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Compressed sensing
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Statistical Physics and Statistical Inference - Lecture 2
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- 1 DATE: 06 January 2020, 16:00 to
- 2 Lecture 1 Public Lecture: 6 January 2020, PM
- 3 Lecture 2: Tuesday 7th January 2020, PM
- 4 Lecture 3: Wednesday 8th January 2020, PM
- 5 Statistical physics and statistical inference Lecture 2
- 6 What is inference?
- 7 Bayesian inference
- 8 Efficient codes : parity checks LDPC codes
- 9 Error decoding: crystal hunting inference problem
- 10 Error decoding: inference problem
- 11 Phase Transitions in Error correcting codes
- 12 Error correction: decoding
- 13 Phase transitions in decoding
- 14 Statistical inference: general scheme
- 15 Bayesian inference with many unknown and many measurements
- 16 Spin glasses
- 17 Phase transition with many states: spin glasses
- 18 Inference, spin- glass and crystal: tomography of binary mixtures
- 19 Tomography of binary mixtures
- 20 Crystal : much more probable
- 21 Inference with many unknowns crystal hunting with mean-field based algorithms
- 22 Historical development of mean field equations
- 23 BP = Bethe-Peierls = Belief Propagation
- 24 BP equations
- 25 Infinite range models :
- 26 Example: SK model
- 27 SK model, TAP equations
- 28 Two important developments
- 29 2 What happens in a glass phase, when there are many pure states, and therefore many solutions?
- 30 SP=BP 2
- 31 Power of message passing algorithms
- 32 An example of fully connected model: Generalized Linear Regression
- 33 Perceptron learning
- 34 Compressed sensing
- 35 Spin glass with multispin interactions, infinite range
- 36 BP equations
- 37 TAP equations
- 38 Benchmark: noiseless limit of compressed sensing with iid measurments
- 39 Analysis of random instances : phase transitions
- 40 Design the matrix so that one nucleates the naive state crystal nucleation idea,
- 41 Getting around the glass trap
- 42 Nucleation and seeding
- 43 Structured measurement matrix.Variances of the matrix elements
- 44 Numerical study
- 45 Performance of AMP with Gauss-Bernoulli prior: phase diagram
- 46 Many glass states
- 47 Q&A
