Related papers: Precise analysis of ridge interpolators under heav…
Multiple randomization designs (MRDs) are a class of experimental designs used to handle interference in two-sided marketplaces. We investigate regression adjustment strategies for estimating total, spillover, and direct effects in MRDs. We…
We study generalization properties of random features (RF) regression in high dimensions optimized by stochastic gradient descent (SGD) in under-/over-parameterized regime. In this work, we derive precise non-asymptotic error bounds of RF…
We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…
In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression…
Random feature ridge regression is often analyzed in the high-dimensional regime under the homogeneous sampling model $x_i=\Sigma^{1/2}x_i'$, where the vectors $x_i'$ have iid entries and the same covariance matrix $\Sigma$ is shared by all…
This paper provides a comprehensive error analysis of learning with vector-valued random features (RF). The theory is developed for RF ridge regression in a fully general infinite-dimensional input-output setting, but nonetheless applies to…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
A regression model with more parameters than data points in the training data is overparametrized and has the capability to interpolate the training data. Based on the classical bias-variance tradeoff expressions, it is commonly assumed…
Motivated by customer loyalty plans and scholarship programs, we study tie-breaker designs which are hybrids of randomized controlled trials (RCTs) and regression discontinuity designs (RDDs). We quantify the statistical efficiency of a…
Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…
For high-dimensional linear regression models, we review and compare several estimators of variances $\tau^2$ and $\sigma^2$ of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty…
This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis…
Recent years have seen substantial advances in our understanding of high-dimensional ridge regression, but existing theories assume that training examples are independent. By leveraging techniques from random matrix theory and free…
We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size,…
We study the problem of estimating the mean of a distribution in high dimensions when either the samples are adversarially corrupted or the distribution is heavy-tailed. Recent developments in robust statistics have established efficient…
We propose an approach to the aggregation of risks which is based on estimation of simple quantities (such as covariances) associated to a vector of dependent random variables, and which avoids the use of parametric families of copulae. Our…
Characterization of local minima draws much attention in theoretical studies of deep learning. In this study, we investigate the distribution of parameters in an over-parametrized finite neural network trained by ridge regularized empirical…
Probabilistic Time Series Forecasting (PTSF) plays a critical role in domains requiring accurate and uncertainty-aware predictions for decision-making. However, existing methods offer suboptimal distribution modeling and suffer from a…