arXiv research

The paper analyzes GTD algorithms with finite-sample bounds.

GANs learn distributions well from samples, with rates depending on intrinsic dimension.

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 non-parametric frequency-domain system identification from finite samples.

Paper adapts ACI for online multi-step time-series forecasting with coverage guarantees.

Crowdsourcing is an effective tool for human-powered computation on many tasks challenging for computers. In this paper, we provide finite-sample exponential bounds on the error rate (in probability and in expectation) of hyperplane binary labeling rules under the Dawid-Skene crowdsourcing model. The bounds can be appl…

New bounds show current methods overestimate system parameter errors.

Improves matrix completion by exploiting biased observation patterns.

Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.

Study tests whether trade-off functions are above or below benchmarks using finite samples.

We address the problem of automatic generation of features for value function approximation. Bellman Error Basis Functions (BEBFs) have been shown to improve the error of policy evaluation with function approximation, with a convergence rate similar to that of value iteration. We propose a simple, fast and robust algor…

Gradient descent converges to a small neighborhood of the true parameter in logistic regression with Gaussian design.

A method for making predictions with a reject option using conformal prediction.

Deep learning method improves regression accuracy.

This study analyzes how well GANs approximate distributions from small samples.

Study optimal transport for stationary processes, estimating joinings and costs.

In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalm…

Crowdsourcing has become an effective and popular tool for human-powered computation to label large datasets. Since the workers can be unreliable, it is common in crowdsourcing to assign multiple workers to one task, and to aggregate the labels in order to obtain results of high quality. In this paper, we provide finit…

The most important aspect of any classifier is its error rate, because this quantifies its predictive capacity. Thus, the accuracy of error estimation is critical. Error estimation is problematic in small-sample classifier design because the error must be estimated using the same data from which the classifier has been…

We formalize AURC and develop estimators for SC systems.

This paper analyzes momentum Q-learning with finite-sample guarantees.

Selective inference controls Type I error in k-means clustering tests.

Paper analyzes convergence rates of two time-scale AC and NAC algorithms.

Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.

We develop a unified approach for classification and regression support vector machines for data subject to right censoring. We provide finite sample bounds on the generalization error of the algorithm, prove risk consistency for a wide class of probability measures, and study the associated learning rates. We apply th…

Despite the increasing interest in multi-agent reinforcement learning (MARL) in multiple communities, understanding its theoretical foundation has long been recognized as a challenging problem. In this work, we address this problem by providing a finite-sample analysis for decentralized batch MARL with networked agents…

We address the problem of estimating the difference between two probability densities. A naive approach is a two-step procedure of first estimating two densities separately and then computing their difference. However, such a two-step procedure does not necessarily work well because the first step is performed without …

Synthetic data augmentation can improve imbalanced classification metrics.

Identifies bilinear systems from a single trajectory with optimal sample complexity.

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the nonconvex estimator, and it attains a linear rate of convergence to the true regres…

Study bounds variance modulation function for K-spider distributions.

A conformal procedure improves CoT reasoning by aggregating reasoning paths and calibrating abstention rules.

Causal invariance can improve finite-sample domain adaptation, but only when the target risk margins are large.

Unified framework for finite-sample RL algorithms using Lyapunov theory.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

Paper introduces a new reinforcement learning method with improved performance.

We learn linear models from nonlinear systems using multiple trajectories and regularization.

The paper develops a method to create non-asymptotic confidence ellipsoids for linear regression without strong noise distribution assumptions.

Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show its finite-sample error bounds while using different stepsizes. The idea is to c…

Adapts RKHS methods to estimate density ratios with optimal error.

New methods improve anomaly detection with reduced false positives.

Unified coverage analysis for linear off-policy evaluation in reinforcement learning.

Minimizes indecisions in selective classification to control misclassification rates.

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the robust statistics approach to consider perturbations under any Wasserstein distance…

Study on discrepancy principle for learning algorithms in nonparametric regression.

The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.

Algorithm learns stochastic system dynamics from data.

Estimates barycenter in geodesic spaces with finite sample bounds.