Related papers: Algebraic Sparse Factor Analysis
We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…
Factor analysis is a way to characterize the relationships between many manifest variables in terms of a smaller number of latent variables (i.e., factors). Particularly, in exploratory factor analysis (EFA), researchers consider various…
Factor models are widely used across diverse areas of application for purposes that include dimensionality reduction, covariance estimation, and feature engineering. Traditional factor models can be seen as an instance of linear embedding…
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…
This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
Sparse coding is a proven principle for learning compact representations of images. However, sparse coding by itself often leads to very redundant dictionaries. With images, this often takes the form of similar edge detectors which are…
Cosmological observables rely heavily on summary statistics such as two-point correlation functions. In many practical cases (e.g. the weak-lensing cosmic shear), those correlation functions are estimated from a finite, discrete sample of…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gr\"obner bases and…
We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a…
Dimension reduction algorithms aim to discover latent variables which describe underlying structures in high-dimensional data. Methods such as factor analysis and principal component analysis have the downside of not offering much…
Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular…
Multi-view problems can be faced with latent variable models since they are able to find low-dimensional projections that fairly capture the correlations among the multiple views that characterise each datum. On the other hand,…
In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…
Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of…
We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…