arXiv research

Develops estimators for near-optimal linear regression under distribution shift.

The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.

This work shows that Gaussian is the only prior for optimal linear estimation in $L^1$ loss.

Two EM algorithms estimate prior distributions in mixture of linear regressions.

The growing size of modern data brings many new challenges to existing statistical inference methodologies and theories, and calls for the development of distributed inferential approaches. This paper studies distributed inference for linear support vector machine (SVM) for the binary classification task. Despite a vas…

Efficiently estimates sparse linear regression with heavy-tailed and outlier-contaminated data.

A novel Bayesian framework for private linear regression with MCMC.

Study on distributional TD learning with linear approximations for better return estimation.

Study robust linear regression without distributional assumptions for heavy-tailed responses.

Estimates causal effects in Gaussian Linear SCMs with finite data.

Robustly estimates linear regression coefficients with adversarial and noisy data.

Study improves distributed linear estimation under adversarial conditions.

We propose a communication-efficient distributed estimation method for sparse linear discriminant analysis (LDA) in the high dimensional regime. Our method distributes the data of size $N$ into $m$ machines, and estimates a local sparse LDA estimator on each machine using the data subset of size $N/m$. After the distri…

New method improves covariance estimation for weighted samples.

Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.

Quantum computing offers a quadratic speedup for estimating non-linear functionals.

Develops asymptotic analysis for RandNLA sampling estimators in least-squares problems.

Although various distributed machine learning schemes have been proposed recently for pure linear models and fully nonparametric models, little attention has been paid on distributed optimization for semi-paramemetric models with multiple-level structures (e.g. sparsity, linearity and nonlinearity). To address these is…

Combines linear and spectral estimators for signal recovery in generalized linear models.

This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and test samples. Conditional on the tuning parameter, the training sample creates …

New robust estimator improves variable selection and coefficient estimation in linear regression with heavy-tailed errors and outliers.

Efficiently estimates sparse linear regression with heavy-tailed data and outliers.

A new algorithm improves stochastic linear bandit performance using residual bootstrap.

Unified strategy for efficient data compression and model estimation.

Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for generalized linear models under the "large $n$, diverging $p_n$" framework, where the di…

Estimates parameters in max-linear Bayesian networks with noise.

A method for estimating parameters from entangled single-sample distributions, robust to high-noise data.

New algorithm for estimating MLR parameters with non-Gaussian noise.

The paper tackles estimating optimal policy value in linear bandits with general context distributions.

New algorithms improve distributional TD learning with linear approximations.

Lower bounds show density estimation requires linear samples or query time.

CNR uses convex optimization to estimate conditional distributions.

Study improves robustness and sparsity in linear regression with adversarial outliers and heavy-tailed noise.

SURF simplifies distribution estimation with simple, robust, and fast algorithms.

TULiP estimates uncertainty for deep learning models safely.

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

Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hatβ$ is hard to determine as the estimator is defined by an optimization problem that in general can only…

New algorithm approximates distributions with near-linear time and optimal sample efficiency.

This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile …

Feature selection problems have been extensively studied for linear estimation, for instance, Lasso, but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection in high-dimensional non-linear function estimation problems. The new procedure is…

New method speeds up distributed linear regression.

Paper tackles distributed quantile regression with improved efficiency and support recovery.

We study the problem of estimating a set of $d$ linear queries with respect to some unknown distribution $\mathbf{p}$ over a domain $\mathcal{J}=[J]$ based on a sensitive data set of $n$ individuals under the constraint of local differential privacy. This problem subsumes a wide range of estimation tasks, e.g., distrib…

This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used for approximate minimization of smooth and strongly convex losses, and specificall…

Paper extends LME models to allow sign constraints on coefficients with SDTN random effects.

A new copula minimizes distance between distributions.

Profile entropy measures learnability and compressibility of discrete distributions.

Optimizes mixture models without parametrizing distributions using tensor decomposition.