DeepAI AI Chat
Log In Sign Up

Scalable inference for crossed random effects models

03/26/2018
by   Omiros Papaspiliopoulos, et al.
Universitat Pompeu Fabra
Università Bocconi
University of Warwick
0

We analyze the complexity of Gibbs samplers for inference in crossed random effect models used in modern analysis of variance. We demonstrate that for certain designs the plain vanilla Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data. We thus propose a simple modification leading to a collapsed Gibbs sampler that is provably scalable. Although our theory requires some balancedness assumptions on the data designs, we demonstrate in simulated and real datasets that the rates it predicts match remarkably the correct rates in cases where the assumptions are violated. We also show that the collapsed Gibbs sampler, extended to sample further unknown hyperparameters, outperforms significantly alternative state of the art algorithms.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/07/2021

Convergence rate of a collapsed Gibbs sampler for crossed random effects models

In this paper, we analyze the convergence rate of a collapsed Gibbs samp...
04/06/2017

Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models

The Gibbs sampler is a particularly popular Markov chain used for learni...
07/21/2020

Backfitting for large scale crossed random effects regressions

Regression models with crossed random effect error models can be very ex...
04/29/2020

On the convergence complexity of Gibbs samplers for a family of simple Bayesian random effects models

The emergence of big data has led to so-called convergence complexity an...
10/29/2020

Rates of convergence for Gibbs sampling in the analysis of almost exchangeable data

Motivated by de Finetti's representation theorem for partially exchangea...
11/15/2021

Amended Gibbs samplers for Cosmic Microwave Background power spectrum estimation

We study different variants of the Gibbs sampler algorithm from the pers...
04/19/2023

Blocked Gibbs sampler for hierarchical Dirichlet processes

Posterior computation in hierarchical Dirichlet process (HDP) mixture mo...