Related papers: Linear Regression with Unknown Truncation Beyond G…

We consider the task of Gaussian mean testing, that is, of testing whether a high-dimensional vector perturbed by white noise has large magnitude, or is the zero vector. This question, originating from the signal processing community, has…

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…

Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…

Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration…

In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian…

The problem of least squares regression of a $d$-dimensional unknown parameter is considered. A stochastic gradient descent based algorithm with weighted iterate-averaging that uses a single pass over the data is studied and its convergence…

There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right-censored survival data. We consider survival data that are subject to both left…

We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…

In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…

In machine learning applications, predictive models are trained to serve future queries across the entire data distribution. Real-world data often demands excessively complex models to achieve competitive performance, however, sacrificing…

This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$,…

In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid…

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

We study the generalization error of randomized learning algorithms -- focusing on stochastic gradient descent (SGD) -- using a novel combination of PAC-Bayes and algorithmic stability. Importantly, our generalization bounds hold for all…

In this paper, we propose an abstract procedure for debiasing constrained or regularized potentially high-dimensional linear models. It is elementary to show that the proposed procedure can produce $\frac{1}{\sqrt{n}}$-confidence intervals…

Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely…

State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference,…

The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study of the asymptotic performance of the posterior distribution…