Related papers: Sparse Factor Analysis for Categorical Data with t…
Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…
A novel approach is presented for group statistical analysis of diffusion weighted MRI datasets through voxelwise Orientation Distribution Functions (ODF). Recent advances in MRI acquisition make it possible to use high quality diffusion…
Sparse PCA is one of the most well-studied problems in high-dimensional statistics. In this problem, we are given samples from a distribution with covariance $\Sigma$, whose top eigenvector $v \in R^d$ is $s$-sparse. Existing sparse PCA…
The state-of-the-art deep neural networks (DNNs) have significant computational and data management requirements. The size of both training data and models continue to increase. Sparsification and pruning methods are shown to be effective…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…
Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
Recently it has become popular to learn sparse Gaussian graphical models (GGMs) by imposing l1 or group l1,2 penalties on the elements of the precision matrix. Thispenalized likelihood approach results in a tractable convex optimization…
We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
Given two data matrices $X$ and $Y$, sparse canonical correlation analysis (SCCA) is to seek two sparse canonical vectors $u$ and $v$ to maximize the correlation between $Xu$ and $Yv$. However, classical and sparse CCA models consider the…
In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: ${\min} \|Lx\|$ subject to ${\min} \|Ax - b\|$, where $L$ is a regularization matrix. Our…
In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
Consider a linear regression model where the design matrix X has n rows and p columns. We assume (a) p is much large than n, (b) the coefficient vector beta is sparse in the sense that only a small fraction of its coordinates is nonzero,…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
This paper introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data…
The performance of sparse matrix computation highly depends on the matching of the matrix format with the underlying structure of the data being computed on. Different sparse matrix formats are suitable for different structures of data.…