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Model-based reinforcement learning (MBRL) is sample-efficient but struggles in sparse reward settings. A critical bottleneck arises from the lack of informative gradients in sparse settings, where standard reward models often yield flat…

We propose a novel, fully nonparametric approach for the multi-task learning, the Multi-task Highly Adaptive Lasso (MT-HAL). MT-HAL simultaneously learns features, samples and task associations important for the common model, while imposing…

The methodology discussed in this paper aims to enhance choice models' comprehensiveness and explanatory power for forecasting choice outcomes. To achieve these, we have developed a data-driven method that leverages machine learning…

We develop new stochastic gradient methods for efficiently solving sparse linear regression in a partial attribute observation setting, where learners are only allowed to observe a fixed number of actively chosen attributes per example at…

Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

Modern soil mapping is characterised by the need to interpolate samples of geostatistical response observations and the availability of relatively large numbers of environmental characteristics for consideration as covariates to aid this…

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…

Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work,…

The application of the lasso is espoused in high-dimensional settings where only a small number of the regression coefficients are believed to be nonzero. Moreover, statistical properties of high-dimensional lasso estimators are often…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

The paper focuses on the automatic selection of the grouped explanatory variables in an high-dimensional model, when the model errors are asymmetric. After introducing the model and notations, we define the adaptive group LASSO expectile…

Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…

Recently, the l0-least mean square (l0-LMS) algorithm has been proposed to identify sparse linear systems by employing a sparsity-promoting continuous function as an approximation of l0 pseudonorm penalty. However, the performance of this…

Discovering governing equations from observational data remains a fundamental challenge in scientific modeling, particularly when the underlying mathematical structure is unknown. Traditional sparse identification methods like SINDy excel…

This paper addresses the sparse representation (SR) problem within a general Bayesian framework. We show that the Lagrangian formulation of the standard SR problem, i.e., $\mathbf{x}^\star=\arg\min_\mathbf{x} \lbrace \|…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…