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A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting

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https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12047
Original languageEnglish
Pages (from-to)580-605
JournalScandinavian Journal of Statistics
Volume41
Issue number3
Early online date31 Oct 2013
DOIs
Publication statusPublished - Sep 2014

Abstract

This paper examines the use of Dirichlet process mixtures for curve fitting. Animportant modelling aspect in this setting is the choice between constant and covariate-dependentweights. By examining the problem of curve fitting from a predictive perspective, we show theadvantages of using covariate-dependent weights. These advantages are a result of the incorpora-tion of covariate proximity in the latent partition. However, closer examination of the partitionyields further complications, which arise from the vast number of total partitions. To overcome this,we propose to modify the probability law of the random partition to strictly enforce the notion ofcovariate proximity, while still maintaining certain properties of the Dirichlet process. This allowsthe distribution of the partition to depend on the covariate in a simple manner and greatly reducesthe total number of possible partitions, resulting in improved curve fitting and faster computations.Numerical illustrations are presented.

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