Related papers: Errors-in-variables models with dependent measurem…

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…

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

This paper considers the recovery of a rank $r$ positive semidefinite matrix $X X^T\in\mathbb{R}^{n\times n}$ from $m$ scalar measurements of the form $y_i := a_i^T X X^T a_i$ (i.e., quadratic measurements of $X$). Such problems arise in a…

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured…

Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation…

Large-scale regression problems where both the number of variables, $p$, and the number of observations, $n$, may be large and in the order of millions or more, are becoming increasingly more common. Typically the data are sparse: only a…

We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…

Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…

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 $y = \Pi_* X \beta_* + w$,…

Gradient descent is one of the most widely used iterative algorithms in modern statistical learning. However, its precise algorithmic dynamics in high-dimensional settings remain only partially understood, which has limited its broader…

We consider observations $(X,y)$ from single index models with unknown link function, Gaussian covariates and a regularized M-estimator $\hat\beta$ constructed from convex loss function and regularizer. In the regime where sample size $n$…

Missing values in datasets are common in applied statistics. For regression problems, theoretical work thus far has largely considered the issue of missing covariates as distinct from missing responses. However, in practice, many datasets…

We consider the problem of linear regression with self-selection bias in the unknown-index setting, as introduced in recent work by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [STOC 2023]. In this model, one observes $m$ i.i.d.…

We consider the non-parametric Poisson regression problem where the integer valued response $Y$ is the realization of a Poisson random variable with parameter $\lambda(X)$. The aim is to estimate the functional parameter $\lambda$ from…

Several recent trends in machine learning theory and practice, from the design of state-of-the-art Gaussian Process to the convergence analysis of deep neural nets (DNNs) under stochastic gradient descent (SGD), have found it fruitful to…