Nonparametric Bayesian models provide a framework for flexible probabilistic modelling of complex datasets. Unfortunately, Bayesian inference methods often require high-dimensional averages and can be slow to compute, especially with the potentially unbounded representations associated with nonparametric models. We address the challenge of scaling nonparametric Bayesian inference to the increasingly large datasets found in real-world applications, focusing on the case of parallelising inference in the Indian Buffet Process (IBP). Our approach divides a large data set between multiple processors. The processors use message passing to compute likelihoods in an asynchronous, distributed fashion and to propagate statistics about the global Bayesian posterior. This novel MCMC sampler is the first parallel inference scheme for IBP-based models, scaling to datasets orders of magnitude larger than had previously been possible.

We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-complexity algorithms systematically fail when the Markov random field develops long-range correlations. More precisely, this phenomenon appears to be related to the Ising model phase transition (although it does not coincide with it).

Language and image understanding are two major goals of artificial intelligence which can both be conceptually formulated in terms of parsing the input signal into a hierarchical representation. Natural language researchers have made great progress by exploiting the 1D structure of language to design efficient polynomialtime parsing algorithms. By contrast, the two-dimensional nature of images makes it much harder to design efficient image parsers and the form of the hierarchical representations is also unclear. Attempts to adapt representations and algorithms from natural language have only been partially successful. In this paper, we propose a Hierarchical Image Model (HIM) for 2D image parsing which outputs image segmentation and object recognition.

We apply robust Bayesian decision theory to improve both generative and discriminative learners under bias in class proportions in labeled training data, when the true class proportions are unknown. For the generative case, we derive an entropy-based weighting that maximizes expected log likelihood under the worst-case true class proportions. For the discriminative case, we derive a multinomial logistic model that minimizes worst-case conditional log loss. We apply our theory to the modeling of species geographic distributions from presence data, an extreme case of label bias since there is no absence data. On a benchmark dataset, we find that entropy-based weighting offers an improvement over constant estimates of class proportions, consistently reducing log loss on unbiased test data.

The rest of the paper is organized as follows.

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in nonparametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

We introduce the first temporal-difference learning algorithms that converge with smooth value function approximators, such as neural networks. Conventional temporal-difference (TD) methods, such as TD($\lambda$), Q-learning and Sarsa have been used successfully with function approximation in many applications. However, it is well known that off-policy sampling, as well as nonlinear function approximation, can cause these algorithms to become unstable (i.e., the parameters of the approximator may diverge). Sutton et al (2009a,b) solved the problem of off-policy learning with linear TD algorithms by introducing a new objective function, related to the Bellman-error, and algorithms that perform stochastic gradient-descent on this function. In this paper, we generalize their work to nonlinear function approximation. We present a Bellman error objective function and two gradient-descent TD algorithms that optimize it. We prove the asymptotic almost-sure convergence of both algorithms for any finite Markov decision process and any smooth value function approximator, under usual stochastic approximation conditions. The computational complexity per iteration scales linearly with the number of parameters of the approximator. The algorithms are incremental and are guaranteed to converge to locally optimal solutions.

In this paper, we address the question of what kind of knowledge is generally transferable from unlabeled text. We suggest and analyze the semantic correlation of words as a generally transferable structure of the language and propose a new method to learn this structure using an appropriately chosen latent variable model. This semantic correlation contains structural information of the language space and can be used to control the joint shrinkage of model parameters for any specific task in the same space through regularization. In an empirical study, we construct 190 different text classification tasks from a real-world benchmark, and the unlabeled documents are a mixture from all these tasks. We test the ability of various algorithms to use the mixed unlabeled text to enhance all classification tasks. Empirical results show that the proposed approach is a reliable and scalable method for semi-supervised learning, regardless of the source of unlabeled data, the specific task to be enhanced, and the prediction model used.

Statistical evolutionary models provide an important mechanism for describing and understanding the escape response of a viral population under a particular therapy. We present a new hierarchical model that incorporates spatially varying mutation and recombination rates at the nucleotide level. It also maintains sep- arate parameters for treatment and control groups, which allows us to estimate treatment effects explicitly. We use the model to investigate the sequence evolu- tion of HIV populations exposed to a recently developed antisense gene therapy, as well as a more conventional drug therapy. The detection of biologically rele- vant and plausible signals in both therapy studies demonstrates the effectiveness of the method.

The coding of information by neural populations depends critically on the statistical dependencies between neuronal responses. However, there is no simple model that combines the observations that (1) marginal distributions over single-neuron spike counts are often approximately Poisson; and (2) joint distributions over the responses of multiple neurons are often strongly dependent. Here, we show that both marginal and joint properties of neural responses can be captured using Poisson copula models. Copulas are joint distributions that allow random variables with arbitrary marginals to be combined while incorporating arbitrary dependencies between them. Different copulas capture different kinds of dependencies, allowing for a richer and more detailed description of dependencies than traditional summary statistics, such as correlation coefficients. We explore a variety of Poisson copula models for joint neural response distributions, and derive an efficient maximum likelihood procedure for estimating them. We apply these models to neuronal data collected in and macaque motor cortex, and quantify the improvement in coding accuracy afforded by incorporating the dependency structure between pairs of neurons.