ベイズ推論を利用して学習したニューラルネットワークによる応答曲面とその最適化問題への適用

摘要

This paper verifies the response surfaces of artificial neural networks (NN) learned by using a method based on Bayesian inference. Mackay showed that the Bayesian method due to Gull and Skilling can be applied to regularization for NN. However, generalization ability has not been verified sufficiently for the NN response surface regularized by using the Bayesian method. If the NN response surface has good generalization ability, it can be used in the optimization process of response surface methodology (RSM). NN therefore was learned by using the Bayesian method to investigate generalization ability. We tried three rules for updating the regularizing constants in an objective function minimized during NN learning. All of the update rules were derived from the Bayesian method. As a result, the response surface of NN had good generalization ability, with the exception of one update rule. The poor update rule failed to determine the regularizing constants. This tendency for the update rules was recognized regardless of response surface geometry. After we selected a superior update rule, the NN response surface by using the Bayesian method was applied to an optimization problem. The response surface didn't fit noises included in teacher data, and consequently, it was effectively used to reach a solution. Finally, we concluded that the NN learned by using the Bayesian method can be used as the response surface in the process of RSM.%ある現象の真の振る舞いを近似するモデル（応答曲面）を作成し．それを使って最適応答を実現する入力条件を探索する応答曲面法は実用性の高さから，様々な分野で適用されている．一般的な応答曲面法では，設計変数の低次多項式を応答曲面とし，その作成と解の探索を繰り返して最適解を得る．一方，大域的な応答曲面を1度だけ作成し，それを使って最適解を探索する方法も近年では採用されている．この方法で使う応答曲面は非線形性の強い応答を表現できなければならなので，応答曲面にはニューラルネットワーク（以降，NNと記す），Kriging．RBF（Radial Basis Function）などが使われる．