Related papers: Regularizers for Structured Sparsity
In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
Many problems in classification involve huge numbers of irrelevant features. Model selection reveals the crucial features, reduces the dimensionality of feature space, and improves model interpretation. In the support vector machine…
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…
Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging. The current paper proposes a new…
This work proposes an efficient batch algorithm for feature selection in reinforcement learning (RL) with theoretical convergence guarantees. To mitigate the estimation bias inherent in conventional regularization schemes, the first…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
This paper aims to improve the feature learning in Convolutional Networks (Convnet) by capturing the structure of objects. A new sparsity function is imposed on the extracted featuremap to capture the structure and shape of the learned…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
Sparse regression and classification estimators that respect group structures have application to an assortment of statistical and machine learning problems, from multitask learning to sparse additive modeling to hierarchical selection.…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…
In this paper, we consider a class of sparse regression problems, whose objective function is the summation of a convex loss function and a cardinality penalty. By constructing a smoothing function for the cardinality function, we propose a…
State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against it. Formulated as a min-max problem, it…
The $L_0$-regularized least squares problem (a.k.a. best subsets) is central to sparse statistical learning and has attracted significant attention across the wider statistics, machine learning, and optimization communities. Recent work has…
Measuring the error by an l^1-norm, we analyze under sparsity assumptions an l^0-regularization approach, where the penalty in the Tikhonov functional is complemented by a general stabilizing convex functional. In this context, ill-posed…
We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…
Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for…