シラバス参照
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シラバス参照
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| 講義概要/Course Information |
| 科目基礎情報/General Information |
| 授業科目名 /Course title (Japanese) |
データ解析最適化論 | ||
|---|---|---|---|
| 英文授業科目名 /Course title (English) |
Advanced Topics in Data Analysis Optimization? | ||
| 科目番号 /Code |
|||
| 開講年度 /Academic year |
2017年度 | 開講年次 /Year offered |
全学年 |
| 開講学期 /Semester(s) offered |
後学期 | 開講コース・課程 /Faculty offering the course |
博士前期課程、博士後期課程 |
| 授業の方法 /Teaching method |
講義 | 単位数 /Credits |
2 |
| 科目区分 /Category |
大学院専門教育科目 - 専門科目Ⅱ | ||
| 開講類・専攻 /Cluster/Department |
情報・ネットワーク工学専攻 | ||
| 担当教員名 /Lecturer(s) |
笠井 裕之 | ||
| 居室 /Office |
東2-611 | ||
| 公開E-mail |
笠井准教授<kasai@is.uec.ac.jp> | ||
| 授業関連Webページ /Course website |
http://www.kasailab.com/lecture/data_optimization | ||
| 更新日 /Last update |
2017/03/14 08:50:57 | 更新状況 /Update status |
公開中 /now open to public |
| 講義情報/Course Description |
| 主題および 達成目標（2,000文字以内） /Themes and goals（up to 2,000 letters） |
This lecture addresses the fundamentals and algorithms of optimization theory which is one of core technologies of machine learning. Especially, non-linear programming is focused. Note that the topics related with combinational optimization, non-differential optimization, discrete optimization and linear programing are not provided. 講義では，データ解析のための機械学習（データ最適化手法）に関する技術と理論について学習する． |
|---|---|
| 前もって履修 しておくべき科目（1,000文字以内） /Prerequisites（up to 1,000 letters） |
Linear algebra basic and calculus basic 線形代数および解析 |
| 前もって履修しておくこ とが望ましい科目（1,000文字以内） /Recommended prerequisites and preparation（up to 1,000 letters） |
Not special |
| 教科書等（1,000文字以内） /Course textbooks and materials（up to 1,000 letters） |
Not special |
| 授業内容と その進め方（2,000文字以内） /Course outline and weekly schedule（up to 2,000 letters） |
以下の内容に従って講義を行うが，学生の理解度に合わせて適宜内容を調整する． 1：Introduction - Big and high-dimensional data analysis and its issues - Linear and logistic regression - Optimization technique basis 2: Mathematic preliminaries - Space R^n and R^{mxn} space - Inner product and norms - Eigenvalues and eigenvectors - Basic topological concepts 3: Optimality conditions for unconstrained optimization - Global and local optima - Classification of matrices - First/second order optimality conditions - Quadratic functions 4: Least squares - Overdetermined systems - Data fitting - Regularized least squares - De-noising 5: Gradient method 1 - Descent direction methods - Gradient method - Condition number - Diagonal scaling 6: Gradient method 2 - Line search (Exact, Backtracking, Wolf conditions, etc.) - Convergence analysis 7: Newton's method - Standard Newton's method - Damped Newton's method - Cholesky factorization based Newton's method 8: Convex sets and functions - Definition and examples of convex sets - First/second order order characterizations of convex functions 9: Convex optimization 1 - Stationarity - Orthogonal projection - Gradient projection method 10: Convex optimization 2 - Convergence analysis 11: Optimality conditions for linearly constrained problems - Separation and alternative theorems (Farkas' lemma) - KKT conditions - Orthogonal regression 12: KKT conditions - Fritz-John theorem - KKT conditions for inequality/equality constrained problem - KKT conditions for convex optimization problem 13: Duality - Motivations - Definition - Weak/strong duality in convex case - Examples (LP, QP, Orthogonal projection, Chebyshev center, Sum of norms, Denoising, etc.) 14: Advanced topics 1 - Stochastic optimization (SGD, SAG, SVRG, etc.) 15: Advanced topics 2 - Proximal (Stochastic) optimization methods - ADMM - Optimization on Riemannian manifolds |
| 実務経験を活かした 授業内容 (実務経験内容も含む) /Course content utilizing practical experience |
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| 授業時間外の学習 （予習・復習等）（1,000文字以内） /Preparation and review outside class（up to 1,000 letters） |
It is strongly recommended to study the related materials such as books and papers. 関連する書籍や論文などを適宜参照して勉強するのが望ましい． |
| 成績評価方法 および評価基準 （最低達成基準を含む） （1,000文字以内） /Evaluation and grading （up to 1,000 letters） |
- Evaluation method Middle term report：50% Final term report：50% - Evaluation metrics How deeply students understand fundamentals and algorithms of optimization theory. |
| オフィスアワー： 授業相談（1,000文字以内） /Office hours（up to 1,000 letters） |
Contact the lecturer by e-mail. メールにてアポイントメントをとるのが望ましい． |
| 学生へのメッセージ（1,000文字以内） /Message for students（up to 1,000 letters） |
- The spoken language can be English if less-than one non-Japanese student attends. - Black board is used. - Matlab simulation tasks are provided to students for their deeper understandings. |
| その他 /Others |
Students who are interested in machine learning, pattern recognition, and big data analysis are welcome. |
| キーワード /Keywords |
Optimization problem, Non-linear programming, Gradient, Hessian, Convex set/function, optimality conditions, Iterative gradient descent fundamentals, Line search methods (Back-tracking, Armijo condition，Wolfe condition), Steepest descent, Newton's method, Quasi Newton's method, Conjugate gradient, Scaled/Preconditioning descent methods, Stochastic gradient descent |