Error Statistics of Hidden Markov Model and Hidden Boltzmann Model Results
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A presentation about the paper titled "Error statistics of hidden Markov model and hidden Boltzmann model results" by Lee A Newberg. The paper is available at http://www.biomedcentral.com/1471-2105/10/212
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Error Statistics of Hidden Markov Model and Hidden Boltzmann Model Results
- 1. Error Statistics of Hidden Markov Model and Hidden Boltzmann Model Results A paper by Lee A Newberg Presented by Yaser Sulaiman 1
- 2. I’m a computer scientist 2
- 3. who recently got interested in bioinformatics 3
- 4. a different “flavor” of probability theory & stochastic processes 4
- 5. HMMs in computer science 5
- 10. 10 photo by John A Burnett
- 11. bioinformatics in 5 minutes 11
- 12. 12
- 14. DNA {A,T,C,G} 14
- 15. 15 stolen from Iowa State University
- 16. RNA {A,U,C,G} 16
- 18. 18 stolen from Wikipedia
- 20. @ the heart of bioinformatics 20
- 21. why? 21
- 22. 22
- 23. not to mention evolution 23
- 25. find optimal alignment 25
- 26. according to a scoring function 26
- 27. align AACGT and AACT to max. identities 27
- 28. AACGT || | AA-CT 28
- 29. AACGT ||| | AAC-T 29
- 30. it’s not always that easy! 30
- 31. 31 photo by JohnGoode
- 32. there’s more to bioinformatics than can fit into this presentation 32
- 33. back to the paper 33
- 34. Error statistics of HMM & hidden Boltzmann model results 34
- 35. Error statistics of HMM & hidden Boltzmann model results 35
- 36. how to interpret a score 36
- 37. 1. is it strong enough to indicate signal? 37
- 38. 2. is it weak enough to indicate noise? 38
- 39. false positive & true positive rates 39
- 40. false positive rate (fpr) for s0 Pr(score of noise≥s0) 40
- 41. true positive rate (tpr) for s0 Pr(score of signal≥s0) 41
- 42. a faster, more general approach to estimating fpr/tpr 42
- 43. we assume that we’re given: 43
- 44. a hidden Boltzmann model 44
- 45. a simple background model describing noise 45
- 46. a computable foreground model describing signal 46
- 47. Error statistics of HMM & hidden Boltzmann model results 47
- 48. a Markov process with unobserved states 48
- 49. transition probabilities + emission probabilities 49
- 50. Error statistics of HMM & hidden Boltzmann model results 50
- 51. generalization of HMM 51
- 52. scores rather than probabilities 52
- 53. states (including start & terminal) 53
- 54. transitions 54
- 55. emitters 55
- 56. emissions 56
- 57. alphabet 57
- 58. each state, transition, & emission has a real-valued score 58
- 59. emission path 59
- 60. sequence 60
- 61. score of emission path ∑(encountered scores) 61
- 62. 62
- 63. hidden? 63
- 64. an emission path can’t be uniquely determined from its sequence 64
- 65. a sequence can be emitted by any of several emission paths 65
- 66. 66
- 67. how to score a given sequence 67
- 69. forward score an HMM interpretation of the hidden Boltzmann model 69
- 70. for anys,exp(s) is treated as if it were an HMM probability 70
- 72. free score definition of free energy from thermodynamics 72
- 73. temperature T∈(0,+∞) 73
- 76. simple model: sequence positions are i.i.d. 76
- 80. algorithm 80
- 81. fpr(s0) can be estimated via naïve sampling 81
- 82. alternatively, fpr(s0) can be estimated via importance sampling 82
- 84. importance sampling is more efficient 84
- 88. sampling of sequences in a nutshell 88
- 89. draw sample sequences according to Pr(D|T) 89
- 90. compute f(D,s0) for each sample 90
- 91. use the average as an estimate for fpr(s0) 91
- 92. estimation of fpr 92
- 96. which estimator is the best? 96
- 97. based on the results, fpr3 97
- 98. choice depends on efficiency of the estimators 98
- 99. estimation of tpr 99
- 100. by extending the technique for estimating tpr 100
- 101. choice of T 101
- 102. which T will be efficient for a given s0? 102
- 103. the relation between T and s0 isn’t straightforward 103
- 104. build a calibration curve 104
- 105. “we have empirically observed lower variances for error statistic estimation when the fraction of sampled sequences exceeding the given score threshold is 20-60%.” 105
- 106. results 106
- 107. HMMER 3.0 107
- 108. randomly generated a length M=100, Plan7 profile-HMM 108
- 109. estimated its error statistics using polypeptide sequences of length L=200 109
- 110. time to calculate error statistics for s0is 4.2-6.3 seconds 110
- 111. runtime for naïve sampling would be much larger 111
- 112. “an error statistic less than 10−20 would require a runtime longer than the present age of the universe.” 112
- 113. a quick check using Wolfram|Alpha 113
- 114. 114
- 115. discussion 115
- 116. 116
- 118. real problem instances 118
- 119. scaling to different problem instances 119
- 120. re-use of simulations 120
- 121. other scoring functions 121
- 122. complex background models 122
- 123. stochastic context-free grammars 123
- 124. to summarize 124
- 125. error statistic estimation for hidden Boltzmann models 125
- 126. applied to HMM 126
- 127. faster than naïve sampling 127
- 128. more general than other approaches 128