We describe a latent variable model for supervised dimensionality reduction and distance metric learning. The model discovers linear projections of high dimensional data that shrink the distance between similarly labeled inputs and expand the distance between differently labeled ones. The model’s continuous latent variables locate pairs of examples in a latent space of lower dimensionality. The model differs significantly from classical factor analysis in that the posterior distribution over these latent variables is not always multivariate Gaussian. Nevertheless we show that inference is completely tractable and derive an Expectation-Maximization (EM) algorithm for parameter estimation. We also compare the model to other approaches in distance metric learning. The model’s main advantage is its simplicity: at each iteration of the EM algorithm, the distance metric is re-estimated by solving an unconstrained least-squares problem. Experiments show that these simple updates are highly effective.

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.

Active learning can substantially improve the yield of neurophysiology experiments by adaptively selecting stimuli to probe a neuron's receptive field (RF) in real time. Bayesian active learning methods maintain a posterior distribution over the RF, and select stimuli to maximally reduce posterior entropy on each time step. However, existing methods tend to rely on simple Gaussian priors, and do not exploit uncertainty at the level of hyperparameters when determining an optimal stimulus. This uncertainty can play a substantial role in RF characterization, particularly when RFs are smooth, sparse, or local in space and time. In this paper, we describe a novel framework for active learning under hierarchical, conditionally Gaussian priors. Our algorithm uses sequential Markov Chain Monte Carlo sampling (''particle filtering'' with MCMC) over hyperparameters to construct a mixture-of-Gaussians representation of the RF posterior, and selects optimal stimuli using an approximate infomax criterion. The core elements of this algorithm are parallelizable, making it computationally efficient for real-time experiments. We apply our algorithm to simulated and real neural data, and show that it can provide highly accurate receptive field estimates from very limited data, even with a small number of hyperparameter samples.

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.

We study how to automatically select and adapt multiple abstractions or representations of the world to support model-based reinforcement learning. We address the challenges of transfer learning in heterogeneous environments with varying tasks. We present an efficient, online framework that, through a sequence of tasks, learns a set of relevant representations to be used in future tasks. Without pre-defined mapping strategies, we introduce a general approach to support transfer learning across different state spaces. We demonstrate the potential impact of our system through improved jumpstart and faster convergence to near optimum policy in two benchmark domains.

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 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.

This paper describes a new acoustic model based on variational Gaussian process dynamical system (VGPDS) for phoneme classification. The proposed model overcomes the limitations of the classical HMM in modeling the real speech data, by adopting a nonlinear and nonparametric model. In our model, the GP prior on the dynamics function enables representing the complex dynamic structure of speech, while the GP prior on the emission function successfully models the global dependency over the observations. Additionally, we introduce variance constraint to the original VGPDS for mitigating sparse approximation error of the kernel matrix. The effectiveness of the proposed model is demonstrated with extensive experimental results including parameter estimation, classification performance on the synthetic and benchmark datasets.