Variational approaches are often used to approximate intractable posteriors or normalization constants in hierarchical latent variable models. While often effective in practice, it is known that the approximation error can be arbitrarily large. We propose a new class of bounds on the marginal log-likelihood of directed latent variable models. Our approach relies on random projections to simplify the posterior. In contrast to standard variational methods, our bounds are guaranteed to be tight with high probability. We provide a new approach for learning latent variable models based on optimizing our new bounds on the log-likelihood. We demonstrate empirical improvements on benchmark datasets in vision and language for sigmoid belief networks, where a neural network is used to approximate the posterior.
For text analysis, one often resorts to a lossy representation that either completely ignores word order or embeds each word as a low-dimensional dense feature vector. In this paper, we propose convolutional Poisson factor analysis (CPFA) that directly operates on a lossless representation that processes the words in each document as a sequence of high-dimensional one-hot vectors. To boost its performance, we further propose the convolutional Poisson gamma belief network (CPGBN) that couples CPFA with the gamma belief network via a novel probabilistic pooling layer. CPFA forms words into phrases and captures very specific phrase-level topics, and CPGBN further builds a hierarchy of increasingly more general phrase-level topics. For efficient inference, we develop both a Gibbs sampler and a Weibull distribution based convolutional variational auto-encoder. Experimental results demonstrate that CPGBN can extract high-quality text latent representations that capture the word order information, and hence can be leveraged as a building block to enrich a wide variety of existing latent variable models that ignore word order.
Much of the work of problem solving or inference lies in structuring exploration of the system's world to reduce this uncertainty. Two general approaches to uncertainty management have become popular. These approaches--symbolic truth maintenance and numeric belief propagation--have been portrayed as rivals in a sometimes acrimonious debate.