A PSO approach for learning transition structures of Higher-Order Dynamic Bayesian Networks

Abstract

Dynamic Bayesian Networks are widely used for modeling neural information flow and gene regulatory networks.Their assumption of first-order Markov, however, is recently being noted as a too restrictive assumption for some applications, specially when these have communication and processing of information at different time delays. Many authors are extending this Markov assumption to higher orders, suggesting the use of Higher-Order Dynamic Bayesian Networks (HO-DBNs). These networks, by their turn, bring some issues to be considered, mainly because of the elevated number of nodes, the necessity of great amounts of data and the high cost for learning their structures. In this work we propose an optimization technique based on Particle Swarm Optimization for learning the transition structures of HO-DBNs, trying to exploit their intrinsic characteristics to suggest efficient representations and simplifications in their learning. Also, we propose a way to introduce extra randomness in the method by reinterpreting the concepts of inertia and social/cognitive contributions to particles. We test the algorithm for correctness and performance, comparing it against a greedy algorithm for learning Bayesian structures.

Structure Learning of High-Order Dynamic Bayesian Networks via Particle Swarm Optimization with Order Invariant Encoding

“…To leverage the increase in complexity of this kind of model, we can restrict the arcs in the network so that they can only be directed to nodes in the most recent time slice, in our case X 0 . This kind of DBN structures are called transition networks [15] and they avoid by definition any kind of cycles, which simplifies the search. The space of possible structures that transition networks allow is also much smaller than that of regular DBN models.…”

“…In this case, velocities matrices can take any value from the set {−1, 0, 1}, representing deletions, non modifications or additions of arcs respectively. This same approach is taken by Santos and Maciel [15], but instead of adjacency matrices they define a structure called causality list that establishes positions and velocities as sets of parent nodes.…”

“…To fix this issue, some authors have translated the space of possible BN graphs into a continuous one over which PSO can be applied [10]. Many other authors [4,6,15,20] have opted for translating the operations of the PSO algorithm to perform discrete movements and then be able to apply the framework of PSO to BN structure learning. In particular, the work of Du et al [4] proposes to encode particles as binary adjacency matrices that are modified as the particle moves to represent additions and deletions of arcs.…”

“…In particular, the work of Du et al [4] proposes to encode particles as binary adjacency matrices that are modified as the particle moves to represent additions and deletions of arcs. Santos and Maciel [15] extend this concept by defining particles as lists with the parents of each node, and so a particle moving means adding or deleting parent nodes. However, these approaches become less efficient as the number of nodes and the Markovian order increase, and the correct order is assumed to be known beforehand.…”

Modeling of an Insect Proprioceptor System based on Different Neuron Response Times

“…The biologically inspired engineering studies biological structures intending to find solutions for engineering problems (Zhang et al, 2015). Examples include the Particle Swarm Optimization Algorithm (Santos and Maciel, 2014), the control of exoskeletons using principles found in biomechanics (Jimnez-Fabin and Verlinden, 2012) and neuronal circuits (Endo et al, 2015). Recent works analyzed neural signals (Jegadeesan et al, 2015) trying to identify patterns and connections inside the nervous system (Subramaniam et al, 2015).…”