Related papers: Estimating Multiple Precision Matrices with Cluste…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
This paper proposes a general framework to estimate coefficients of generalized polynomial chaos (gPC) used in uncertainty quantification via rotational sparse approximation. In particular, we aim to identify a rotation matrix such that the…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…
We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate,…
We study the problem of estimating multiple predictive functions from a dictionary of basis functions in the nonparametric regression setting. Our estimation scheme assumes that each predictive function can be estimated in the form of a…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
The SparseStep algorithm is presented for the estimation of a sparse parameter vector in the linear regression problem. The algorithm works by adding an approximation of the exact counting norm as a constraint on the model parameters and…
Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…
We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…
We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…