TechTalks from event: ICML 2011
Topic Modeling with Nonparametric Markov TreeA new hierarchical tree-based topic model is developed, based on nonparametric Bayesian techniques. The model has two unique attributes: (i) a child node in the tree may have more than one parent, with the goal of eliminating redundant sub-topics deep in the tree; and (ii) parsimonious sub-topics are manifested, by removing redundant usage of words at multiple scales. The depth and width of the tree are unbounded within the prior, with a retrospective sampler employed to adaptively infer the appropriate tree size based upon the corpus under study. Excellent quantitative results are manifested on five standard data sets, and the inferred tree structure is also found to be highly interpretable.
Infinite SVM: a Dirichlet Process Mixture of Large-margin Kernel MachinesWe present Infinite SVM (iSVM), a Dirichlet process mixture of large-margin kernel machines for multi-way classification. An iSVM enjoys the advantages of both Bayesian nonparametrics in handling the unknown number of mixing components, and large-margin kernel machines in robustly capturing local nonlinearity of complex data. We develop an efficient variational learning algorithm for posterior inference of iSVM, and we demonstrate the advantages of iSVM over Dirichlet process mixture of generalized linear models and other benchmarks on both synthetic and real Flickr image classification datasets.
Piecewise Bounds for Estimating Bernoulli-Logistic Latent Gaussian ModelsBernoulli-logistic latent Gaussian models (bLGMs) are a useful model class, but accurate parameter estimation is complicated by the fact that the marginal likelihood contains an intractable logistic-Gaussian integral. In this work, we propose the use of fixed piecewise linear and quadratic upper bounds to the logistic-log-partition (LLP) function as a way of circumventing this intractable integral. We describe a framework for approximately computing minimax optimal piecewise quadratic bounds, as well a generalized expectation maximization algorithm based on using piecewise bounds to estimate bLGMs. We prove a theoretical result relating the maximum error in the LLP bound to the maximum error in the marginal likelihood estimate. Finally, we present empirical results showing that piecewise bounds can be significantly more accurate than previously proposed variational bounds.
A Spectral Algorithm for Latent Tree Graphical ModelsLatent variable models are powerful tools for probabilistic modeling, and have been successfully applied to various domains, such as speech analysis and bioinformatics. However, parameter learning algorithms for latent variable models have predominantly relied on local search heuristics such as expectation maximization (EM). We propose a fast, local-minimum-free spectral algorithm for learning latent variable models with arbitrary tree topologies, and show that the joint distribution of the observed variables can be reconstructed from the marginals of triples of observed variables irrespective of the maximum degree of the tree. We demonstrate the performance of our spectral algorithm on synthetic and real datasets; for large training sizes, our algorithm performs comparable to or better than EM while being orders of magnitude faster.