arXiv research

LoCoV reduces portfolio optimization errors from sample covariance matrices.

New error bounds for flow matching methods using deterministic sampling.

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…

Paper introduces a new method for error estimation in classification tasks with limited data.

In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling probabilities. The sampling dependent error bound (i) allows us to better understand the …

We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…

Improved sample complexity for training diffusion models.

Predictive models ground many state-of-the-art developments in statistical brain image analysis: decoding, MVPA, searchlight, or extraction of biomarkers. The principled approach to establish their validity and usefulness is cross-validation, testing prediction on unseen data. Here, I would like to raise awareness on e…

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

Combining diffusion models with Langevin dynamics improves posterior sampling efficiency.

New bounds show multicalibration error is close to prediction error.

Randomly sampled interpolators achieve zero generalization error with enough data.

iTimER learns from reconstruction errors to represent irregularly sampled time series.

The paper analyzes the probabilistic structure of DDPMs and bounds their sampling error.

Neural network accuracy improves with denser training samples.

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…

This paper provides a general framework to study the effect of sampling properties of training data on the generalization error of the learned machine learning (ML) models. Specifically, we propose a new spectral analysis of the generalization error, expressed in terms of the power spectra of the sampling pattern and t…

The study analyzes and mitigates errors in PC-based causal discovery methods.

We study the problem of out-of-sample risk estimation in the high dimensional regime where both the sample size $n$ and number of features $p$ are large, and $n/p$ can be less than one. Extensive empirical evidence confirms the accuracy of leave-one-out cross validation (LO) for out-of-sample risk estimation. Yet, a un…

Novel method for nonlinear data assimilation using Langevin sampling.

This study calculates the maximum error of a famous estimation method.

New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.

Training on some out-of-distribution data improves generalization error before it deteriorates.

New method for group testing robust to errors in group membership specifications.

A new sampling method called Restart improves both speed and quality of generative processes.

New method addresses error bounds for PnP-ULA under mismatched models.

LMC improves sampling from complex distributions using quasi-random sequences.

While active learning offers potential cost savings, the actual data efficiency---the reduction in amount of labeled data needed to obtain the same error rate---observed in practice is mixed. This paper poses a basic question: when is active learning actually helpful? We provide an answer for logistic regression with t…

The study provides a comprehensive error analysis for diffusion models.

Estimates error for robust M-estimators with convex penalties.

Estimates support in distributions with sampling artifacts and errors.

With a growing interest in using non-representative samples to train prediction models for numerous outcomes it is necessary to account for the sampling design that gives rise to the data in order to assess the generalized predictive utility of a proposed prediction rule. After learning a prediction rule based on a non…

Optimal number of voters for a voting ensemble can be estimated from the distribution of classifier errors.

Analysis of non-asymptotic estimation error and structured statistical recovery based on norm regularized regression, such as Lasso, needs to consider four aspects: the norm, the loss function, the design matrix, and the noise model. This paper presents generalizations of such estimation error analysis on all four aspe…

Robust estimators for Gaussian sparse tasks with optimal error under contamination.

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

Recent theoretical work has guaranteed that overparameterized networks trained by gradient descent achieve arbitrarily low training error, and sometimes even low test error. The required width, however, is always polynomial in at least one of the sample size $n$, the (inverse) target error $1/ε$, and the (inverse) fail…

Study precise sample covariance error for Gaussian centered data.

Paper extends nonparametric regression bounds for dependent $\beta$-mixing samples.

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

This work uses sampling theory to analyze smoothness and error bounds of finite neural networks.

The paper provides guarantees for feedback control with sensor errors.

New algorithm learns changing discrete distributions with minimal drift error.

New characterization limits sampling with inexact scores.

Active-LATHE boosts error exponent for learning homogeneous trees.

Near-optimal algorithms for mean estimation and linear regression with Gaussian covariates and Huber contamination.

A new method for sampling complex posterior distributions in DDMs.

Improved TD learning reduces batch sampling error.