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## ECE Course Syllabus

### ECE6254 Course Syllabus

#### Statistical Machine Learning (3-0-3)

Technical Interest
Group
Digital Signal Processing

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)

Strategic
Performance
Indicators (SPIs)
SPIs are a subset of the abilities a student will be able to demonstrate upon successfully completing the course.

Topical Outline
```Basic techniques for modeling discrete-time sequences (3 weeks)
Problem formulation
The direct (least squares) method
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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