Felix L. Rios

Felix Leopoldo Rios, Alex Markham, Liam Solus

Several approaches to graphically representing context-specific relations among jointly distributed categorical variables have been proposed, along with structure learning algorithms. While existing optimization-based methods have limited scalability due to the large number of context-specific models, the constraint-based methods are more prone to error than even constraint-based directed acyclic graph learning algorithms since more relations must be tested. We present an algorithm for learning context-specific models that scales to hundreds of variables. Scalable learning is achieved through a combination of an order-based Markov chain Monte-Carlo search and a novel, context-specific sparsity assumption that is analogous to those typically invoked for directed acyclic graphical models. Unlike previous Markov chain Monte-Carlo search methods, our Markov chain is guaranteed to have the true posterior of the variable orderings as the stationary distribution. To implement the method, we solve a first case of an open problem recently posed by Alon and Balogh. Future work solving increasingly general instances of this problem would allow our methods to learn increasingly dense models. The method is shown to perform well on synthetic data and real world examples, in terms of both accuracy and scalability.

Felix L. Rios, Giusi Moffa, Jack Kuipers

Describing the relationship between the variables in a study domain and modelling the data generating mechanism is a fundamental problem in many empirical sciences. Probabilistic graphical models are one common approach to tackle the problem. Learning the graphical structure for such models is computationally challenging and a fervent area of current research with a plethora of algorithms being developed. To facilitate the benchmarking of different methods, we present a novel Snakemake workflow, called Benchpress for producing scalable, reproducible, and platform-independent benchmarks of structure learning algorithms for probabilistic graphical models. Benchpress is interfaced via a simple JSON-file, which makes it accessible for all users, while the code is designed in a fully modular fashion to enable researchers to contribute additional methodologies. Benchpress currently provides an interface to a large number of state-of-the-art algorithms from libraries such as BDgraph, BiDAG, bnlearn, causal-learn, gCastle, GOBNILP, pcalg, r.blip, scikit-learn, TETRAD, and trilearn as well as a variety of methods for data generating models and performance evaluation. Alongside user-defined models and randomly generated datasets, the workflow also includes a number of standard datasets and graphical models from the literature, which may be included in a benchmarking study. We demonstrate the applicability of this workflow for learning Bayesian networks in five typical data scenarios. The source code and documentation is publicly available from http://benchpressdocs.readthedocs.io.

Tatjana Pavlenko, Felix Leopoldo Rios

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. An explicit evaluation of the model probabilities is well known to be infeasible. To address this issue, we consider the particle Gibbs strategy of Olsson et al. (2018b) for posterior sampling from decomposable graphical models which utilizes the Christmas tree algorithm of Olsson et al. (2018a) as proposal kernel. We also derive a strong hyper Markov law which we call the hyper normal Wishart law that allow to perform the resultant Bayesian calculations locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.

Felix L. Rios, John M. Noble, Timo J. T. Koski

The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into categories (or blocks); the blocks have a natural ordering. The presence of a relationship between two objects is denoted by an arrow, from the object of lower category to the object of higher category. The models considered here were introduced in Kemp et al. (2004) for relational data and extended to multivariate data in Mansinghka et al. (2006). The prior over graph structures presented here has an explicit formula. The number of nodes in each layer of the graph follow a Hoppe Ewens urn model. We consider the situation where the nodes of the graph represent random variables, whose joint probability distribution factorises along the DAG. We describe Monte Carlo schemes for finding the optimal aposteriori structure given a data matrix and compare the performance with Mansinghka et al. (2006) and also with the uniform prior.