A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting

This paper examines the use of Dirichlet process (DP) mixtures for curve fitting. An important modelling aspect in this setting is the choice between constant or 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 DP. 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.