Statistical signal processing has its roots in probability theory, mathematical statistics and, more recently, systems theory and statistical communications theory. A Wavelet Tour of Signal Processing (Mallat), Pattern Recognition and Machine Learning (Bishop), A Probabilistic Theory of Pattern Recognition (Devroye, Gyorfi, and Lugosi), Elements of Statistical Learning (Hastie, Tibshirani, and Friedman). Google maps: just awesome.
Class Schedule for Spring 2020
|Week||Topic||HW (Due Thursdays)|
Probability: random variables and random vectors, expected values, characteristic functions.
Random processes: Definitions
|Random processes: Second-order description (mean, correlation function, power spectrum).|
Linear vector spaces: inner products, norms, Hilbert spaces, separability.
|PS I: 2.3, 2.4, 2.8, 2.10, 2.11|
|Vector space for random processes: inner product, Karhunen-Loève expansion.|
Optimization theory: constrained and unconstrained problems.
Estimation theory: notions of error.
|PS II: 2.17, 2.19, 2.35, 2.47|
|Estimation theory: parameter estimation, minimum mean-squared error estimation, MAP estimation, linear estimators and the Orthogonality Principle, maximum likelihood estimation, Cramér-Rao bound.|
Tuesday, Tuesday audio backup, Thursday
|PS III: 2.14, 2.16, 3.1, 4.1|
|Estimation theory: The Cramér-Rao bound.|
Poisson processes and estimating their characteristics.
|Linear and nonlinear waveform parameter estimates. Linear signal estimation: Wiener filters.|
|PS IV: 4.2, 4.3, 4.9, 4.11, 4.14|
|Linear signal estimation: Wiener filters, adaptive filters.|
|PS V: 4.8, 4.12, 4.16, 4.23|
|Linear signal estimation: Kalman filters. General signal estimation: Bayesian filtering.|
Tuesday (missing some audio), (backup audio); Thursday
|Quiz I Due|
|Estimation theory: spectral estimation.|
Filtering in the context of basis expansions: Denoising, wavelets, compressive sensing.
Detection theory: likelihood ratio test.
|Detection theory: ROC curves, Neymann-Pearson detection, Stein’s lemma.|
|PS VI: 4.31, 4.36, 4.38, 4.41|
|Distance measures for densities, M models, null-hypothesis testing.|
|PS VII: 4.44, 4.46, 4.54, 5.1|
Uncertainties in models: simultaneous estimation and detection.
|PS VIII: 5.2, 5.4, 5.6, 5.10, 5.13|
|Detection theory: Signals in additive noise.|
Signal and noise unknowns.
|PS IX: 5.5, 5.23, 5.27, 5.51|
|Non-Gaussian detection theory, type-based detection.|
|Quiz II Due|
- Click here for all my publications.
- Click here for preprints on arXiv
- Recent papers: JMLR,IEEE Info Theory, ICML, Nature Comm, IEEE Automatic Control, IEEE Signal Proc (Inverse RL for Identifying Cognitive Radar), IEEE Signal Proc (Inverse HMM Filters and Counter-adversarial Systems), IEEE Signal Proc (Anticipatory Decision Making and Quickest Change Detection).
|Fundamental Areas||Application Areas|
|POMDPs & Controlled Sensing||Social Networks (fusion & control)|
|Stochastic Optimization, Game Theory||Cognitive Radar & Intent Inference|
|Stochastic Calculus, filtering (old stuff)||Biosensors, Artificial Membranes|
Statistical Signal Processing Using Matlab
Fundamentals Of Statistical Signal Processing
- Partially Observed Markov Decision Processes book, Cambridge, 2016
- Dynamics of Engineered Artificial Membranes & Biosensors,Cambridge, 2018.