We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

Statistical learning and sequential prediction are two different but related formalisms to study the quality of predictions. Mapping out their relations and transferring ideas is an active area of investigation. We provide another piece of the puzzle by showing that an important concept in sequential prediction, the mixability of a loss, has a natural counterpart in the statistical setting, which we call stochastic mixability. Just as ordinary mixability characterizes fast rates for the worst-case regret in sequential prediction, stochastic mixability characterizes fast rates in statistical learning. We show that, in the special case of log-loss, stochastic mixability reduces to a well-known (but usually unnamed) martingale condition, which is used in existing convergence theorems for minimum description length and Bayesian inference. In the case of 0/1-loss, it reduces to the margin condition of Mammen and Tsybakov, and in the case that the model under consideration contains all possible predictors, it is equivalent to ordinary mixability.

A fundamental problem in the analysis of structured relational data like graphs, networks, databases, and matrices is to extract a summary of the common structure underlyingrelations between individual entities. Relational data are typically encoded in the form of arrays; invariance to the ordering of rows and columns corresponds to exchangeable arrays. Results in probability theory due to Aldous, Hoover and Kallenberg show that exchangeable arrays can be represented in terms of a random measurable function which constitutes the natural model parameter in a Bayesian model. We obtain a flexible yet simple Bayesian nonparametric model by placing a Gaussian process prior on the parameter function. Efficient inference utilises elliptical slice sampling combined with a random sparse approximation to the Gaussian process. We demonstrate applications of the model to network data and clarify its relation to models in the literature, several of which emerge as special cases.

An effective strategy to exploit the supervising side information for discovering predictive topic representations is to impose discriminative constraints induced by such information on the posterior distributions under a topic model. This strategy has been adopted by a number of supervised topic models, such as MedLDA, which employs max-margin posterior constraints. However, unlike the likelihood-based supervised topic models, of which posterior inference can be carried out using the Bayes' rule, the max-margin posterior constraints have made Monte Carlo methods infeasible or at least not directly applicable, thereby limited the choice of inference algorithms to be based on variational approximation with strict mean field assumptions. In this paper, we develop two efficient Monte Carlo methods under much weaker assumptions for max-margin supervised topic models based on an importance sampler and a collapsed Gibbs sampler, respectively, in a convex dual formulation. We report thorough experimental results that compare our approach favorably against existing alternatives in both accuracy and efficiency.

Discrete mixtures are used routinely in broad sweeping applications ranging from unsupervised settings to fully supervised multi-task learning. Indeed, finite mixtures and infinite mixtures, relying on Dirichlet processes and modifications, have become a standard tool. One important issue that arises in using discrete mixtures is low separation in the components; in particular, different components can be introduced that are very similar and hence redundant. Such redundancy leads to too many clusters that are too similar, degrading performance in unsupervised learning and leading to computational problems and an unnecessarily complex model in supervised settings. Redundancy can arise in the absence of a penalty on components placed close together even when a Bayesian approach is used to learn the number of components. To solve this problem, we propose a novel prior that generates components from a repulsive process, automatically penalizing redundant components. We characterize this repulsive prior theoretically and propose a Markov chain Monte Carlo sampling algorithm for posterior computation. The methods are illustrated using synthetic examples and an iris data set.

Reinforcement learning (RL) methods based on direct policy search (DPS) have been actively discussed to achieve an efficient approach to complicated Markov decision processes (MDPs). Although they have brought much progress in practical applications of RL, there still remains an unsolved problem in DPS related to model selection for the policy. In this paper, we propose a novel DPS method, {\it weighted likelihood policy search (WLPS)}, where a policy is efficiently learned through the weighted likelihood estimation. WLPS naturally connects DPS to the statistical inference problem and thus various sophisticated techniques in statistics can be applied to DPS problems directly. Hence, by following the idea of the {\it information criterion}, we develop a new measurement for model comparison in DPS based on the weighted log-likelihood.

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, an Indian Buffet-like generative process for network growth, and a simple and efficient Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

We present a new variational inference algorithm for Gaussian process regression withnon-conjugate likelihood functions, with application to a wide array of problems including binary and multi-class classification, and ordinal regression. Our method constructs a concave lower bound that is optimized using an efficient fixed-point updating algorithm. We show that the new algorithm has highly competitive computationalcomplexity, matching that of alternative approximate inference methods. We also prove that the use of concave variational bounds provides stable and guaranteed convergence - a property not available to other approaches. We show empirically for both binary and multi-class classification that our new algorithm converges much faster than existing variational methods, and without any degradation in performance.

We present a novel marginalized particle Gaussian process (MPGP) regression, which provides a fast, accurate online Bayesian filtering framework to model the latent function. Using a state space model established by the data construction procedure, our MPGP recursively filters out the estimation of hidden function values by a Gaussian mixture. Meanwhile, it provides a new online method for training hyperparameters with a number of weighted particles. We demonstrate the estimated performance of our MPGP on both simulated and real large data sets. The results show that our MPGP is a robust estimation algorithm with high computational efficiency, which outperforms other state-of-art sparse GP methods.

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We then develop a time-varying extension of our model, and apply our model to the New York Times lists of weekly bestselling books.