Related papers: Generalized Sparse Additive Models
In high-dimensional linear models, sparsity is often exploited to reduce variability and achieve parsimony. Equi-sparsity, where one assumes that predictors can be aggregated into groups sharing the same effects, is an alternative…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
Penalty functions or regularization terms that promote structured solutions to optimization problems are of great interest in many fields. Proposed in this work is a nonconvex structured sparsity penalty that promotes one-sparsity within…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such…
We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…
We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of…
We present the framework of slowly varying regression under sparsity, allowing sparse regression models to exhibit slow and sparse variations. The problem of parameter estimation is formulated as a mixed-integer optimization problem. We…
We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…
Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define…
Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample…
Sparse additive models are families of $d$-variate functions that have the additive decomposition $f^* = \sum_{j \in S} f^*_j$, where $S$ is an unknown subset of cardinality $s \ll d$. In this paper, we consider the case where each…
Generalized additive models (GAMs) play an important role in modeling and understanding complex relationships in modern applied statistics. They allow for flexible, data-driven estimation of covariate effects. Yet researchers often have a…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
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…
In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice…
Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…