In this paper, learning a Bayesian network structure that optimizes a scoring function for a given dataset is viewed as a shortest path problem in an implicit state-space search graph. This perspective highlights the importance of two research issues: the development of search strategies for solving the shortest path problem, and the design of heuristic functions for guiding the search. This paper introduces several techniques for addressing the issues. One is an A* search algorithm that learns an optimal Bayesian network structure by only searching the most promising part of the solution space. The others are mainly two heuristic functions. The first heuristic function represents a simple relaxation of the acyclicity constraint of a Bayesian network. Although admissible and consistent, the heuristic may introduce too much relaxation and result in a loose bound. The second heuristic function reduces the amount of relaxation by avoiding directed cycles within some groups of variables. Empirical results show that these methods constitute a promising approach to learning optimal Bayesian network structures.

The Hick-Hyman law describes a linear increase in reaction time (RT) as a function of the information entropy of response selection, which is computed as the binary logarithm of the number of response alternatives. While numerous behavioral studies have provided evidence for the Hick-Hyman law, its neural underpinnings have rarely been examined and are still unclear. In this functional magnetic resonance imaging study, by utilizing a choice reaction time task to manipulate the entropy of response selection, we examined brain activity mediating the input and the output, as well as the connectivity between corresponding regions in human participants. Beyond confirming the Hick-Hyman law in RT performance, we found that activation of the cognitive control network (CCN) increased and activation of the default mode network (DMN) decreased, both as a function of entropy. However, only the CCN, but not the DMN, was involved in mediating the relationship between entropy and RT. The CCN was involved in both stages of uncertainty representation and response generation, while the DMN was mainly involved at the stage of uncertainty representation. These findings indicate that the CCN serves as a core entity underlying the Hick-Hyman law by coordinating uncertainty representation and response generation in the brain.

Cognitive control, with a limited capacity, is a core process in human cognition for the coordination of thoughts and actions. Although the regions involved in cognitive control have been identified as the cognitive control network (CCN), it is still unclear whether a specific region of

In this work, we empirically evaluate the capability of various scoring functions of Bayesian networks for recovering true underlying structures. Similar investigations have been carried out before, but they typically relied on approximate learning algorithms to learn the network structures. The suboptimal structures found by the approximation methods have unknown quality and may affect the reliability of their conclusions. Our study uses an optimal algorithm to learn Bayesian network structures from datasets generated from a set of gold standard Bayesian networks. Because all optimal algorithms always learn equivalent networks, this ensures that only the choice of scoring function affects the learned networks. Another shortcoming of the previous studies stems from their use of random synthetic networks as test cases. There is no guarantee that these networks reflect real-world data. We use real-world data to generate our gold-standard structures, so our experimental design more closely approximates real-world situations. A major finding of our study suggests that, in contrast to results reported by several prior works, the Minimum Description Length (MDL) (or equivalently, Bayesian information criterion (BIC)) consistently outperforms other scoring functions such as Akaike's information criterion (AIC), Bayesian Dirichlet equivalence score (BDeu), and factorized normalized maximum likelihood (fNML) in recovering the underlying Bayesian network structures. We believe this finding is a result of using both datasets generated from real-world applications rather than from random processes used in previous studies and learning algorithms to select high-scoring structures rather than selecting random models. Other findings of our study support existing work, e.g., large sample sizes result in learning structures closer to the true underlying structure; the BDeu score is sensitive to the parameter settings; and the fNML performs pretty well on small datasets. We also tested a greedy hill climbing algorithm and observed similar results as the optimal algorithm.