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ECE Course Syllabus
ECE6254 Course Syllabus
ECE6254
Statistical Machine Learning (3-0-3)
- Prerequisites
- ECE 4270
- Corequisites
- None
- Catalog Description
- An introduction to the theory of statistical learning and practical machine learning algorithms with applications in signal processing and data analysis.
- Textbook(s)
- T. Hastie, R. Tibshirani, and J.H. Friedman, The Elements of Statistical Learning (2nd edition), Springer, 2009. ISBN 9780387848570 (required) (comment: Available for download with corrections in the 5th printing with course resources at:
http://www-stat.stanford.edu/~tibs/ElemStatLearn/
)
Hayes, Statistical Digital Signal Processing and Modeling, John Wiley and Sons, 1996. ISBN 9780471594314 (required) - Topical Outline
Basic techniques for modeling discrete-time sequences (3 weeks) Problem formulation The direct (least squares) method The Pad\'{e} approximation Prony's method Shanks' method, iterative prefiltering All-pole modeling and linear prediction The autocorrelation and covariance methods FIR least squares inverse filter design Applications and examples Fast algorithms for solving Toeplitz equations (3 weeks) The Levinson-Durbin recursion Step-up, step-down, inverse Levinson-Durbin recursion Minimum phase property of PEF Cholesky decomposition of autocorrelation matrix and its consequences Lattice filters The Levinson recursion The Trench algorithm and the Schur recursion - optional Split Levinson recursion and line spectral pairs - optional Fast covariance algorithm - optional Applications and examples Lattice methods (2 weeks) Lattice filters (FIR, all-pole, and pole/zero) Forward and backward covariance methods The Burg recursion and the modified covariance algorithm Examples Application - wave propagation in layered material Wiener filtering (2 weeks) Review of Discrete-time random processes FIR Wiener filters Noncausal IIR Wiener filters Causal Wiener filters Applications - Linear prediction, deconvolution, smoothing Power spectrum estimation (4 weeks) Classical methods The minimum variance method The maximum entropy method and relation to minimum variance method Parametric spectrum estimation Comparison of methods Subspace methods Applications
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