Related papers: Univariate-Guided Interaction Modeling
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling…
Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…
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…
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…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
This paper introduces a new sparse spatio-temporal structured Gaussian process regression framework for online and offline Bayesian inference. This is the first framework that gives a time-evolving representation of the interdependencies…
We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing…
Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…
We consider the problem of learning the link parameters as well as the structure of a binary-valued pairwise Markov model. Under sparsity assumption, we propose a method based on $l_1$- regularized logistic regression, which estimate…
This paper addresses the problem of inferring sparse causal networks modeled by multivariate auto-regressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network…
Many applications of machine learning involve the analysis of large data frames-matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples-with missing values. Low-rank models, as studied by Udell et al.…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…
This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
Pairwise debiasing is one of the most effective strategies in reducing position bias in learning-to-rank (LTR) models. However, limiting the scope of this strategy, are the underlying assumptions required by many pairwise debiasing…
Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a…
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…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…