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We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…

Statistics Theory · Mathematics 2009-08-24 Ursula U. Müller

In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…

Computation · Statistics 2015-06-23 Willem van den Boom , Galen Reeves , David B. Dunson

We consider signals that follow a parametric distribution where the parameter values are unknown. To estimate such signals from noisy measurements in scalar channels, we study the empirical performance of an empirical Bayes (EB) approach…

Information Theory · Computer Science 2014-05-12 Yanting Ma , Jin Tan , Nikhil Krishnan , Dror Baron

This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…

Computer Vision and Pattern Recognition · Computer Science 2014-11-18 Xiangyu Zhang , Jianhua Zou , Xiang Ming , Kaiming He , Jian Sun

This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…

Methodology · Statistics 2020-11-10 Han Lin Shang , Xibin Zhang

We consider the problem of recovering a vector $\beta_o \in \mathbb{R}^p$ from $n$ random and noisy linear observations $y= X\beta_o + w$, where $X$ is the measurement matrix and $w$ is noise. The LASSO estimate is given by the solution to…

Statistics Theory · Mathematics 2015-11-05 Ali Mousavi , Arian Maleki , Richard G. Baraniuk

This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…

Optimization and Control · Mathematics 2020-07-15 Jineng Ren , Jarvis Haupt

We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…

Statistics Theory · Mathematics 2008-10-27 Béatrice Laurent , Carenne Ludeña , Clémentine Prieur

We consider large-scale linear inverse problems in Bayesian settings. Our general approach follows a recent line of work that applies the approximate message passing (AMP) framework in multi-processor (MP) computational systems by storing…

Information Theory · Computer Science 2016-11-17 Junan Zhu , Ahmad Beirami , Dror Baron

This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were…

Numerical Analysis · Mathematics 2022-10-06 Albert Cohen , Matthieu Dolbeault , Olga Mula , Agustin Somacal

In this paper, we consider the problem of piecewise affine abstraction of nonlinear systems, i.e., the overapproximation of its nonlinear dynamics by a pair of piecewise affine functions that "includes" the dynamical characteristics of the…

Optimization and Control · Mathematics 2018-11-07 Kanishka Raj Singh , Qiang Shen , Sze Zheng Yong

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step…

Machine Learning · Statistics 2012-11-13 Pedro A. Ortega , Jordi Grau-Moya , Tim Genewein , David Balduzzi , Daniel A. Braun

To improve the convergence property of approximate message-passing (AMP), convolutional AMP (CAMP) has been proposed. CAMP replaces the Onsager correction in AMP with a convolution of messages in all preceding iterations while it uses the…

Information Theory · Computer Science 2021-05-11 Keigo Takeuchi

Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…

Information Theory · Computer Science 2018-10-23 Cynthia Rush , Ramji Venkataramanan

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…

Machine Learning · Computer Science 2013-09-27 Oluwasanmi Koyejo , Joydeep Ghosh

In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…

Numerical Analysis · Mathematics 2015-07-07 Alessio Spantini , Antti Solonen , Tiangang Cui , James Martin , Luis Tenorio , Youssef Marzouk

This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large…

Methodology · Statistics 2024-07-22 Xiaomeng Ju , Hyung G. Park , Thaddeus Tarpey

Approximate Message Passing (AMP) algorithms are a family of iterative algorithms based on large random matrices with the special property of tracking the statistical properties of their iterates. They are used in various fields such as…

Probability · Mathematics 2025-03-27 Mohammed-Younes Gueddari , Walid Hachem , Jamal Najim

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Statistics Theory · Mathematics 2013-02-19 Michael Vogt

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Statistics Theory · Mathematics 2023-02-16 Christina Auer , Thomas Paireder , Oliver Ploder , Oliver Lang , Mario Huemer