Normalization constant in factored probabilistic models (e.g., MRFs, MLNs with soft probabilistic constraints) Z = Sum over exponentially many configurations Hard to compute.

We propose a novel Adaptive Markov Chain Monte Carlo algorithm to compute the partition function. In particular, we show how to accelerate a flat histogram sampling technique by significantly reducing the number of "null moves" in the chain, while maintaining asymptotic convergence properties. Our experiments show that our method converges quickly to highly accurate solutions on a range of benchmark instances, outperforming other state-of-the-art methods such as IJGP, TRW, and Gibbs sampling both in run-time and accuracy. We also show how obtaining a so-called density of states distribution allows for efficient weight learning in Markov Logic theories.

Variational methods have been previously explored as a tractable approximation to Bayesian inference for neural networks. However the approaches proposed so far have only been applicable to a few simple network architectures. This paper introduces an easy-to-implement stochastic variational method (or equivalently, minimum description length loss function) that can be applied to most neural networks. Along the way it revisits several common regularisers from a variational perspective. It also provides a simple pruning heuristic that can both drastically reduce the number of network weights and lead to improved generalisation. Experimental results are provided for a hierarchical multidimensional recurrent neural network applied to the TIMIT speech corpus.

A model of human visual search is proposed. It predicts both response time (RT) and error rates (RT) as a function of image parameters such as target contrast and clutter. The model is an ideal observer, in that it optimizes the Bayes ratio of target present vs target absent. The ratio is computed on the firing pattern of V1/V2 neurons, modeled by Poisson distributions. The optimal mechanism for integrating information over time is shown to be a'soft max' of diffusions, computed over the visual field by'hypercolumns' of neurons that share the same receptive field and have different response properties to image features. An approximation of the optimal Bayesian observer, based on integrating local decisions, rather than diffusions, is also derived; it is shown experimentally to produce very similar predictions to the optimal observer in common psychophysics conditions. A psychophyisics experiment is proposed that may discriminate between which mechanism is used in the human brain.

Neurons in the neocortex code and compute as part of a locally interconnected population. Large-scale multi-electrode recording makes it possible to access these population processes empirically by fitting statistical models to unaveraged data. What statistical structure best describes the concurrent spiking of cells within a local network? We argue that in the cortex, where firing exhibits extensive correlations in both time and space and where a typical sample of neurons still reflects only a very small fraction of the local population, the most appropriate model captures shared variability by a low-dimensional latent process evolving with smooth dynamics, rather than by putative direct coupling. We test this claim by comparing a latent dynamical model with realistic spiking observations to coupled generalised linear spike-response models (GLMs) using cortical recordings. We find that the latent dynamical approach outperforms the GLM in terms of goodness-offit, and reproduces the temporal correlations in the data more accurately. We also compare models whose observations models are either derived from a Gaussian or point-process models, finding that the non-Gaussian model provides slightly better goodness-of-fit and more realistic population spike counts.

Compositional models provide an elegant formalism for representing the visual appearance of highly variable objects. While such models are appealing from a theoretical point of view, it has been difficult to demonstrate that they lead to performance advantages on challenging datasets. Here we develop a grammar model for person detection and show that it outperforms previous high-performance systems on the PASCAL benchmark. Our model represents people using a hierarchy of deformable parts, variable structure and an explicit model of occlusion for partially visible objects. To train the model, we introduce a new discriminative framework for learning structured prediction models from weakly-labeled data.

We introduce HD (or "Hierarchical-Deep") models, a new compositional learning architecture that integrates deep learning models with structured hierarchical Bayesian models. Specifically we show how we can learn a hierarchical Dirichlet process (HDP) prior over the activities of the top-level features in a Deep Boltzmann Machine (DBM). This compound HDP-DBM model learns to learn novel concepts from very few training examples, by learning low-level generic features, high-level features that capture correlations among low-level features, and a category hierarchy for sharing priors over the high-level features that are typical of different kinds of concepts. We present efficient learning and inference algorithms for the HDP-DBM model and show that it is able to learn new concepts from very few examples on CIFAR-100 object recognition, handwritten character recognition, and human motion capture datasets.

We propose a novel class of Bayesian nonparametric models for sequential data called fragmentation-coagulation processes (FCPs).

Variational Message Passing (VMP) is an algorithmic implementation of the Variational Bayes (VB) method which applies only in the special case of conjugate exponential family models. We propose an extension to VMP, which we refer to as Non-conjugate Variational Message Passing (NCVMP) which aims to alleviate this restriction while maintaining modularity, allowing choice in how expectations are calculated, and integrating into an existing message-passing framework: Infer.NET. We demonstrate NCVMP on logistic binary and multinomial regression. In the multinomial case we introduce a novel variational bound for the softmax factor which is tighter than other commonly used bounds whilst maintaining computational tractability.

Many applications in computer vision measure the similarity between images or image patches based on some statistics such as oriented gradients. These are often modeled implicitly or explicitly with a Gaussian noise assumption, leading to the use of the Euclidean distance when comparing image descriptors. In this paper, we show that the statistics of gradient based image descriptors often follow a heavy-tailed distribution, which undermines any principled motivation for the use of Euclidean distances. We advocate for the use of a distance measure based on the likelihood ratio test with appropriate probabilistic models that fit the empirical data distribution. We instantiate this similarity measure with the Gammacompound-Laplace distribution, and show significant improvement over existing distance measures in the application of SIFT feature matching, at relatively low computational cost.