Related papers: Exploring Sparsity in Multi-class Linear Discrimin…
We revisit vertex discriminant analysis (VDA) from the perspective of proximal distance algorithms. By specifying sparsity sets as constraints that directly control the number of active features, VDA is able to fit multiclass classifiers…
We develop a class of rules spanning the range between quadratic discriminant analysis and naive Bayes, through a path of sparse graphical models. A group lasso penalty is used to introduce shrinkage and encourage a similar pattern of…
Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…
By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…
This paper proposes a convex formulation for sparse multicategory linear discriminant analysis and then extend it to the distributed setting when data are stored across multiple sites. The key observation is that for the purpose of…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…
This paper introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. The sparse-group LASSO estimator can take advantage of such time series data structures and…
Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…
The aim of this paper is to provide a comprehensive introduction for the study of L1-penalized estimators in the context of dependent observations. We define a general $\ell_{1}$-penalized estimator for solving problems of stochastic…
Sparse prediction with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection…
We explore estimation and forecast accuracy for sparse linear models, focusing on scenarios where both predictors and errors carry serial correlations. We establish a clear link between predictor serial correlation and the performance of…
Recent results have proven the minimax optimality of LASSO and related algorithms for noisy linear regression. However, these results tend to rely on variance estimators that are inefficient or optimizations that are slower than LASSO…
We propose a novel sparsity model for distributed compressed sensing in the multiple measurement vectors (MMV) setting. Our model extends the concept of row-sparsity to allow more general types of structured sparsity arising in a variety of…
For high-dimensional omics data, sparsity-inducing regularization methods such as the Lasso are widely used and often yield strong predictive performance, even in settings when the assumption of sparsity is likely violated. We demonstrate…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
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…
We review recent results for high-dimensional sparse linear regression in the practical case of unknown variance. Different sparsity settings are covered, including coordinate-sparsity, group-sparsity and variation-sparsity. The emphasis is…
The multi-label classification framework, where each observation can be associated with a set of labels, has generated a tremendous amount of attention over recent years. The modern multi-label problems are typically large-scale in terms of…
Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation…