課程名稱 |
訊號處理和機器學習之數學基礎 Mathematics in Signal Processing and Machine Learning |
開課學期 |
112-1 |
授課對象 |
理學院 應用數學科學研究所 |
授課教師 |
黃文良 |
課號 |
MATH5246 |
課程識別碼 |
221 U8820 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期四7,8,9(14:20~17:20) |
上課地點 |
天數302 |
備註 |
總人數上限:40人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Almost all problems in signal processin and machine learning, after problem formulation, we resort to optimization method to find a solution. I focus on un-constranied optimization problem and constrained optimization problem for convex functions. Then, I will add some result on non-convex optimization. I plan to cover:
Part I (basic)
1. Convex function and gradient method and conjugate gradient method
2. Convergence rate and strongly convex function
3. Conjugate function and subgradient
4. Directional derivation, subgradient calculation and method
5. Proximal point method and proximal gradient method
Part II (basic)
6. Projected gradient method and Penalty method
7. Lagrangian method and augmented Lagrangian method
8. Block coordinate descent method and alternating direction method of multipliers
Part III: beyond convex optimizations
9. Variational inequality for non-convex optimization
10. PALM algorithm
11. Liearlization methods |
課程目標 |
After this lecture, the students will be able to read papers related to convex analysis. |
課程要求 |
Students like mathematics. |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
Stanford lecture note EE236C (which I will upload) and other lecture notes, UCLA ECE236C, my lecture notes, and papers/book chapters listed in my lecture notes.
Convex optimization by Boyd and VAndenberghe
Introductory lectures on convex optimization by Nesterov
Convex analysis and monotone operator theory in Hilber spaces by Bauschke and Combettes
Augmented Lagrangian: Nonlinear programming by Bertsekas |
評量方式 (僅供參考) |
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針對學生困難提供學生調整方式 |
上課形式 |
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作業繳交方式 |
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考試形式 |
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其他 |
由師生雙方議定 |
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