Related papers: Sparsity of the Main Effect Matrix Factor Model
We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…
Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…
Causal representation learning aims at identifying high-level causal variables from perceptual data. Most methods assume that all latent causal variables are captured in the high-dimensional observations. We instead consider a partially…
By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection…
Latent variable models provide a powerful framework for incorporating and inferring unobserved factors in observational data. In causal inference, they help account for hidden factors influencing treatment or outcome, thereby addressing…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…
We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…
This paper studies the problem of estimating a large coefficient matrix in a multiple response linear regression model when the coefficient matrix could be both of low rank and sparse in the sense that most nonzero entries concentrate on a…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…
Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. This paper develops a sparse additive model focused on estimation of treatment effect-modification with simultaneous…
Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically…
In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…