A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting
Article first published online: 31 OCT 2013
© 2013 Board of the Foundation of the Scandinavian Journal of Statistics.
Scandinavian Journal of Statistics
Volume 41, Issue 3, pages 580–605, September 2014
How to Cite
2014), A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting, Scandinavian Journal of Statistics, 41, pages 580–605, doi: 10.1111/sjos.12047, and (
- Issue published online: 11 AUG 2014
- Article first published online: 31 OCT 2013
- Manuscript Accepted: 15 JUL 2013
- Manuscript Revised: 11 MAY 2013
- Manuscript Received: 12 JUL 2012
- Dirichlet process;
- mixture models;
- random partitions;
This paper examines the use of Dirichlet process mixtures for curve fitting. An important modelling aspect in this setting is the choice between constant and covariate-dependent weights. By examining the problem of curve fitting from a predictive perspective, we show the advantages of using covariate-dependent weights. These advantages are a result of the incorporation of covariate proximity in the latent partition. However, closer examination of the partition yields 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 of covariate proximity, while still maintaining certain properties of the Dirichlet process. This allows the distribution of the partition to depend on the covariate in a simple manner and greatly reduces the total number of possible partitions, resulting in improved curve fitting and faster computations. Numerical illustrations are presented.