Dependent nonparametric processes extend distributions over measures, such as the Dirichlet process and the beta process, to give distributions over collections of measures, typically indexed by values in some covariate space. Such models are appropr
iate priors when exchangeability assumptions do not hold, and instead we want our model to vary fluidly with some set of covariates. Since the concept of dependent nonparametric processes was formalized by MacEachern [1], there have been a number of models proposed and used in the statistics and machine learning literatures. Many of these models exhibit underlying similarities, an understanding of which, we hope, will help in selecting an appropriate prior, developing new models, and leveraging inference techniques.
Distributions over exchangeable matrices with infinitely many columns, such as the Indian buffet process, are useful in constructing nonparametric latent variable models. However, the distribution implied by such models over the number of features ex
hibited by each data point may be poorly- suited for many modeling tasks. In this paper, we propose a class of exchangeable nonparametric priors obtained by restricting the domain of existing models. Such models allow us to specify the distribution over the number of features per data point, and can achieve better performance on data sets where the number of features is not well-modeled by the original distribution.
A single, stationary topic model such as latent Dirichlet allocation is inappropriate for modeling corpora that span long time periods, as the popularity of topics is likely to change over time. A number of models that incorporate time have been prop
osed, but in general they either exhibit limited forms of temporal variation, or require computationally expensive inference methods. In this paper we propose non-parametric Topics over Time (npTOT), a model for time-varying topics that allows an unbounded number of topics and exible distribution over the temporal variations in those topics popularity. We develop a collapsed Gibbs sampler for the proposed model and compare against existing models on synthetic and real document sets.
Latent feature models are attractive for image modeling, since images generally contain multiple objects. However, many latent feature models ignore that objects can appear at different locations or require pre-segmentation of images. While the trans
formed Indian buffet process (tIBP) provides a method for modeling transformation-invariant features in unsegmented binary images, its current form is inappropriate for real images because of its computational cost and modeling assumptions. We combine the tIBP with likelihoods appropriate for real images and develop an efficient inference, using the cross-correlation between images and features, that is theoretically and empirically faster than existing inference techniques. Our method discovers reasonable components and achieve effective image reconstruction in natural images.
