Related papers: A statistical and computational theory for robust …
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
Non-linear statistical inverse problems pose major challenges both for statistical analysis and computation. Likelihood-based estimators typically lead to non-convex and possibly multimodal optimization landscapes, and Markov chain Monte…
When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
In this paper, we consider a squared $L_1/L_2$ regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal…
We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
In many statistical modeling problems, such as classification and regression, it is common to encounter sparse and blocky coefficients. Sparse fused Lasso is specifically designed to recover these sparse and blocky structured features,…
We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner…
We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…
To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state…
This paper provides a comprehensive estimation framework via nuclear norm plus $l_1$ norm penalization for high-dimensional approximate factor models with a sparse residual covariance. The underlying assumptions allow for non-pervasive…
Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…
The paper motivates high dimensional smoothing with penalized splines and its numerical calculation in an efficient way. If smoothing is carried out over three or more covariates the classical tensor product spline bases explode in their…
We consider the estimation of smoothing parameters and variance components in models with a regular log likelihood subject to quadratic penalization of the model coefficients, via a generalization of the method of Fellner (1986) and Schall…