Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates, robustness to over-fitting, and principled ways for tuning hyper-parameters. However the scalability of these models to big datasets remains an active topic of research. We introduce a novel re-parametrisation of variational inference for sparse GP regression and latent variable models that allows for an efficient distributed algorithm. This is done by exploiting the decoupling of the data given the inducing points to re-formulate the evidence lower bound in a Map-Reduce setting. We show that the inference scales well with data and computational resources, while preserving a balanced distribution of the load among the nodes. We further demonstrate the utility in scaling Gaussian processes to big data. We show that GP performance improves with increasing amounts of data in regression (on flight data with 2 million records) and latent variable modelling (on MNIST). The results show that GPs perform better than many common models often used for big data.

We develop collaborative topic Poisson factorization (CTPF), a generative model of articles and reader preferences. CTPF can be used to build recommender systems by learning from reader histories and content to recommend personalized articles of interest. In detail, CTPF models both reader behavior and article texts with Poisson distributions, connecting the latent topics that represent the texts with the latent preferences that represent the readers. This provides better recommendations than competing methods and gives an interpretable latent space for understanding patterns of readership. Further, we exploit stochastic variational inference to model massive real-world datasets. For example, we can fit CPTF to the full arXiv usage dataset, which contains over 43 million ratings and 42 million word counts, within a day. We demonstrate empirically that our model outperforms several baselines, including the previous state-of-the art approach.

Lifted inference algorithms for probabilistic first-order logic frameworks such as Markov logic networks (MLNs) have received significant attention in recent years. These algorithms use so called lifting rules to identify symmetries in the first-order representation and reduce the inference problem over a large probabilistic model to an inference problem over a much smaller model. In this paper, we present two new lifting rules, which enable fast MAP inference in a large class of MLNs. Our first rule uses the concept of single occurrence equivalence class of logical variables, which we define in the paper. The rule states that the MAP assignment over an MLN can be recovered from a much smaller MLN, in which each logical variable in each single occurrence equivalence class is replaced by a constant (i.e., an object in the domain of the variable). Our second rule states that we can safely remove a subset of formulas from the MLN if all equivalence classes of variables in the remaining MLN are single occurrence and all formulas in the subset are tautology (i.e., evaluate to true) at extremes (i.e., assignments with identical truth value for groundings of a predicate). We prove that our two new rules are sound and demonstrate via a detailed experimental evaluation that our approach is superior in terms of scalability and MAP solution quality to the state of the art approaches.

We present max-margin Bayesian clustering (BMC), a general and robust framework that incorporates the max-margin criterion into Bayesian clustering models, as well as two concrete models of BMC to demonstrate its flexibility and effectiveness in dealing with different clustering tasks. The Dirichlet process max-margin Gaussian mixture is a nonparametric Bayesian clustering model that relaxes the underlying Gaussian assumption of Dirichlet process Gaussian mixtures by incorporating max-margin posterior constraints, and is able to infer the number of clusters from data. We further extend the ideas to present max-margin clustering topic model, which can learn the latent topic representation of each document while at the same time cluster documents in the max-margin fashion. Extensive experiments are performed on a number of real datasets, and the results indicate superior clustering performance of our methods compared to related baselines.

We develop an automated variational method for approximate inference in Gaussian process (GP) models whose posteriors are often intractable. Using a mixture of Gaussians as the variational distribution, we show that (i) the variational objective and its gradients can be approximated efficiently via sampling from univariate Gaussian distributions and (ii) the gradients wrt the GP hyperparameters can be obtained analytically regardless of the model likelihood. We further propose two instances of the variational distribution whose covariance matrices can be parametrized linearly in the number of observations. These results allow gradientbased optimization to be done efficiently in a black-box manner. Our approach is thoroughly verified on five models using six benchmark datasets, performing as well as the exact or hard-coded implementations while running orders of magnitude faster than the alternative MCMC sampling approaches. Our method can be a valuable tool for practitioners and researchers to investigate new models with minimal effort in deriving model-specific inference algorithms.

We consider the problem of inferring direct neural network connections from Calcium imaging time series. Inverse covariance estimation has proven to be a fast and accurate method for learning macro-and micro-scale network connectivity in the brain and in a recent Kaggle Connectomics competition inverse covariance was the main component of several top ten solutions, including our own and the winning team's algorithm. However, the accuracy of inverse covariance estimation is highly sensitive to signal preprocessing of the Calcium fluorescence time series. Furthermore, brute force optimization methods such as grid search and coordinate ascent over signal processing parameters is a time intensive process, where learning may take several days and parameters that optimize one network may not generalize to networks with different size and parameters. In this paper we show how inverse covariance estimation can be dramatically improved using a simple convolution filter prior to applying sample covariance. Furthermore, these signal processing parameters can be learned quickly using a supervised optimization algorithm. In particular, we maximize a binomial log-likelihood loss function with respect to a convolution filter of the time series and the inverse covariance regularization parameter. Our proposed algorithm is relatively fast on networks the size of those in the competition (1000 neurons), producing AUC scores with similar accuracy to the winning solution in training time under 2 hours on a cpu. Prediction on new networks of the same size is carried out in less than 15 minutes, the time it takes to read in the data and write out the solution.

The Indian Buffet Process is a versatile statistical tool for modeling distributions over binary matrices. We provide an efficient spectral algorithm as an alternative to costly Variational Bayes and sampling-based algorithms. We derive a novel tensorial characterization of the moments of the Indian Buffet Process proper and for two of its applications. We give a computationally efficient iterative inference algorithm, concentration of measure bounds, and reconstruction guarantees. Our algorithm provides superior accuracy and cheaper computation than comparable Variational Bayesian approach on a number of reference problems.

Bayes-adaptive planning offers a principled solution to the explorationexploitation trade-off under model uncertainty. It finds the optimal policy in belief space, which explicitly accounts for the expected effect on future rewards of reductions in uncertainty. However, the Bayes-adaptive solution is typically intractable in domains with large or continuous state spaces. We present a tractable method for approximating the Bayes-adaptive solution by combining simulationbased search with a novel value function approximation technique that generalises appropriately over belief space. Our method outperforms prior approaches in both discrete bandit tasks and simple continuous navigation and control tasks.

Submodular optimization has found many applications in machine learning and beyond. We carry out the first systematic investigation of inference in probabilistic models defined through submodular functions, generalizing regular pairwise MRFs and Determinantal Point Processes.

We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab prior; the latter makes it possible to perform feature selection. One important advantage of our approach is that it is amenable to powerful Bayesian computational tools. We derive in particular a Sequential Monte Carlo algorithm, as an efficient method which may be used as a gold standard, and an Expectation-Propagation algorithm, as a much faster but approximate method. We also extend our method to a class of non-linear score functions, essentially leading to a nonparametric procedure, by considering a Gaussian process prior.