No abstract

No abstract

Many real-world phenomena arise from causal relationships among a set of variables. As a powerful tool, Bayesian Network (BN) has been successful in describing high-dimensional distributions. However, the faithfulness condition, enforced in most BN learning algorithms, is violated in the settings where multiple variables synergistically affect the outcome (i.e., with polyadic dependencies). Building upon recent development in cluster causal diagrams (C-DAGs), we initiate the formal study of learning C-DAGs from observational data to relax the faithfulness condition. We propose a new scoring function, the Clustering Information Criterion (CIC), based on information-theoretic measures that represent various complex interactions among variables. The CIC score also contains a penalization of the model complexity under the minimum description length principle. We further provide a searching strategy to learn structures of high scores. Experiments on both synthetic and real data support the effectiveness of the proposed method.

Multisensory integration areas such as dorsal medial superior temporal (MSTd) and ventral intraparietal (VIP) areas in macaques combine visual and vestibular cues to produce better estimates of self-motion. Congruent and opposite neurons, two types of neurons found in these areas, prefer congruent inputs and opposite inputs from the two modalities, respectively. A recently proposed computational model of congruent and opposite neurons reproduces their tuning properties and shows that congruent neurons optimally integrate information while opposite neurons compute disparity information. However, the connections in the network are fixed rather than learned, and in fact the connections of opposite neurons, as we will show, cannot arise from Hebbian learning rules. We therefore propose a new model of multisensory integration in which congruent neurons and opposite neurons emerge through Hebbian and anti-Hebbian learning rules, and show that these neurons exhibit experimentally observed tuning properties.