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Cross-Validation: What Does It Estimate and How Well Does It Do It?

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2024年第546期119卷 1434-1445页

作者： Bates, Stephen Hastie, Trevor Tibshirani, Robert Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Univ Calif Berkeley EECS Berkeley CA 94720 USA Stanford Univ Dept Stat & Biomed Data Sci Stanford CA USA Stanford Univ Dept Biomed Data Sci & Stat Stanford CA USA

Cross-validation is a widely used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit to the training data. We prove that this is not the case for the linear model fit by ordinary least squares;rather it estimates the average prediction error of models fit on other unseen training sets drawn from the same population. We further show that this phenomenon occurs for most popular estimates of prediction error, including data splitting, bootstrapping, and Mallow's C-p. Next, the standard confidence intervals for prediction error derived from cross-validation may have coverage far below the desired level. Because each data point is used for both training and testing, there are correlations among the measured accuracies for each fold, and so the usual estimate of variance is too small. We introduce a nested cross-validation scheme to estimate this variance more accurately, and show empirically that this modification leads to intervals with approximately correct coverage in many examples where traditional cross-validation intervals fail. Lastly, our analysis also shows that when producing confidence intervals for prediction accuracy with simple data splitting, one should not refit the model on the combined data, since this invalidates the confidence intervals. for this article are available online.

关键词： Bootstrap/resampling computationally intensive methods Cross-validation Goodness-of-fit methods

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Template Independent Component Analysis with Spatial Priors for Accurate Subject-Level Brain Network Estimation and Inference

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2023年第2期32卷 413-433页

作者： Mejia, Amanda F. Bolin, David Yue, Yu Ryan Wang, Jiongran Caffo, Brian S. Nebel, Mary Beth Indiana Univ Dept Stat Bloomington IN 47408 USA King Abdullah Univ Sci & Technol CEMSE Div Stat Program Thuwal Saudi Arabia CUNY Baruch Coll Paul H Chook Dept Informat Syst & Stat New York NY 10021 USA Johns Hopkins Univ Dept Biostat Baltimore MD 21205 USA Kennedy Krieger Inst eCtr Neurodev & Imaging Res Baltimore MD USA Johns Hopkins Univ Dept Neurol Baltimore MD 21218 USA

Independent component analysis is commonly applied to functional magnetic resonance imaging (fMRI) data to extract independent components (ICs) representing functional brain networks. While ICA produces reliable group-level estimates, single-subject ICA often produces noisy results. Template ICA is a hierarchical ICA model using empirical population priors to produce more reliable subject-level estimates. However, this and other hierarchical ICA models assume unrealistically that subject effects are spatially independent. Here, we propose spatial template ICA (stICA), which incorporates spatial priors into the template ICA framework for greater estimation efficiency. Additionally, the joint posterior distribution can be used to identify brain regions engaged in each network using an excursions set approach. By leveraging spatial dependencies and avoiding massive multiple comparisons, stICA has high power to detect true effects. We derive an efficient expectation-maximization algorithm to obtain maximum likelihood estimates of the model parameters and posterior moments of the latent fields. Based on analysis of simulated data and fMRI data from the Human Connectome Project, we find that stICA produces estimates that are more accurate and reliable than benchmark approaches, and identifies larger and more reliable areas of engagement. The algorithm is computationally tractable, achieving convergence within 12 hr for whole-cortex fMRI analysis. Supplementary materials for this article are available online.

关键词： Bayesian methods computationally intensive methods Expectation-maximization Neuroimaging Spatial analysis

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An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models

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Stat 2023年第1期12卷

作者： Timonen, Juho Siccha, Nikolas Bales, Ben Lähdesmäki, Harri Vehtari, Aki Department of Computer Science Aalto University Espoo 02150 Finland Earth Institute University of Columbia New York 10025 NY United States

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation error inherently biases statistical inference results, but the amount of this bias is generally unknown and often ignored in Bayesian parameter inference. We propose a computationally efficient method for verifying the reliability of posterior inference for such models, when the inference is performed using Markov chain Monte Carlo methods. We validate the efficiency and reliability of our workflow in experiments using simulated and real data and different ODE solvers. We highlight problems that arise with commonly used adaptive ODE solvers and propose robust and effective alternatives, which, accompanied by our workflow, can now be taken into use without losing reliability of the inferences. © 2023 The Authors. Stat published by John Wiley & Sons Ltd.

