Related papers: Max-Linear Regression by Convex Programming

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a…

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…

Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…

We consider parameter estimation under sparse linear regression -- an extensively studied problem in high-dimensional statistics and compressed sensing. While the minimax framework has been one of the most fundamental approaches for…

Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the dataset. This article provides…

This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…

Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…

We study the problem of estimation and testing in logistic regression with class-conditional noise in the observed labels, which has an important implication in the Positive-Unlabeled (PU) learning setting. With the key observation that the…

In system identification, estimating parameters of a model using limited observations results in poor identifiability. To cope with this issue, we propose a new method to simultaneously select and estimate sensitive parameters as key model…

We propose a new method for multivariate response regression and covariance estimation when elements of the response vector are of mixed types, for example some continuous and some discrete. Our method is based on a model which assumes the…

We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are…

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an…

We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…

This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite…

We study the problem of recovering a hidden binary $k$-sparse $p$-dimensional vector $\beta$ from $n$ noisy linear observations $Y=X\beta+W$ where $X_{ij}$ are i.i.d. $\mathcal{N}(0,1)$ and $W_i$ are i.i.d. $\mathcal{N}(0,\sigma^2)$. A…

Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…

In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…