Vinayak Rao

Bridging the gap: transitive associations between items presented in similar temporal contexts.

In episodic memory tasks, associations are formed between items presented close together in time. The temporal context model (TCM) hypothesizes that this contiguity effect is a consequence of shared temporal context rather than temporal proximity per se. Using double-function lists of paired associates (e.g., A-B, B-C) presented in a random order, the authors examined associations between items that were not presented close together in time but that were presented in similar temporal contexts. After learning, across-pair associations fell off with distance in the list, as if subjects had integrated the pairs into a coherent memory structure. Within-pair associations (e.g., A-B) were strongly asymmetric favoring forward transitions; across-pair associations (e.g., A-C) showed no evidence of asymmetry. While this pattern of results presented a stern challenge for a heteroassociative mediated chaining model, TCM provided an excellent fit to the data. These findings suggest that contiguity effects in episodic memory do not reflect direct associations between items but rather a process of binding, encoding, and retrieval of a gradually changing representation of temporal context.

Hierarchical Infinite Divisibility for Multiscale Shrinkage

A new shrinkage-based construction is developed for a compressible vector \mmb x ∈ \BBRn, for cases in which the components of \mmb x are naturally associated with a tree structure. Important examples are when \mmb x corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on the gamma distribution. The gamma distribution is a heavy-tailed distribution that is infinitely divisible, and these characteristics are leveraged within the model. We further demonstrate that the general framework is appropriate for many other types of infinitely divisible heavy-tailed distributions. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.

Data augmentation for models based on rejection sampling

Abstract We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea is a simple scheme to instantiate the rejected proposals preceding each data point. The resulting joint probability over observed and rejected variables can be much simpler than the marginal distribution over the observed variables, which often involves intractable integrals. We consider three problems: modelling flow-cytometry measurements subject to truncation; the Bayesian analysis of the matrix Langevin distribution on the Stiefel manifold; and Bayesian inference for a nonparametric Gaussian process density model. The latter two are instances of doubly-intractable Markov chain Monte Carlo problems, where evaluating the likelihood is intractable. Our experiments demonstrate superior performance over state-of-the-art sampling algorithms for such problems.