Related papers: Sparse quadratic classification rules via linear d…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

Matrix-covariate is now frequently encountered in many biomedical researches. It is common to fit conventional statistical models by vectorizing matrix-covariate. This strategy, however, results in a large number of parameters, while the…

We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…

The sparse-group lasso performs both variable and group selection, simultaneously using the strengths of the lasso and group lasso. It has found widespread use in genetics, a field that regularly involves the analysis of high-dimensional…

Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…

Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…

Consider a two-class classification problem where we observe samples $(X_i, Y_i)$ for i = 1, ..., n, $X_i \in R^p$ and $Y_i$ in {0, 1}. Given $Y_i = k$, $X_i$ is assumed to follow a multivariate normal distribution with mean $\mu_k \in R^k$…

Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…

We consider support recovery in the quadratic logistic regression setting - where the target depends on both p linear terms $x_i$ and up to $p^2$ quadratic terms $x_i x_j$. Quadratic terms enable prediction/modeling of higher-order effects…

We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…

Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking…

Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is…

Breast cancer is the most common cancer among women both in developed and developing countries. Early detection and diagnosis of breast cancer may reduce its mortality and improve the quality of life. Computer-aided detection (CADx) and…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…