arXiv research

Novel approach for SEM in small samples with $p>n$.

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

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

We study the effects of approximate inference on the performance of Thompson sampling in the $k$-armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often must be approximated in practice. We show that even small constant inference error …

Langevin dynamics fails to produce accurate samples even with small score function errors.

Binary classification improves with a small fraction of corrupted labels.

New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.

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

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…

Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator follows a known distribution to form a confidence set [Kohavi 1995, Martin 1996,Yang…

The two-sample hypothesis testing problem is studied for the challenging scenario of high dimensional data sets with small sample sizes. We show that the two-sample hypothesis testing problem can be posed as a one-class set classification problem. In the set classification problem the goal is to classify a set of data …

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

Simple private estimators for mean and covariance outperform existing methods.

Study proposes a stopping criterion for active learning based on error stability.

Gradient descent with polylogarithmic width achieves arbitrarily low test error for shallow ReLU networks.

Paper analyzes online tensorial ICA convergence with stochastic approximation.

We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small sample sizes, and is scalable to high dimensions. We establish asymptotic bounds f…

K-Medoids(KM) is a standard clustering method, used extensively on semi-metric data.Error analyses of KM have traditionally used an in-sample notion of error,which can be far from the true error and suffer from generalization gap. We formalize the true K-Medoid error based on the underlying data distribution.We decompo…

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

Improved TD learning reduces variance and bias errors.

OTS error shows small training error doesn't guarantee small test error.

Estimates policy performance in small-data settings without sacrificing data.

Random feature model shows slow self-correction of generalization gap.

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

This paper shows how many samples are needed for smooth functions in high dimensions.

Dimensionality reduction is a first step of many machine learning pipelines. Two popular approaches are principal component analysis, which projects onto a small number of well chosen but non-interpretable directions, and feature selection, which selects a small number of the original features. Feature selection can be…

We consider the problem of performing linear regression over a stream of $d$-dimensional examples, and show that any algorithm that uses a subquadratic amount of memory exhibits a slower rate of convergence than can be achieved without memory constraints. Specifically, consider a sequence of labeled examples $(a_1,b_1)…

The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small changes in the returns as well as the VaR of the ES-optimized portfolio are also…

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

New algorithm learns changing discrete distributions with minimal drift error.

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

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

Estimates error for robust M-estimators with convex penalties.

A new framework for brain mapping using statistical agnostic methods.

Stochastic gradient descent updates parameters with summation gradient computed from a random data batch. This summation will lead to unbalanced training process if the data we obtained is unbalanced. To address this issue, this paper takes the error variance and error mean both into consideration. The adaptively adjus…

One-pass algorithm finds small subset for $\ell_p$ subspace approximation with additive error.

This work improves trace norm regularization for multi-task learning with limited data.

The paper proposes a method to solve L1 regression with fewer labels using Lewis weights.

Deep learning has transformed computer vision, natural language processing, and speech recognition\cite{badrinarayanan2017segnet, dong2016image, ren2017faster, ji20133d}. However, two critical questions remain obscure: (1) why do deep neural networks generalize better than shallow networks; and (2) does it always hold …

We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer vision, system identification, etc. The challenge is to design provable algorithms…

Small sample size hinders accurate long-term COVID-19 case predictions.

Probabilistic Autoencoder learns latent space weights' distribution.

New approach for reward-free exploration reduces estimation error.

Paper presents a new way to analyze machine learning generalization without probabilistic assumptions.

New findings on complexity limits in fixed budget bandit identification.

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level $α$. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people h…

Efficiently tests two distributions with few label queries.