Discussion of “ Bayesian Nonparametric Latent Feature Models ” by Zoubin Ghahramani

Ghahramani and colleagues have proposed an interesting class of infinite latent feature (ILF) models. The basic premise of ILF models is that there are infinitely many latent predictors represented in the population, with any particular subject having a finite selection. This is presented as an important advance over models that allow a finite number of latent variables. ILF models are most useful when all but a few of the features are very rare, so that one obtains a sparse representation. Otherwise, one cannot realistically hope to learn about the latent feature structure from the available data. The utility of sparse latent factor models has been compellingly illustrated in large p, small n problems by West (2003) and Carvalho et al. (2006). Given that performance is best when the number of latent features represented in the sample is much less than the sample size, it is not clear whether there are practical advantages to the ILF formulation over finite latent variable models that allow uncertainty in the dimension. For example, Lopes and West (2004) and Dunson (2006) allow the number of latent factors to be unknown using Bayesian methods. That said, it is conceptually appealing to allow additional features to be represented in the data set as additional subjects are added, and it is also appealing to allow partial clustering of subjects. In particular, under an ILF model, subjects can have some features in common, leading to a degree of similarity based on the number of shared features and the