相关论文: Selection of tuning parameters in bridge regressio…

We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to…

Recent advances in artificial intelligence have been fueled by the development of foundation models such as BERT, GPT, T5, and Vision Transformers. These models are first pretrained on vast and diverse datasets and then adapted to specific…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…

Regression plays a key role in many research areas and its variable selection is a classic and major problem. This study emphasizes cost of predictors to be purchased for future use, when we select a subset of them. Its economic aspect is…

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted…

Adjustable hyperparameters of machine learning models typically impact various key trade-offs such as accuracy, fairness, robustness, or inference cost. Our goal in this paper is to find a configuration that adheres to user-specified limits…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

We address the problem of constructing varying-coefficient models based on basis expansions along with the technique of regularization. A crucial point in our modeling procedure is the selection of smoothing parameters in the regularization…

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Variable selection is an important statistical problem. This problem becomes more challenging when the candidate predictors are of mixed type (e.g. continuous and binary) and impact the response variable in nonlinear and/or non-additive…

In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation…

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix…

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…

For many nonlinear Bayesian state estimation problems, the posterior recursion is not analytically tractable, leading to algorithms that are influenced by numerical approximation errors. These algorithms depend on parameters that affect the…

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…