Related papers: Efficient Sparse Group Feature Selection via Nonco…
Popular sparse estimation methods based on $\ell_1$-relaxation, such as the Lasso and the Dantzig selector, require the knowledge of the variance of the noise in order to properly tune the regularization parameter. This constitutes a major…
We introduce a novel nonlinear model, Sparse Adaptive Bottleneck Centroid-Encoder (SABCE), for determining the features that discriminate between two or more classes. The algorithm aims to extract discriminatory features in groups while…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more…
Variable selection for recovering sparsity in nonadditive nonparametric models has been challenging. This problem becomes even more difficult due to complications in modeling unknown interaction terms among high dimensional variables. There…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal…
Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive…
We formulate the sparse classification problem of $n$ samples with $p$ features as a binary convex optimization problem and propose a cutting-plane algorithm to solve it exactly. For sparse logistic regression and sparse SVM, our algorithm…
Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
Deep sparse networks are widely investigated as a neural network architecture for prediction tasks with high-dimensional sparse features, with which feature interaction selection is a critical component. While previous methods primarily…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…
Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
Feature selection is a critical component in predictive analytics that significantly affects the prediction accuracy and interpretability of models. Intrinsic methods for feature selection are built directly into model learning, providing a…