Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is the LASSO problem, where the l1 norm regularizes a quadratic function. A multilevel framework is presented for solving such l1 regularized sparse optimizati...

We introduce an R package named picasso, which implements a unified framework of pathwise coordinate optimization for a variety of sparse learning problems (Sparse Linear Regression, Sparse Logistic Regression and Sparse Poisson Regression), combined with efficient active set selection strategies. Besides, the package allows users to choose different sparsityinducing regularizers, including the...

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimization problem by using the sketch. In particular, we use this approach to obta...

Abstract Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification nonlinear dynamics (SINDy) framework, powered by heuristic regression methods, has become dominant tool for learning parsimonious models. We propose an exact formulation SINDy using mixed-integer optimization (MI...

At present, the sparse recovery problem is mainly solved by convx optimization algorithm and greedy tracking method. However, former has defects in efficiency latter ability, neither of them can obtain effective under large sparsity or small observation degree. In this paper, we propose a new based on arithmetic combine ideas The proposed uses to solve coefficient signal transform domain, so as...

In this paper, we present a L1 regularized projection pursuit algorithm for additive model learning. Two new algorithms are developed for regression and classification respectively: sparse projection pursuit regression and sparse Jensen-Shannon Boosting. The introduced L1 regularized projection pursuit encourages sparse solutions, thus our new algorithms are robust to overfitting and present be...

Compressed sensing is a new sampling technique which can exactly reconstruct sparse signal from a few measurements. In this article, we consider the blocksparse compressed sensing with special structure assumption about the signal. A novel non-convex model is proposed to reconstruct the block-sparse signals. In addition, the conditions of the proposed model for recovering the block-sparse noise...