关键词： Bayesian methods computationally intensive methods Markov chain Monte Carlo statistical computing statistical inference

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A comparison of logistic regression models with alternative machine learning methods to predict the risk of in-hospital mortality in emergency medical admissions via external validation

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HEALTH INFORMATICS JOURNAL 2020年第1期26卷 34-44页

作者： Faisal, Muhammad Scally, Andy Howes, Robin Beatson, Kevin Richardson, Donald Mohammed, Mohammed A. Univ Bradford Bradford W Yorkshire England Bradford Inst Hlth Res Bradford W Yorkshire England Northern Lincolnshire & Goole Hosp NHS Fdn Trust Scunthorpe England York Teaching Hosp NHS Fdn Trust York N Yorkshire England

We compare the performance of logistic regression with several alternative machine learning methods to estimate the risk of death for patients following an emergency admission to hospital based on the patients' first blood test results and physiological measurements using an external validation approach. We trained and tested each model using data from one hospital (n = 24,696) and compared the performance of these models in data from another hospital (n = 13,477). We used two performance measures - the calibration slope and area under the receiver operating characteristic curve. The logistic model performed reasonably well - calibration slope: 0.90, area under the receiver operating characteristic curve: 0.847 compared to the other machine learning methods. Given the complexity of choosing tuning parameters of these methods, the performance of logistic regression with transformations for in-hospital mortality prediction was competitive with the best performing alternative machine learning methods with no evidence of overfitting.

关键词： classification and prediction computationally intensive methods databases and data mining electronic health records modelling healthcare services statistical modelling

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Template Independent Component Analysis: Targeted and Reliable Estimation of Subject-level Brain Networks Using Big Data Population Priors

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2020年第531期115卷 1151-1177页

作者： Mejia, Amanda F. Nebel, Mary Beth Wang, Yikai Caffo, Brian S. Guo, Ying Indiana Univ Dept Stat Bloomington IN 47408 USA Kennedy Krieger Inst Ctr Neurodev & Imaging Res Baltimore MD USA Johns Hopkins Univ Dept Neurol Baltimore MD 21218 USA Emory Univ Rollins Sch Publ Hlth Dept Biostat & Bioinformat Atlanta GA 30322 USA Johns Hopkins Univ Dept Biostat Baltimore MD 21205 USA

Large brain imaging databases contain a wealth of information on brain organization in the populations they target, and on individual variability. While such databases have been used to study group-level features of populations directly, they are currently underutilized as a resource to inform single-subject analysis. Here, we propose leveraging the information contained in large functional magnetic resonance imaging (fMRI) databases by establishing population priors to employ in an empirical Bayesian framework. We focus on estimation of brain networks as source signals in independent component analysis (ICA). We formulate a hierarchical "template" ICA model where source signals-including known population brain networks and subject-specific signals-are represented as latent variables. For estimation, we derive an expectation-maximization (EM) algorithm having an explicit solution. However, as this solution is computationally intractable, we also consider an approximate subspace algorithm and a faster two-stage approach. Through extensive simulation studies, we assess performance of both methods and compare with dual regression, a popular but ad-hoc method. The two proposed algorithms have similar performance, and both dramatically outperform dual regression. We also conduct a reliability study utilizing the Human Connectome Project and find that template ICA achieves substantially better performance than dual regression, achieving 75-250% higher intra-subject reliability. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

关键词： Applications and case studies Bayesian methods computationally intensive methods Expectation-maximization Neuroimaging

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Acceleration of hidden Markov model fitting using graphical processing units, with application to low-frequency tremor classification

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COMPUTERS & GEOSCIENCES 2021年 156卷 104902-104902页

作者： Stoltz, Marnus Stoltz, Gene Obara, Kazushige Wang, Ting Bryant, David Univ Otago Dept Math & Stat Otago New Zealand Council Sci & Ind Res South Africa Pretoria South Africa Univ Tokyo Earthquake Res Inst Tokyo Japan

