Related papers: Local shrinkage rules, Levy processes, and regular…

Reconstructing a gene network from high-throughput molecular data is often a challenging task, as the number of parameters to estimate easily is much larger than the sample size. A conventional remedy is to regularize or penalize the model…

Penalization of the likelihood by Jeffreys' invariant prior, or by a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building upon a global-local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are…

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with…

This study proposed an exhaustive stable/reproducible rule-mining algorithm combined to a classifier to generate both accurate and interpretable models. Our method first extracts rules (i.e., a conjunction of conditions about the values of…

In this study, we propose shrinkage methods based on {\it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also,…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

Long-time limit of one-dimensional L\'{e}vy processes weighted and normalized with respect to the exponential functional of two-point local times are studied. The limit processes may vary according to the choice of random clocks.

Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of…

This article introduces two absolutely continuous global-local shrinkage priors to enable stochastic variable selection in the context of high-dimensional matrix exponential spatial specifications. Existing approaches as a means to dealing…

Over-parameterized models like deep nets and random forests have become very popular in machine learning. However, the natural goals of continuity and differentiability, common in regression models, are now often ignored in modern…

We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…

Global-local shrinkage prior has been recognized as useful class of priors which can strongly shrink small signals towards prior means while keeping large signals unshrunk. Although such priors have been extensively discussed under Gaussian…

Several long-time limit theorems of one-dimensional L\'{e}vy processes weighted and normalized by functions of the local time are studied. The long-time limits are taken via certain families of random times, called clocks: exponential…

High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…

This article study the class of distributions obtained by subordinating L\'evy processes and L\'evy bases. To do this we derive properties of a suitable mapping obtained via L\'evy mixing. We show that our results can be used to solve the…

Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It…

We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler…