前期 木曜日 ３講時. 単位数/Credit(s): 2. 対象学科・専攻/Departments: 情報基礎科学専攻、システム情報科学専攻、応用情報科学専攻. 学期/Term: 前期. 履修年度: 2024. 使用言語: 講義: 日本語, 講義ノートとスライド: 英語, テキスト: 日本語 Lecture: Japanese, Lecture Note and Slides: English, Textbook: Japanese.
2024
物理フラクチュオマティクス論
Physical Fluctuomatics
当該年度のGoogle Classroomのクラスコードは情報科学研究科Webpage
https://www.is.tohoku.ac.jp/jp/forstudents/syllabus.html
にて確認すること．
制御・信号処理等の工学の諸分野あるいは情報科学の応用を意識しつつ，確率論・統計学および確率過程を基礎とする確率的情報処理の十分な理解を与える．特にベイズ統計にもとづく予測・推論のモデル化，情報統計力学の導入によるアルゴリズム化について画像処理，パターン認識，確率推論などを例として講義する．
また，確率的情報処理によるデータに内在するゆらぎの取り扱いにも触れ，さらに量子確率場をもちいた情報処理，複雑ネットワーク科学の最近の展開についても概説する．
本講義はGoogle ClassroomからのGoogle Meetsからのリアルタイムオンライン授業として行う．
受講希望者はGoogle Classroomのクラスコードを情報科学研究科Webpage
https://www.is.tohoku.ac.jp/jp/forstudents/syllabus.html
にて各自事前に確認すること。
The class code for Google Classroom of the present class in this year can be confirmed on the webpage of Graduate School of Information Sciences:
https://www.is.tohoku.ac.jp/en/forstudents/syllabus.html
Applications to many fields in engineering like control, signal processing etc. and in information sciences are in mind through the lecture course for the basic knowledge of statistical machine learning theory as well as stochastic processes. Brief introduction will be given to methods for applications like statistical estimation etc., and to the relationship with statistical-mechanical informatics. We first lecture probability and statistics and their fundamental properties and explain the basic frameworks of Bayesian estimation and maximum likelihood estimation. Particularly, we show EM algorithm as one of familiar computational schemes to realize the maximum likelihood estimation. As one of linear statistical models, we introduce Gaussian graphical model and show the explicit procedure for Bayesian estimation and EM algorithm from observed data. We show some useful probabilistic models which are applicable to probabilistic information processing in the stand point of Bayesian estimation. We mention that some of these models can be regarded as physical models in statistical mechanics. Fundamental structure of belief propagation methods are reviewed as powerful key algorithms to compute some important statistical quantities, for example, averages, variances and covariances. Particularly, we clarify the relationship between belief propagations and some approximate methods in statistical mechanics. As ones of application to probabilistic information processing based on Bayesian estimation and maximum likelihood estimations, we show probabilistic image processing and probabilistic reasoning. Moreover, we review also quantum-mechanical extensions of probabilistic information processing.
The present class will be proceeded in the google classroom for the present class. Students should confirm the google class code in the following website by themselves:
https://www.is.tohoku.ac.jp/en/forstudents/syllabus.html
[授業スケジュール]
第1回 確率的情報処理の概観
第2回 数学的準備(1)：確率・統計
第3回 数学的準備(2)：離散関数の変分原理と直交関数展開
第4回 最尤推定とEMアルゴリズム
第5回 ガウシアングラフィカルモデルによる確率的情報処理(1)
第6回 ガウシアングラフィカルモデルによる確率的情報処理(2)
第7回 確率伝搬法(1)
第8回 確率伝搬法(2)
第9回 確率伝搬法(3)
第10回 確率伝搬法(4)
第11回 確率的画像処理と確率伝搬法
第12回 確率推論におけるベイジアンネットと確率伝搬法
第13回 量子力学からみた確率的情報処理と確率伝搬法
第14回 複雑ネットワーク
第15回 まとめ
[Progress Schedule of Class]
1st Review of probabilistic information processing
2nd Mathematical Preparations (1): Probability and statistics
3rd Mathematical Preparations (2): Variational principles and orthonomal expansion of descrite functions
4th Maximum likelihood estimation and EM algorithm
5th Probabilistic information processing by Gaussian graphical model (1)
6th Probabilistic information processing by Gaussian graphical model (2)
7th Belief propagation (1)
8th Belief propagation (2)
9th Belief propagation (3)
10th Belief propagation (4)
11th Probabilistic image processing by means of physical models
12th Bayesian network and belief propagation in statistical inference
13th Quantum-mechanical extentions of probabilistic information processing
14th Complex networks and physical fluctuations
15th Summary
課題を出題し，提出されたレポートにより成績の評価をする．
Evaluation is performed comprehensively based on submitted reports.
The main lecture note in English is available at
https://doi.org/10.1007/978-981-16-4095-7_10
授業時間は限られているので，2時間程度の自主学習が重要になる．
The session time is limited and therefore self-directed learning of about two hours is important.
電子メール (kazu [at mark] tohoku.ac.jp) にてアポイントをとった上で来室すること．
Students should visit my office after taking an appointment by e-mail (kazu [at mark] tohoku.ac.jp).
[履修上の要件]
履修には微分積分学，数理統計学，複素関数論およびフーリエ解析の知識が必要です． 講義は日本語で行われます． 講義ノートの英語版はWebpage
https://doi.org/10.1007/978-981-16-4095-7_10
からダウンロード可能です．
[Remark]
Differential and integral calculus, statistical mathematics, complex analysis and Fourier analysis are necessary as background knowledge. This lecture is presented in Japanese. English version lecture note is available in the webpape:
https://doi.org/10.1007/978-981-16-4095-7_10