distributed learning's generalization error.

New bounds for SMC show its advantage over MCMC in multimodal distributions.

In this work, we consider the sample complexity required for testing the monotonicity of distributions over partial orders. A distribution $p$ over a poset is monotone if, for any pair of domain elements $x$ and $y$ such that $x \preceq y$, $p(x) \leq p(y)$. To understand the sample complexity of this problem, we intro…

The paper extends statistical estimation techniques under differential privacy.

Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.

The paper bounds the complexity of GCNs using Rademacher complexity.

The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribut…

Paper studies signal detection in noisy environments with limited communication.

New bounds for low-regularity Riemannian metrics defined via distributional curvature.

Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.

New combinatorial dimension VCL refines learning curve theory.