Related papers: Max-Linear Regression by Convex Programming
This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
We consider regression of a max-affine model that produces a piecewise linear model by combining affine models via the max function. The max-affine model ubiquitously arises in applications in signal processing and statistics including…
Mixed linear regression is a well-studied problem in parametric statistics and machine learning. Given a set of samples, tuples of covariates and labels, the task of mixed linear regression is to find a small list of linear relationships…
In this paper, we study the issue of estimating a structured signal $x_0 \in \mathbb{R}^n$ from non-linear and noisy Gaussian observations. Supposing that $x_0$ is contained in a certain convex subset $K \subset \mathbb{R}^n$, we prove that…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and probability in recent years. While convex cases, such as the…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
With an eye towards human-centered automation, we contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human…
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The…
Many recent theoretical works on \emph{meta-learning} aim to achieve guarantees in leveraging similar representational structures from related tasks towards simplifying a target task. The main aim of theoretical guarantees on the subject is…
We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…