Related papers: Subset selection for linear mixed models

Bayesian multinomial logistic regression provides a principled, interpretable approach to multiclass classification, but posterior sampling becomes increasingly expensive as the model dimension grows. Prior work has studied scalability in…

We consider an equivariant approach imposing data-driven bounds for the variances to avoid singular and spurious solutions in maximum likelihood (ML) estimation of clusterwise linear regression models. We investigate its use in the choice…

Large language models (LLMs) have shown strong results on a range of applications, including regression and scoring tasks. Typically, one obtains outputs from an LLM via autoregressive sampling from the model's output distribution. We show…

Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis…

Bayesian Generalized Nonlinear Models (BGNLM) offer a flexible nonlinear alternative to GLM while still providing better interpretability than machine learning techniques such as neural networks. In BGNLM, the methods of Bayesian Variable…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

The Latent Block Model (LBM) is a prominent model-based co-clustering method, returning parametric representations of each block cluster and allowing the use of well-grounded model selection methods. The LBM, while adapted in literature to…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…

This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined…

In many practices, scientists are particularly interested in detecting which of the predictors are truly associated with a multivariate response. It is more accurate to model multiple responses as one vector rather than separating each…

Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…

Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables,…

Variable selection in linear regression settings is a much discussed problem. Best subset selection (BSS) is often considered the intuitive 'gold standard', with its use being restricted only by its NP-hard nature. Alternatives such as the…

We consider linear mixed models in which the observations are grouped. A L1-penalization on the fixed effects coefficients of the log-likelihood obtained by considering the random effects as missing values is proposed. A multicycle ECM…

We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates $C$ includes cluster-level partially observed…

State of the art large language models (LLMs) have shown impressive performance on a variety of benchmark tasks and are increasingly used as components in larger applications, where LLM-based predictions serve as proxies for human…