檢測與估計理論
Detection and Estimation Theory
| 節 | 週二 |
|---|---|
5 13:20–14:10 | 檢測與估計理論 ED201 3 節連堂 |
6 14:20–15:10 | |
7 15:30–16:20 |
* 根據陽明交大上課時間表所列
這門課設定成銜接古典檢估理論與現代機器學習與深度學習的橋樑。秉持理論演算法與數值模擬相互搭配的原則,課程設計上包含有古典的訊號檢測演算法,如hypothesis testing,Neyman-Pearson method, multiple hypothesis testing 檢測器, 和古典的估計理論,如minimum variance unbiased (MVU), best linear unbiased estimator (BLUE), maximum likelihood (ML), least square (LS), minimum mean square error (MMSE), 與Kalman等估計器。 再配合現代以資料為基礎的檢估方法,如Markov Chain Monte Carlo (MCMC), Particle filter, variational expectation maximization (VEM), convolutional neural networks (CNN), recurrent neural network (RNN), 和variational auto-encoder (VAE) 等各式演算法。而針對此類以數值方法實現的檢估理論,我們也設計了包含無線通道估計、動態通道追蹤,複雜訊號分群,圖形識別等相關軟體模擬。希望透過實際資料處理、分析與期末專題,讓學生能充分運用理論於實務的研究問題上。
Linear Algebra Basic knowledge on Probability Theory
Lecture notes will be made available at E3
Homework : 30% Midterms: 40% Final projects: 30%
| 週次 | 主題 |
|---|---|
| 第 1 週 | Minimum variance unbiased (MVU) estimation:1. Unbiased estimators2. Minimum variance cirterion3. Existence of the MVU estimator |
| 第 2 週 | Cramer-Rao lower bound (CRLB):1. Estimator accuracy consideration2. Cramer-Rao lower bound (CRLB)3. CRLB for signals in white Gaussian noise |
| 第 3 週 | General MVU estimators:1. Sufficient statistics2. Finding sufficient statistics3. Using sufficiency to find the MVU estimator |
| 第 4 週 | Best linear unbiased estimation (BLUE):1. Finding the BLUE2. Extension to a vector parameter |
| 第 5 週 | Maximum likelihood estimation (MLE):1. Finding the MLE2. MLE of the transformed parameters3. Asymptotic MLE |
| 第 6 週 | Least squared (LS) estimation:1. Linear least squared estimation2. Recursive least squared estimation3. Constrained least squared estimation |
| 第 7 週 | Midterm Examination |
| 第 8 週 | Recursive Estimation Algorithms:1. Steepest descent method2. The scoring method3. The Gauss-Siedel Method4. The Expectation Maximization (EM) algorithm5. Applications of the EM algorithm |
| 第 9 週 | The Bayesian Philosophy:1. Prior knowledge and estimation2. The Bayesian linear model3. Properties of Gaussian PDF |
| 第 10 週 | Bayesian estimation:1. The MAP estimator2. The inimum mean squared error (MMSE) estimator3. The medium estimator |
| 第 11 週 | Linear Minimum mean squared error (MMSE) estimation:1. Linear MMSE estimators2. Sequential Linear MMSE estimator3. Kalman filter |
| 第 12 週 | Sampling methods for Estimation I:1. The Monte Carlo sampling methods2. The Metropolis-Hastings method |
| 第 13 週 | Sampling methods for Estimation II:1. Sequential MCMC2. Particle filtering |
| 第 14 週 | Advanced topics on EM algorithm1. Variational Expectation Maximization method |
| 第 15 週 | Advanced topics on learning methods. Variational auto-encoding method |
| 第 16 週 | Final Project Proposal |
| 第 17 週 | Final Project Presentation |
Fundamentals of Statistical Signal Processing: Estimation Theory (Vol I) by Steven M. Kay
- 地點
- ED832
- 時間
- Tue. GH
- 聯絡方式
- Ext. 54531 Email: sauhsuan@nctu.edu.tw