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Model inference, such as model comparison, model checking, and model selection, is an important part of model development. Leave-one-out cross-validation (LOO) is a general approach for assessing the generalizability of a model, but…

Machine Learning · Statistics 2020-08-12 Måns Magnusson , Michael Riis Andersen , Johan Jonasson , Aki Vehtari

Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of…

Applications · Statistics 2020-05-28 Riko Kelter

It is useful to estimate the expected predictive performance of models planned to be used for prediction. We focus on leave-one-out cross-validation (LOO-CV), which has become a popular method for estimating predictive performance of…

Methodology · Statistics 2025-10-29 Tuomas Sivula , Måns Magnusson , Asael Alonzo Matamoros , Aki Vehtari

In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on…

Methodology · Statistics 2022-09-07 Swen Kuh , Lauren Kennedy , Qixuan Chen , Andrew Gelman

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…

Computation · Statistics 2016-08-09 Aki Vehtari , Tommi Mononen , Ville Tolvanen , Tuomas Sivula , Ole Winther

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the…

Computation · Statistics 2023-09-28 Luca Silva , Giacomo Zanella

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the…

Computation · Statistics 2017-12-18 Aki Vehtari , Andrew Gelman , Jonah Gabry

Cross-validation can be used to measure a model's predictive accuracy for the purpose of model comparison, averaging, or selection. Standard leave-one-out cross-validation (LOO-CV) requires that the observation model can be factorized into…

Methodology · Statistics 2021-06-21 Paul-Christian Bürkner , Jonah Gabry , Aki Vehtari

The paper considers the problem of out-of-sample risk estimation under the high dimensional settings where standard techniques such as $K$-fold cross validation suffer from large biases. Motivated by the low bias of the leave-one-out cross…

Methodology · Statistics 2020-02-12 Kamiar Rahnama Rad , Arian Maleki

One of the common goals of time series analysis is to use the observed series to inform predictions for future observations. In the absence of any actual new data to predict, cross-validation can be used to estimate a model's future…

Methodology · Statistics 2020-07-02 Paul-Christian Bürkner , Jonah Gabry , Aki Vehtari

For a large class of regularized models, leave-one-out cross-validation can be efficiently estimated with an approximate leave-one-out formula (ALO). We consider the problem of adjusting hyperparameters so as to optimize ALO. We derive…

Machine Learning · Statistics 2020-11-23 Ryan Burn

In many real-world applications, we are interested in approximating black-box, costly functions as accurately as possible with the smallest number of function evaluations. A complex computer code is an example of such a function. In this…

Computation · Statistics 2022-03-22 Hossein Mohammadi , Peter Challenor , Daniel Williamson , Marc Goodfellow

Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…

Computation · Statistics 2025-07-04 Zhedong Liu , Janet Van Niekerk , Haavard Rue

We present a weighted version of Leave-One-Out (LOO) cross-validation for estimating the Integrated Squared Error (ISE) when approximating an unknown function by a predictor that depends linearly on evaluations of the function over a finite…

Machine Learning · Statistics 2025-05-27 Luc Pronzato , Maria-João Rendas

Recursive partitioning approaches producing tree-like models are a long standing staple of predictive modeling, in the last decade mostly as ``sub-learners'' within state of the art ensemble methods like Boosting and Random Forest. However,…

Machine Learning · Statistics 2015-12-14 Amichai Painsky , Saharon Rosset

The out-of-sample error (OO) is the main quantity of interest in risk estimation and model selection. Leave-one-out cross validation (LO) offers a (nearly) distribution-free yet computationally demanding approach to estimate OO. Recent…

Statistics Theory · Mathematics 2023-10-27 Arnab Auddy , Haolin Zou , Kamiar Rahnama Rad , Arian Maleki

Cross-validation is a common method for estimating the predictive performance of machine learning models. In a data-scarce regime, where one typically wishes to maximize the number of instances used for training the model, an approach…

Methodology · Statistics 2025-03-25 George I. Austin , Itsik Pe'er , Tal Korem

There is a clear need for efficient algorithms to tune hyperparameters for statistical learning schemes, since the commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate.…

Machine Learning · Computer Science 2020-04-07 Luis Miguel Lopez-Ramos , Baltasar Beferull-Lozano

We study the problem of out-of-sample risk estimation in the high dimensional regime where both the sample size $n$ and number of features $p$ are large, and $n/p$ can be less than one. Extensive empirical evidence confirms the accuracy of…

Machine Learning · Statistics 2020-03-05 Kamiar Rahnama Rad , Wenda Zhou , Arian Maleki

Penalized logistic regression methods are frequently used to investigate the relationship between a binary outcome and a set of explanatory variables. The model performance can be assessed by measures such as the concordance statistic…

Methodology · Statistics 2021-01-20 Angelika Geroldinger , Lara Lusa , Mariana Nold , Georg Heinze
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