arXiv subjects

Felix L. Rios

Publications and source records attributed to Felix L. Rios.

5 recordsLinked to original sources

arXiv2025

Exact discovery is polynomial for certain sparse causal Bayesian networks

Causal Bayesian networks are widely used tools for summarising the dependencies between variables and elucidating their putative causal relationships. By restricting the search to trees, for example, learning the optimum from data is polynomial, but this does not guarantee finding the optimal network overall. Without similar restrictions, exact discovery of the optimum is computationally hard in general and no polynomial results are known. The current state-of-the-art approaches are integer linear programming over the underlying space of directed acyclic graphs, dynamic programming and shortest-path searches over the space of topological orders, and constraint programming combining both. For dynamic programming over orders, the computational complexity is known to be exponential base 2 in the number of variables in the network. We demonstrate how to use properties of Bayesian networks to prune the search space and lower the computational cost, while still guaranteeing exact discovery of the provably optimal network. We also include new path-search and divide-and-conquer criteria. Without a priori constraining the search to certain types of networks, the algorithm completes in quadratic time when the optimum is a matching, and in polynomial time when the optimum belongs to any network class with logarithmically-bound largest connected components. In simulation studies we observe the polynomial dependence for sparse networks and that, beyond some critical value, the logarithm of the base grows with the network density. Our approach then out-competes the state-of-the-art at lower densities. These results therefore pave the way for faster exact causal discovery in larger and sparser networks.

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arXiv2023

Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithms

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.

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arXiv2021

Sequential sampling of junction trees for decomposable graphs

The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present two novel stochastic algorithms, which we call the junction-tree expander and junction-tree collapser for sequential sampling of junction trees for decomposable graphs. We show that recursive application of the junction-tree expander, expanding incrementally the underlying graph with one vertex at a time, has full support on the space of junction trees with any given number of underlying vertices. On the other hand, the junction-tree collapser provides a complementary operation for removing vertices in the underlying decomposable graph of a junction tree, while maintaining the junction tree property. A direct application of our suggested algorithms is demonstrated in a sequential-Monte-Carlo setting designed for sampling from distributions on spaces of decomposable graphs. Numerical studies illustrate the utility of the proposed algorithms for combinatorial computations on decomposable graphs and junction trees. All the methods proposed in the paper are implemented in the Python library trilearn.

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arXiv2019

Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods

We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the problem of graph estimation, which in general lacks natural sequential interpretation, can be recast into a sequential setting by proposing a recursive Feynman-Kac model that generates a flow of junction tree distributions over a space of increasing dimensions. We focus on particle McMC methods to provide samples on this space, in particular on particle Gibbs (PG), as it allows for generating McMC chains with global moves on an underlying space of decomposable graphs. To further improve the PG mixing properties, we incorporate a systematic refreshment step implemented through direct sampling from a backward kernel. The theoretical properties of the algorithm are investigated, showing that the proposed refreshment step improves the performance in terms of asymptotic variance of the estimated distribution. The suggested sampling methodology is illustrated through a collection of numerical examples demonstrating high accuracy in Bayesian graph structure learning in both discrete and continuous graphical models.

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arXiv2015

A Prior Distribution over Directed Acyclic Graphs for Sparse Bayesian Networks

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.

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