Probabilistic graphical models are powerful tools which allow us to formalise our knowledge about the world and reason about its inherent uncertainty. There exist a considerable number of methods for performing inference in probabilistic graphical models; however, they can be computationally costly due to significant time burden and/or storage requirements; or they lack theoretical guarantees of convergence and accuracy when applied to large scale graphical models. To this end, we propose the Universal Marginaliser Importance Sampler (UM-IS) -- a hybrid inference scheme that combines the flexibility of a deep neural network trained on samples from the model and inherits the asymptotic guarantees of importance sampling. We show how combining samples drawn from the graphical model with an appropriate masking function allows us to train a single neural network to approximate any of the corresponding conditional marginal distributions, and thus amortise the cost of inference. We also show that the graph embeddings can be applied for tasks such as: clustering, classification and interpretation of relationships between the nodes. Finally, we benchmark the method on a large graph (>1000 nodes), showing that UM-IS outperforms sampling-based methods by a large margin while being computationally efficient.

In the modern age, rankings data is ubiquitous and it is useful for a variety of applications such as recommender systems, multi-object tracking and preference learning. However, most rankings data encountered in the real world is incomplete, which forbids the direct application of existing modelling tools for complete rankings. Our contribution is a novel way to extend kernel methods for complete rankings to partial rankings, via consistent Monte Carlo estimators of Gram matrices. These Monte Carlo kernel estimators are based on extending kernel mean embeddings to the embedding of a set of full rankings consistent with an observed partial ranking. They form a computationally tractable alternative to previous approaches for partial rankings data. We also present a novel variance reduction scheme based on an antithetic variate construction between permutations to obtain an improved estimator. An overview of the existing kernels and metrics for permutations is also provided.

Latent feature modeling allows capturing the latent structure responsible for generating the observed properties of a set of objects. It is often used to make predictions either for new values of interest or missing information in the original data, as well as to perform data exploratory analysis. However, although there is an extensive literature on latent feature models for homogeneous datasets, where all the attributes that describe each object are of the same (continuous or discrete) nature, there is a lack of work on latent feature modeling for heterogeneous databases. In this paper, we introduce a general Bayesian nonparametric latent feature model suitable for heterogeneous datasets, where the attributes describing each object can be either discrete, continuous or mixed variables. The proposed model presents several important properties. First, it accounts for heterogeneous data while keeping the properties of conjugate models, which allow us to infer the model in linear time with respect to the number of objects and attributes. Second, its Bayesian nonparametric nature allows us to automatically infer the model complexity from the data, i.e., the number of features necessary to capture the latent structure in the data. Third, the latent features in the model are binary-valued variables, easing the interpretability of the obtained latent features in data exploratory analysis. We show the flexibility of the proposed model by solving both prediction and data analysis tasks on several real-world datasets. Moreover, a software package of the GLFM is publicly available for other researcher to use and improve it.

This paper concerns the introduction of a new Markov Chain Monte Carlo scheme for posterior sampling in Bayesian nonparametric mixture models with priors that belong to the general Poisson-Kingman class. We present a novel and compact way of representing the infinite dimensional component of the model such that while explicitly representing this infinite component it has less memory and storage requirements than previous MCMC schemes. We describe comparative simulation results demonstrating the efficacy of the proposed MCMC algorithm against existing marginal and conditional MCMC samplers.