Development of time series algorithms based on kernel Bayesian inference

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K11933
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 61030:Intelligent informatics-related
• Research Institution: The University of Electro-Communications
• Principal Investigator: Nishiyama Yu 電気通信大学, 大学院情報理工学研究科, 准教授 (60586395)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: カーネル平均埋め込み / カーネルベイズ推論 / 状態空間モデル / フィルタリング / スムージング / 最適輸送 / Sinkhorn divergence

Outline of Final Research Achievements

Kernel Bayesian inference infers kernel means (functions belonging to the reproducing kernel Hilbert space) of probability distributions. The kernel Bayes' filter (KBF) and kernel Bayes' smoother (KBS), which perform filtering and smoothing of state-space models in a kernel Bayesian framework, were proposed. In this study, we apply KBF and KBS to various state-space models to identify problems, refine and improve the framework, and discover new research topics. The following research results were obtained: A filtering algorithm (mbn-KBF) for continuous-discrete models was developed considering continuous-time state-space models. We developed a smoothing algorithm (mbn-KBS), visualized the results in the Stochastic Volatility model in detail, and created a movie. Three variants of the kernel Bayes' rule and kernel Kalman rule were numerically compared.

Free Research Field

機械学習

Academic Significance and Societal Importance of the Research Achievements

ベイズ学習はデータと事前分布から事後分布を計算する重要な学習法の1つであり，様々な応用の学習システムの基礎に位置付けられる．構造データ・高次元データに対する複雑な形を持つ事前分布，尤度，事後分布をコンピュータ上で実現するベイズ推論システムの構築が予測精度向上に重要である．カーネルベイズ推論はカーネル法の立場からこれにアプローチする．ベイズ推論を時系列に計算する応用事例に状態空間モデルのフィルタリングとスムージングがある．このタスクに対してカーネルベイズ推論の有効性を検証し，問題点の抽出・整理，更なる枠組みの改良・改善，新たな研究課題の発見につながる意義がある．