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General |
MATH 858R / AMSC 808R , Spring 2014: Notes and Summary
| Lecture | Date | What was covered | Notes |
| 1 | Jan. 28 | Introduction; Hilbert spaces | get assignment 1 |
| 2 | Jan. 30 | Convex sets; Projections | sect. 6.2, and Theorem 8 in sec. 5.2 in Lax[E] |
| 3 | Feb. 4 | Convex analysis (II): Variational Inequality, Lipschitz constant; Examples | Theorem 8 in sec. 5.2 in Lax[E]; turn in assignment 1 |
| 4 | Feb. 6 | Banach space; completion | sect 8.3 in BacNar[F] |
| 5 | Feb. 11 | Fourier analysis: Fourier Series | |
| university closed due to snow | |||
| 7 | Feb. 18 | Fourier analysis: Fourier Series (2): Smoothness - Decay Relations; | turn in assignment 2 |
| 8 | Feb. 20. | Fourier analysis: Fourier Series (3): Pointwise and MSE approximation order | - |
| 9 | Feb. 25 | Fourier analysis: Fourier transform |
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| 10 | Feb. 27 | Sampling Theory: Shannon Formula; Oversampling | turn in assignment 3 |
| 11 | Mar. 4 | Fourier Analysis: Smoothness Decay Duality; Sampling Theory:Approximations (2) | |
| 12 | Mar. 6 | Fourier analysis: Windowed Fourier Transform (1) | turn in assignment 4 |
| 13 | Mar. 11 | Windowed Fourier Transform (2); Continuous Wavelet Transform | |
| 14 | Mar. 13 | Reproducing Kernel Hilbert Space; | |
| - | Mar.18 | SPRING BREAK |
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| - | Mar. 20 | SPRING BREAK | |
| 15 | Mar. 25 | Statistical Descriptions: Moments, Cumulants, Characteristic Functions | turn in assignment 5 |
| 16 | Mar. 27 | Stochastic Approximations: Karhunen-Loev Expansion , PCA; Independent Component Analysis: ICA(Identifiability) | |
| 17 | Apr. 1 | ICA (Identifiability) | |
| 18 | Apr. 3 | ICA (Algorithms): Cumulants, JADE |
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| 19 | Apr. 8 | NO CLASS | |
| 20 | Apr. 10 | ICA: Max Entropy approach; | |
| 21 (*) | Apr. 15 | Frequentist Approach:MLE; Bayesian Approach: MAP, MMSE; Sparse Component Analysis; Blind Source Separation (BSS) | DIFFERRENT TIMES: 11:00am-1:00pm and 5:00pm-7:00pm Deadline for Project/Report decision |
| 22 | Apr. 17 | Mixing Matrix Learning | turn in assignment 6 |
| 23 (*) | Apr. 22 | BSS (audio case);Inequalities: Deterninistic Uncertainty Inequality: Fourier-Heisenberg; uncertainty inequality in finite setting |
DIFFERRENT TIMES: 11:00am-1:00pm and 5:00pm-7:00pm |
| 24 | Apr. 24 | Inequalities: Stochastic Bounds: Cramer-Rao Lower Bound | |
| 25(*) | Apr. 29 | Model Selection: AIC, BIC, MDL | DIFFERRENT TIMES: 11:00am-1:00pm and 5:00pm-7:00pm |
| 26 | May 1 | Compressive Sampling: L0-L1 "trick" | |
| 27 | May. 6 | NO CLASS | |
| 28 | May. 8 | CS Part II | |
| 29 | May. 13 | Projects/Reports Submission Deadline; Final Exam |
FINAL EXAM |
