We extend the Bayesian skill rating system TrueSkill to infer entire time series of skills of players by smoothing through time instead of filtering. The skill of each participating player, say, every year is represented by a latent skill variable which is affected by the relevant game outcomes that year, and coupled with the skill variables of the previous and subsequent year. Inference in the resulting factor graph is carried out by approximate message passing (EP) along the time series of skills. As before the system tracks the uncertainty about player skills, explicitly models draws, can deal with any number of competing entities and can infer individual skills from team results. We extend the system to estimate player-specific draw margins. Based on these models we present an analysis of the skill curves of important players in the history of chess over the past 150 years. Results include plots of players' lifetime skill development as well as the ability to compare the skills of different players across time. Our results indicate that a) the overall playing strength has increased over the past 150 years, and b) that modelling a player's ability to force a draw provides significantly better predictive power.

Content-based image suggestion (CBIS) targets the recommendation of products based on user preferences on the visual content of images. In this paper, we motivate both feature selection and model order identification as two key issues for a successful CBIS. We propose a generative model in which the visual features and users are clustered into separate classes. We identify the number of both user and image classes with the simultaneous selection of relevant visual features using the message length approach. The goal is to ensure an accurate prediction of ratings for multidimensional non-Gaussian and continuous image descriptors. Experiments on a collected data have demonstrated the merits of our approach.

Bayesian models of multisensory perception traditionally address the problem of estimating an underlying variable that is assumed to be the cause of the two sensory signals. The brain, however, has to solve a more general problem: it also has to establish which signals come from the same source and should be integrated, and which ones do not and should be segregated. In the last couple of years, a few models have been proposed to solve this problem in a Bayesian fashion. One of these has the strength that it formalizes the causal structure of sensory signals. We first compare these models on a formal level. Furthermore, we conduct a psychophysics experiment to test human performance in an auditory-visual spatial localization task in which integration is not mandatory. We find that the causal Bayesian inference model accounts for the data better than other models.

In order to represent state in controlled, partially observable, stochastic dynamical systems, some sort of sufficient statistic for history is necessary. Predictive representations of state (PSRs) capture state as statistics of the future. We introduce a new model of such systems called the "Exponential family PSR," which defines as state the time-varying parameters of an exponential family distribution which models n sequential observations in the future. This choice of state representation explicitly connects PSRs to state-of-the-art probabilistic modeling, which allows us to take advantage of current efforts in high-dimensional density estimation, and in particular, graphical models and maximum entropy models. We present a parameter learning algorithm based on maximum likelihood, and we show how a variety of current approximate inference methods apply. We evaluate the quality of our model with reinforcement learning by directly evaluating the control performance of the model.

A general modeling framework is proposed that unifies nonparametric-Bayesian models, topic-models and Bayesian networks. This class of infinite state Bayes nets (ISBN) can be viewed as directed networks of'hierarchical Dirichlet processes' (HDPs) where the domain of the variables can be structured (e.g.

We present a novel Bayesian model for semi-supervised part-of-speech tagging. Our model extends the Latent Dirichlet Allocation model and incorporates the intuition that words' distributions over tags, p(t w), are sparse. In addition we introduce a model for determining the set of possible tags of a word which captures important dependencies in the ambiguity classes of words. Our model outperforms the best previously proposed model for this task on a standard dataset.

A wide variety of Dirichlet-multinomial'topic' models have found interesting applications in recent years. While Gibbs sampling remains an important method of inference in such models, variational techniques have certain advantages such as easy assessment of convergence, easy optimization without the need to maintain detailed balance, a bound on the marginal likelihood, and sidestepping of issues with topic-identifiability. The most accurate variational technique thus far, namely collapsed variational latent Dirichlet allocation, did not deal with model selection nor did it include inference for hyperparameters. We address both issues by generalizing the technique, obtaining the first variational algorithm to deal with the hierarchical Dirichlet process and to deal with hyperparameters of Dirichlet variables. Experiments show a significant improvement in accuracy.

We introduce a new Bayesian model for hierarchical clustering based on a prior over trees called Kingman's coalescent. We develop novel greedy and sequential Monte Carlo inferences which operate in a bottom-up agglomerative fashion. We show experimentally the superiority of our algorithms over the state-of-the-art, and demonstrate our approach in document clustering and phylolinguistics.

Motivated by stochastic systems in which observed evidence and conditional dependencies between states of the network change over time, and certain quantities of interest (marginal distributions, likelihood estimates etc.) must be updated, we study the problem of adaptive inference in tree-structured Bayesian networks. We describe an algorithm for adaptive inference that handles a broad range of changes to the network and is able to maintain marginal distributions, MAP estimates, and data likelihoods in all expected logarithmic time. We give an implementation of our algorithm and provide experiments that show that the algorithm can yield up to two orders of magnitude speedups on answering queries and responding to dynamic changes over the sum-product algorithm.

We give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints. When combined with a concave upper bound on the entropy, this gives a new variational inference algorithm for probabilistic inference in discrete Markov Random Fields (MRFs). Valid constraints on the marginal polytope are derived through a series of projections onto the cut polytope. As a result, we obtain tighter upper bounds on the log-partition function. We also show empirically that the approximations of the marginals are significantly more accurate when using the tighter outer bounds. Finally, we demonstrate the advantage of the new constraints for finding the MAP assignment in protein structure prediction.