Statistical Physics and Statistical Inference - Lecture 2

Statistical Physics and Statistical Inference - Lecture 2

International Centre for Theoretical Sciences via YouTube Direct link

SP=BP 2

30 of 47

30 of 47

SP=BP 2

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Statistical Physics and Statistical Inference - Lecture 2

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

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