arXiv research

Logistic regression gets a new, simpler uniform bound.

Sharp bounds on uniform generalization errors in binary linear classification.

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…

Uniform TD(0) bound derived for function approximation with Markov noise.

The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.

One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability. Both types of generalization are commonly used in the literature. For instance, …

Proves convergence of gradient Ricci shrinkers with uniform bounds.

New sampling bounds improve uniform coverage verification in machine learning.

We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance, extending classical Bernstein inequalities, and sharpening and simplifying prior wor…

Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.

Unified framework for robust clustering under various dissimilarity measures.

The paper derives uniform stability-based coverage bounds for conformal prediction methods.

The paper analyzes SMOTE for imbalanced classification, providing theoretical bounds and guidelines.

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

New concentration inequality for U-statistics of Markov chains.

We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors, depending on the dimension of the models and the cardinalities of their sample sp…

NUTS mixing time scales as d^(1/4) for Gaussian distributions.

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 …

Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form $(ρ(λX))_{λ\ge 0}$, where $ρ$ is a convex risk measure and $X$ a random variable, and we call such a curve a \emph{liqu…

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

New bounds on self-normalized martingales improve online linear regression performance.

New stability framework relaxes boundedness assumptions for generalization bounds.

The paper develops bounds for predictive values in binary classification.

New inequalities for unbounded functions improve denoising score matching.

We give a unified statement and proof of a class of wellknown mean value inequalities for nonnegative functions with a nonlinear bound on the Laplacian. We generalize these to domains with boundary, requiring a (possibly nonlinear) bound on the normal derivative at the boundary. These inequalities give rise to an energ…

Greedy algorithm achieves sublinear regret for various distributions.

UCRL3 improves UCRL2's efficiency in reinforcement learning by reducing exploration.

New method removes scalar curvature assumption in Ricci flow smoothing.

Max-sliced Wasserstein metric reduces high-dimensional data to 1D for better estimation.

Paper improves CI and CS for bounded means using betting and mixtures.

Uniform scaling limits in AdamW-trained transformers converge to ODEs.

Paper introduces risk assessment for contextual bandits without experiments.

This guide simplifies high-probability regret bounds in empirical risk minimization.

Paper tightens PAC-Bayes bounds using coin-betting for better estimates.

New property ensures neural networks generalize well with limited data.

Paper quantizes heavy-tailed data for near optimal estimation rates.

New method certifies anti-concentration for various non-Gaussian distributions.

Tests for overfitting in machine learning models.

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …

Proposes a new latent variable model for hyperspherical latent spaces.

Study uniform convergence of random walk Laplacians to diffusion Laplacian on smooth manifolds.

Paper improves learning efficiency by focusing on effective dimensionality.

Study provides bounds for estimating intrinsic dimension using Gaussian kernels.

Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.

Q-learning for average cost MDPs gets a concentration bound.

In this paper, we observe a set of functionals of metrics which are all decrease under the Calabi flow and have uniform lower bound along the flow, which give rise to a set of integral estimates on the curvature flow. Using these estimates, together with weak compactness we obtained in previous papers [8] and [10], we …

Unified framework for risk-aware policy learning in contextual bandits.

New algorithm learns policies without uniform overlap assumption.