arXiv research

Proposes a new bound on generalization error using conditional mutual information.

This work bounds classification error in machine learning for low Bayes error conditions.

This paper analyzes error bounds for biased SMC samplers in conditional sampling.

New bound on machine learning model performance using Jensen-Shannon information.

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error rates of sample-consistent classifiers with monotonic error regions, in the real…

Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide conditions under which an appropriate scaling allows to improve the error bounds in…

We show how to compute lower bounds for the supremum Bayes error if the class-conditional distributions must satisfy moment constraints, where the supremum is with respect to the unknown class-conditional distributions. Our approach makes use of Curto and Fialkow's solutions for the truncated moment problem. The lower …

In this paper, we obtain generic bounds on the variances of estimation and prediction errors in time series analysis via an information-theoretic approach. It is seen in general that the error bounds are determined by the conditional entropy of the data point to be estimated or predicted given the side information or p…

Study shows exponential error reduction in multiclass classification without bias-variance trade-off.

New bounds on learning algorithm generalization error derived using information density.

Paper analyzes convergence of two time-scale stochastic approximation using martingale approach.

Enhanced $H$-consistency bounds derived under relaxed conditions.

New bounds study class-specific generalization error in machine learning.

Improved bounds on learning algorithms' performance using conditional mutual information.

This paper improves entropy bounds for ranking time-series complexity.

Paper establishes a universal growth rate for smooth surrogate losses in classification.

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems. In this paper, we present a new framework for establis…

New method improves understanding of machine learning model performance.

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on thes…

Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find upper bounds on the rates of convergence of the LSE when the errors have uniformly …

Study selective classification with halfspaces, achieving error bounds under Gaussian distributions.

New error bounds for flow matching methods using deterministic sampling.

This paper tackles worst-class error rate in classification tasks.

In this paper, we derive generic bounds on the maximum deviations in prediction errors for sequential prediction via an information-theoretic approach. The fundamental bounds are shown to depend only on the conditional entropy of the data point to be predicted given the previous data points. In the asymptotic case, the…

This paper tightens information-theoretic bounds on generalization errors.

Improved estimator for least squares using random projections achieves smaller error.

Establishes upper bounds on generalization error in active learning.

An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the learning algorithm. The bound is derived under more general conditions on the loss func…

Study improves error bounds for sparse regression with heavy-tailed covariates.

Bounds on factual and counterfactual distributions under measurement error in discrete models.

New sampling algorithms for complex distributions without log-concavity.

Hierarchical Federated Learning bounds generalize using Wasserstein distance.

SGD handles label noise with bounds improving over SGLD.

Sharp bounds on uniform generalization errors in binary linear classification.

New bounds for sequential tests under power-one error levels.

This paper concerns error bounds for recursive equations subject to Markovian disturbances. Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) and Reinforcement Learning (RL), and many of these algorithms can be interpreted as special cases of stochastic approximation (SA). It is argued tha…

Weighted SVM (or fuzzy SVM) is the most widely used SVM variant owning its effectiveness to the use of instance weights. Proper selection of the instance weights can lead to increased generalization performance. In this work, we extend the span error bound theory to weighted SVM and we introduce effective hyperparamete…

The study analyzes numerical stability in large language models using mixed-precision arithmetic.

PD-PINNs accelerate PINN training by incorporating task-specific dictionaries.

Paper improves risk bounds for nonconvex-strongly-concave minimax problems.

New bound matches exact generalization error for quadratic Gaussian problem.

In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we derive a relative upper bound for recovering the best low-rank approximation of t…

For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometr…

We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-$\ell_1$ regularization. While the current theory provides promis…

This work bounds the generalization error of private algorithms for discrete data.

Improved efficient robust regression with near-linear time and subquadratic samples.

We derive upper bounds on the generalization error of learning algorithms based on their \emph{algorithmic transport cost}: the expected Wasserstein distance between the output hypothesis and the output hypothesis conditioned on an input example. The bounds provide a novel approach to study the generalization of learni…