Slice sampling in nested IBP

We develop a nonparametric Bayesian method that explores the infinite space of latent features and finds the best subset in the sense of posterior probability. When the data appear in several groups, there should be different measures reflecting the differences between the groups. We formalize this as a nested Indian buffet process (nIBP) by assuming different measures according to the specific types where corresponding set of groups belong to. For efficiently running the Gibbs sampling, slice sampling method is applied to our model with proper choice of stick components. Our contributions here are two fold. First we extended the Indian buffet process model by imposing nested structure above the groups of data sets and hence providing a hierarchically clustering method for objects having multiple features like images in nonparametric approach without imposing class numbers or feature numbers. We followed similar formulation as in nDP model except extending the IBP model instead of the DP model (Rodriguez, Dunson & Gelfand, 2008). Secondly in the computation of the stick breaking expressions, we applied the slice sampling method used in IBP model for properly expanding the stick components (Teh, Gorur & Ghahramani, 2007).