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Monte Carlo Methods for Inference and Learning

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Monte Carlo Methods for Inference and Learning

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    1. Monte Carlo Methods for Inference and Learning Guest Lecturer: Ryan Adams CSC 2535

    2. Overview Monte Carlo basics Rejection and Importance sampling Markov chain Monte Carlo Metropolis-Hastings and Gibbs sampling Slice sampling Hamiltonian Monte Carlo

    3. Computing Expectations We often like to use probabilistic models for data.

    4. Computing Expectations

    5. Computing Expectations

    6. The Monte Carlo Principle

    7. The Monte Carlo Principle

    8. Properties of MC Estimators

    9. Why Monte Carlo?

    10. Why Monte Carlo?

    11. Generating Fantasy Data

    12. Sampling Basics

    13. Inversion Sampling

    14. Inversion Sampling

    15. The Big Picture

    16. Standard Random Variates

    17. Rejection Sampling

    18. Rejection Sampling

    19. Rejection Sampling

    20. Importance Sampling Recall that we’re really just after an expectation.

    21. Importance Sampling

    22. Importance Sampling

    23. Scaling Up

    24. Exploding Importance Weights

    25. Scaling Up

    26. Summary So Far

    27. Revisiting Independence

    28. Revisiting Independence

    29. Markov chain Monte Carlo

    30. Markov chain Monte Carlo

    31. Markov chain Monte Carlo

    32. A Discrete Transition Operator

    33. Detailed Balance

    34. Metropolis-Hastings

    35. Metropolis-Hastings

    36. Metropolis-Hastings

    37. Effect of M-H Step Size

    38. Effect of M-H Step Size

    39. Effect of M-H Step Size

    40. Gibbs Sampling

    41. Gibbs Sampling

    42. Gibbs Sampling

    43. Summary So Far

    44. An MCMC Cartoon

    45. Slice Sampling

    46. Slice Sampling

    47. Slice Sampling

    48. Slice Sampling

    49. Slice Sampling

    50. Slice Sampling

    51. Multiple Dimensions

    52. Multiple Dimensions

    53. Auxiliary Variables

    54. An MCMC Cartoon

    55. Avoiding Random Walks

    56. Hamiltonian Monte Carlo

    57. Hamiltonian Monte Carlo

    58. Hamiltonian Monte Carlo

    59. Alternating HMC

    60. Perturbative HMC

    61. HMC Leapfrog Integration

    62. Overall Summary

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