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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…
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
Stochastic Closed-Loop Active Fault Diagnosis (CLAFD) aims to select the input sequentially in order to improve the discrimination of different models by minimizing the predicted error probability. As computation of these error…
Dictionary learning and sparse representation (DLSR) is a recent and successful mathematical model for data representation that achieves state-of-the-art performance in various fields such as pattern recognition, machine learning, computer…
Least-squares models such as linear regression and Linear Discriminant Analysis (LDA) are amongst the most popular statistical learning techniques. However, since their computation time increases cubically with the number of features, they…
The key to reconciling the polynomial-time intractability of many machine learning tasks in the worst case with the surprising solvability of these tasks by heuristic algorithms in practice seems to be exploiting restrictions on real-world…
Linear Discriminant Analysis (LDA) is commonly used for dimensionality reduction in pattern recognition and statistics. It is a supervised method that aims to find the most discriminant space of reduced dimension that can be further used…
In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning…
Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm…
Linear Discriminant Analysis (LDA) is a widely-used supervised dimensionality reduction method in computer vision and pattern recognition. In null space based LDA (NLDA), a well-known LDA extension, between-class distance is maximized in…
This paper considers smooth convex optimization problems with many functional constraints. To solve this general class of problems we propose a new stochastic perturbed augmented Lagrangian method, called SGDPA, where a perturbation is…
We consider the task of classification in the high dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose a heuristic, called sparse…
High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular classes of convex ones and concave ones. A long debate has been on whether one class dominates…
Sequencing-based technologies provide an abundance of high-dimensional biological datasets with skewed and zero-inflated measurements. Classification of such data with linear discriminant analysis leads to poor performance due to the…
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…
Supervised dimensionality reduction maps labeled data into a low-dimensional feature space while preserving class discriminability. A common approach is to maximize a statistical measure of dissimilarity between classes in the feature…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…