Related papers: Shrinkage Tuning Parameter Selection in Precision …
One of the common challenges faced by researchers in recent data analysis is missing values. In the context of penalized linear regression, which has been extensively explored over several decades, missing values introduce bias and yield a…
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…
We consider a Gaussian sequence space model $X_{\lambda}=f_{\lambda} + \xi_{\lambda},$ where $\xi $ has a diagonal covariance matrix $\Sigma=\diag(\sigma_\lambda ^2)$. We consider the situation where the parameter vector $(f_{\lambda})$ is…
Model averaging is an important alternative to model selection with attractive prediction accuracy. However, its application to high-dimensional data remains under-explored. We propose a high-dimensional model averaging method via…
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…
Many modern spatial models express the stochastic variation component as a basis expansion with random coefficients. Low rank models, approximate spectral decompositions, multiresolution representations, stochastic partial differential…
Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting,…
We consider the problem of estimating the factors of a rank-$1$ matrix with i.i.d. Gaussian, rank-$1$ measurements that are nonlinearly transformed and corrupted by noise. Considering two prototypical choices for the nonlinearity, we study…
With the increasing size of today's data sets, finding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which…
Sparse estimation of the precision matrix under high-dimensional scaling constitutes a canonical problem in statistics and machine learning. Numerous regression and likelihood based approaches, many frequentist and some Bayesian in nature…
The empirical covariance matrix is not necessarily the best estimator for the population covariance matrix: we describe a simple method which gives better estimates in two examples. The method models the covariance matrix using truncated…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
Many varieties of cross validation would be statistically appealing for the estimation of smoothing and other penalized regression hyperparameters, were it not for the high cost of evaluating such criteria. Here it is shown how to…
Sparse graphical modelling has attained widespread attention across various academic fields. We propose two new graphical model approaches, Gslope and Tslope, which provide sparse estimates of the precision matrix by penalizing its sorted…
The horseshoe prior has proven to be a noteworthy alternative for sparse Bayesian estimation, but as shown in this paper, the results can be sensitive to the prior choice for the global shrinkage hyperparameter. We argue that the previous…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…
We address the subset selection problem for matrices, where the goal is to select a subset of $k$ columns from a "short-and-fat" matrix $X \in \mathbb{R}^{m \times n}$, such that the pseudoinverse of the sampled submatrix has as small…
A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse…
Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…