Bayesian Network Constraint-Based Structure Learning Algorithms: Parallel and Optimised Implementations in the bnlearn R Package (1406.7648v2)

Abstract: It is well known in the literature that the problem of learning the structure of Bayesian networks is very hard to tackle: its computational complexity is super-exponential in the number of nodes in the worst case and polynomial in most real-world scenarios. Efficient implementations of score-based structure learning benefit from past and current research in optimisation theory, which can be adapted to the task by using the network score as the objective function to maximise. This is not true for approaches based on conditional independence tests, called constraint-based learning algorithms. The only optimisation in widespread use, backtracking, leverages the symmetries implied by the definitions of neighbourhood and Markov blanket. In this paper we illustrate how backtracking is implemented in recent versions of the bnlearn R package, and how it degrades the stability of Bayesian network structure learning for little gain in terms of speed. As an alternative, we describe a software architecture and framework that can be used to parallelise constraint-based structure learning algorithms (also implemented in bnlearn) and we demonstrate its performance using four reference networks and two real-world data sets from genetics and systems biology. We show that on modern multi-core or multiprocessor hardware parallel implementations are preferable over backtracking, which was developed when single-processor machines were the norm.

Parallel and Optimized Implementations of Bayesian Network Structure Learning in bnlearn

The paper authored by Marco Scutari presents a crucial discussion on the computational challenges associated with Bayesian network (BN) structure learning. It explores the implementation of parallel and optimized algorithms for constraint-based structure learning within the \pkg{bnlearn} R package. Bayesian networks are significant due to their ability to model complex dependencies through directed acyclic graphs (DAGs), yet learning these structures from data is computationally intensive, particularly when involving a large number of variables.

Constraint-Based Structure Learning

The paper addresses the challenges in constraint-based approach, which unlike score-based learning, does not readily lend itself to optimizations beyond basic backtracking. Constraint-based methods employ conditional independence tests to infer network structure by identifying dependencies and independencies among variables. These methods historically required sequential processing, which limits scalability in large datasets typically found in genetics and systems biology.

Limitations of Backtracking

Backtracking, the main optimization previously in use, is not without its drawbacks. While it can reduce the number of required independence tests by leveraging symmetry in neighborhood constructions, it introduces potential for errors and inconsistencies based solely on variable ordering, as demonstrated by increased variability in simulation results with reordered data. Its benefits in terms of speed are marginal and do not outweigh these downsides in modern multi-core computing environments.

Parallelization Framework and Implementation

Scutari's work proposes a parallelizable framework for executing constraint-based algorithms, which offers a substantial efficiency improvement by distributing computational tasks across multiple cores or processors. This is achieved by independently processing tasks related to Markov blanket learning (optional step for reducing candidates), neighborhood identification, and arc direction establishment during learning. The parallel implementation does not alter the nature or number of tests—preserving the validity of inferential conclusions—but executes them concurrently for reduced run times.

Experimental Validation

The paper utilizes both reference networks of varying complexity and real-world datasets to validate the proposed architecture. The results indicate that the parallel implementation scales effectively up to multiple cores, significantly outperforming backtracking methods across various standard BN learning scenarios without introducing substantial overhead.

Implications and Future Directions

The implications of this work are twofold. Practically, it offers a scalable solution to BN structure learning, vital for analyses in fields like genomics where data dimensionality is high. Theoretically, it encourages further exploration on how parallel processing strategies can be generalized to accommodate even larger datasets and more complex network topologies. Future developments might also consider the integration of dynamic load balancing to ensure more efficient resource utilization during parallel computing.

In conclusion, this paper outlines a significant step forward in optimizing Bayesian network structure learning. By exploiting advances in parallel computing, the approach not only enhances the efficiency of constraint-based algorithms but also enriches the toolkit available to researchers engaged in the analysis of high-dimensional data. This work underscores the importance of adapting classical methods to meet contemporary computational needs.