Can Global Optimization Strategy Outperform Myopic Strategy for Bayesian Parameter Estimation?

Bayesian adaptive inference is widely used in psychophysics to estimate psychometric parameters. Most applications used myopic one-step ahead strategy which only optimizes the immediate utility. The widely held expectation is that global optimization strategies that explicitly optimize over some horizon can largely improve the performance of the myopic strategy. With limited studies that compared myopic and global strategies, the expectation was not challenged and researchers are still investing heavily to achieve global optimization. Is that really worthwhile? This paper provides a discouraging answer based on experimental simulations comparing the performance improvement and computation burden between global and myopic strategies in parameter estimation of multiple models. The finding is that the added horizon in global strategies has negligible contributions to the improvement of optimal global utility other than the most immediate next steps (of myopic strategy). Mathematical recursion is derived to prove that the contribution of utility improvement of each added horizon step diminishes fast as that step moves further into the future.

Interpreting Basis Path Set in Neural Networks

Based on basis path set, G-SGD algorithm significantly outperforms conventional SGD algorithm in optimizing neural networks. However, how the inner mechanism of basis paths work remains mysterious. From the aspect of graph theory, this paper defines basis path, investigates structure properties of basis paths in regular fully connected neural network and interprets the graph representation of basis path set. Moreover, we propose hierarchical algorithm HBPS to find basis path set B in fully connected neural network by decomposing the network into several independent and parallel substructures. Algorithm HBPS demands that there doesn't exist shared edges between any two independent substructure paths.