Hidden Markov models (HMMs) are general purpose models for time-series data widely used across the sciences because of their flexibility and elegance. Fitting HMMs can often be computationally demanding and time consuming, particularly when the number of hidden states is large or the Markov chain itself is long. Here we introduce a new Graphical Processing Unit (GPU)-based algorithm designed to fit long-chain HMMs, applying our approach to a model for low-frequency tremor events. Even on a modest GPU, our implementation resulted in an increase in speed of several orders of magnitude compared to the standard single processor algorithm. This permitted a full Bayesian inference of uncertainty related to model parameters and forecasts based on posterior predictive distributions. Similar improvements would be expected for HMM models given large number of observations and moderate state spaces (< 80 states with current hardware). We discuss the model, general GPU architecture and algorithms and report performance of the method on a tremor dataset from the Shikoku region, Japan. The new approach led to improvements in both computational performance and forecast accuracy, compared to existing frequentist methodology.

关键词： Bayesian methods computationally intensive methods Low-frequency tremors Shikoku region Shikoku region Tremor forecast

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On the error in Laplace approximations of high-dimensional integrals

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STAT 2021年第1期10卷

作者： Ogden, Helen Univ Southampton Sch Math Sci Southampton S017 1BJ Hants England

Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we provide a new result on the size of the error in first- and higher-order Laplace approximations, in terms of the rate of growth of information about each of the integrated variables. By contrast with many existing results, we allow for variation in the rate of information growth among the different integrated variables. We apply our results to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models.

关键词： Bayesian methods computationally intensive methods generalized linear models large sample theory

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Low-rank approximation for smoothing spline via eigensystem truncation

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STAT 2021年第1期10卷

作者： Xu, Danqing Wang, Yuedong Univ Calif Santa Barbara Dept Stat & Appl Probabil Santa Barbara CA 93106 USA

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low-rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast and compare favourably against existing methods.

关键词： algorithms computationally intensive methods large and complex data sets nonparametric regression smoothing statistical computing

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Likelihood-based inference for generalized linear mixed models: Inference with the R package glmm

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STAT 2021年第1期10卷

作者： Knudson, Christina Benson, Sydney Geyer, Charles Jones, Galin Univ St Thomas Dept Math OSS 2012115 Summit Ave St Paul MN 55105 USA Univ Minnesota Div Biostat Minneapolis MN 55455 USA Univ Minnesota Sch Stat Minneapolis MN 55455 USA

The R package glmm enables likelihood-based inference for generalized linear mixed models with a canonical link. No other publicly available software accurately conducts likelihood-based inference for generalized linear mixed models with crossed random effects. glmm is able to do so by approximating the likelihood function and two derivatives using importance sampling. The importance sampling distribution is an essential piece of Monte Carlo likelihood approximation, and developing a good one is the main challenge in implementing it. The package glmm uses the data to tailor the importance sampling distribution and is constructed to ensure finite Monte Carlo standard errors. In the context of the generalized linear mixed model, the salamander model with crossed random effects has become a benchmark example. We use this model to illustrate the complexities of the likelihood function and to demonstrate the use of the R package glmm.

关键词： computationally intensive methods generalized linear models likelihood regression statistical inference statistical modelling

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Efficient Algorithms for Bayesian Nearest Neighbor Gaussian Processes

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2019年第2期28卷 401-414页

作者： Finley, Andrew O. Datta, Abhirup Cook, Bruce D. Morton, Douglas C. Andersen, Hans E. Banerjee, Sudipto Michigan State Univ E Lansing MI 48824 USA Johns Hopkins Univ Baltimore MD USA NASA Washington DC 20546 USA US Forest Serv Washington DC 20250 USA Univ Calif Los Angeles Los Angeles CA 90024 USA

We consider alternate formulations of recently proposed hierarchical nearest neighbor Gaussian process (NNGP) models for improved convergence, faster computing time, and more robust and reproducible Bayesian inference. Algorithms are defined that improve CPU memory management and exploit existing high-performance numerical linear algebra libraries. Computational and inferential benefits are assessed for alternate NNGP specifications using simulated datasets and remotely sensed light detection and ranging data collected over the U.S. Forest Service Tanana Inventory Unit (TIU) in a remote portion of Interior Alaska. The resulting data product is the first statistically robust map of forest canopy for the TIU. Supplemental materials for this article are available online.

关键词： Bayesian methods computationally intensive methods Spatial analysis Statistical computing Stochastic processes

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