Projection Predictive Inference for Generalized Linear and Additive Multilevel Models

Alejandro Catalina*, Paul Burkner, Aki Vehtari

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive inference projects its posterior onto a constrained space of a subset of variables. Variable selection is then performed by sequentially adding relevant variables until predictive performance is satisfactory. Previously, projection predictive inference has been demonstrated only for generalized linear models (GLMs) and Gaussian processes (GPs) where it showed superior performance to competing variable selection procedures. In this work, we extend projection predictive inference to support variable and structure selection for generalized linear multilevel models (GLMMs) and generalized additive multilevel models (GAMMs). Our simulative and real-world experiments demonstrate that our method can drastically reduce the model complexity required to reach reference predictive performance and achieve good frequency properties.

Original languageEnglish
Title of host publicationINTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 151
EditorsG Camps-Valls, FJR Ruiz, Valera
PublisherJMLR
Number of pages16
Publication statusPublished - 2022
MoE publication typeA4 Article in a conference publication
EventInternational Conference on Artificial Intelligence and Statistics - Valencia, Spain
Duration: 28 Mar 202230 Mar 2022
Conference number: 25

Publication series

NameProceedings of Machine Learning Research
PublisherJMLR
Volume151
ISSN (Print)2640-3498

Conference

ConferenceInternational Conference on Artificial Intelligence and Statistics
Abbreviated titleAISTATS
Country/TerritorySpain
CityValencia
Period28/03/202230/03/2022

Keywords

  • BAYESIAN VARIABLE SELECTION
  • MAXIMUM-LIKELIHOOD
  • REGULARIZATION
  • HORSESHOE
  • SHRINKAGE

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