Related papers: Simultaneous Best Subset Selection and Dimension R…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
In this paper, we consider a recursive estimation problem for linear regression where the signal to be estimated admits a sparse representation and measurement samples are only sequentially available. We propose a convergent parallel…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
We study an estimator with a convex formulation for recovery of low-rank matrices from rank-one projections. Using initial estimates of the factors of the target $d_1\times d_2$ matrix of rank-$r$, the estimator admits a practical…
This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…
The scalability of statistical estimators is of increasing importance in modern applications. One approach to implementing scalable algorithms is to compress data into a low dimensional latent space using dimension reduction methods. In…
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…
In large-scale modern data analysis, first-order optimization methods are usually favored to obtain sparse estimators in high dimensions. This paper performs theoretical analysis of a class of iterative thresholding based estimators defined…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
We propose a novel sparse preference learning/ranking algorithm. Our algorithm approximates the true utility function by a weighted sum of basis functions using the squared loss on pairs of data points, and is a generalization of the kernel…
We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a…
Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high…
In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…