複雑な相関をもつ確率モデルに対する統計的近似理論の数理と応用に関する研究

摘要

膨大な数のデータから統計的に学習を行うシステrnムの構築は計算機科学における重要な課題の一つでrnある．例えば，組み合わせ最適化問題，ニューラルrnネットワーク，べイジアンネットワーク，機械学習，rnパターン認識，画像処理などはその例である．%Probabilistic models with intricately correlations are important for problems in the information science and the engineering field. However, because of a computational cost which grows exponentially, an exact treatment of those models is extremely difficult. Therefore, various statistical approximate theories have developed to avoid that computational difficulty. It is important for further developments of those theories to clarify their mathematical properties, and so on. In this paper, hence, we analyze the conventional statistical approximate theories for intricately correlated probabilistic models, and investigate mathematical structures of them and analogies among them. Furthermore, as applications of their mathematical knowledge, we propose a new learning algorithm of Boltzmann machines. Boltzmann machines are important learning models which can learn intricately prior distributions of data.