This document discusses probabilistic modeling in Python using the pomegranate library. It begins with an overview of probabilistic modeling tasks and when to use pomegranate. It then discusses the major models supported by pomegranate including general mixture models, hidden Markov models, Bayesian networks, and Bayes classifiers. It provides examples of using these models and shows how pomegranate allows for complex probabilistic models to be built from simpler component distributions and submodels. The document concludes by demonstrating how mixtures of hidden Markov models can be trained in parallel using pomegranate.

1. fast and flexible probabilistic modeling in python
jmschreiber91
@jmschrei
@jmschreiber91
Jacob Schreiber
PhD student, Paul G. Allen School of
Computer Science, University of
Washington, Seattle WA
Maxwell Libbrecht
Postdoc, Department of Genome Sciences,
University of Washington, Seattle WA
Assistant Professor, Simon Fraser University,
Vancouver BC
noble.gs.washington.edu/~maxwl/

2. fast and flexible probabilistic modeling in python
jmschreiber91
@jmschrei
@jmschreiber91
Jacob Schreiber
PhD student, Paul G. Allen School of
Computer Science, University of
Washington, Seattle WA
Maxwell Libbrecht
Postdoc, Department of Genome Sciences,
University of Washington, Seattle WA
Assistant Professor, Simon Fraser University,
Vancouver BC
noble.gs.washington.edu/~maxwl/

3. Follow along with the Jupyter tutorial
3
goo.gl/cbE7rs

4. What is probabilistic modeling?
4goo.gl/cbE7rs
Tasks:
• Sample from a distribution.
• Learn parameters of a
distribution from data.
• Predict which distribution
generated a data example.

5. When should you use pomegranate?
5
complexity of probabilistic modeling task
simple complexz }| {
• logistic regression
• sample from a Gaussian
distribution
• speed is not important
Use scipy or
scikit-learn
z }| {
• distributions not implemented in
pomegranate
• problem-specific inference
algorithms
Use custom
packages (in R or
stand-alone)
z }| {
Use
pomegranate
goo.gl/cbE7rs

6. When should you use pomegranate?
6
z }| {
Use pomegranate
probabilistic modeling tasks
orthogonaltasks
• Scientific computing: Use numpy, scipy
• Non-probabilistic supervised learning (SVMs,
neural networks): Use scikit-learn
• Visualizing probabilistic models: Use matplotlib
• Bayesian statistics: Check out PyMC3
goo.gl/cbE7rs

7. Overview: this talk
7
Overview
Major Models/Model Stacks
1. General Mixture Models
2. Hidden Markov Models
3. Bayesian Networks
4. Bayes Classifiers
Finale: Train a mixture of HMMs in parallel

8. The API is common to all models
8
All models have these methods!
All models composed of
distributions (like GMM, HMM...)
have these methods too!
model.log_probability(X) / model.probability(X)
model.sample()
model.fit(X, weights, inertia)
model.summarize(X, weights)
model.from_summaries(inertia)
model.predict(X)
model.predict_proba(X)
model.predict_log_proba(X)
Model.from_samples(X, weights)
goo.gl/cbE7rs

9. Overview: supported models
Six Main Models:
1. Probability Distributions
2. General Mixture Models
3. Markov Chains
4. Hidden Markov Models
5. Bayes Classifiers / Naive Bayes
6. Bayesian Networks
9
Two Helper Models:
1. k-means++/kmeans||
2. Factor Graphs

10. pomegranate supports many distributions
10
Univariate Distributions
1. UniformDistribution
2. BernoulliDistribution
3. NormalDistribution
4. LogNormalDistribution
5. ExponentialDistribution
6. BetaDistribution
7. GammaDistribution
8. DiscreteDistribution
9. PoissonDistribution
Kernel Densities
1. GaussianKernelDensity
2. UniformKernelDensity
3. TriangleKernelDensity
Multivariate Distributions
1. IndependentComponentsDistributio
n
2. MultivariateGaussianDistribution
3. DirichletDistribution
4. ConditionalProbabilityTable
5. JointProbabilityTable

11. 11
mu, sig = 0, 2
a = NormalDistribution(mu, sig)
X = [0, 1, 1, 2, 1.5, 6, 7, 8, 7]
a = GaussianKernelDensity(X)
Models can be created from known values

12. 12
Models can be learned from data
X = numpy.random.normal(0, 1, 100)
a = NormalDistribution.from_samples(X)

13. Overview: model stacking in pomegranate
13
Distributions
Bayes Classifiers
Markov Chains
General Mixture Models
Hidden Markov Models
Bayesian Networks
D BC MC GMM HMM BN
Sub-model
Wrapper model

14. Overview: model stacking in pomegranate
14
Distributions
Bayes Classifiers
Markov Chains
General Mixture Models
Hidden Markov Models
Bayesian Networks
D BC MC GMM HMM BN
Sub-model
Wrapper model

15. Overview: model stacking in pomegranate
15
Distributions
Bayes Classifiers
Markov Chains
General Mixture Models
Hidden Markov Models
Bayesian Networks
D BC MC GMM HMM BN
Sub-model
Wrapper model

16. Overview: model stacking in pomegranate
16
Distributions
Bayes Classifiers
Markov Chains
General Mixture Models
Hidden Markov Models
Bayesian Networks
D BC MC GMM HMM BN

17. 17
pomegranate can be faster than numpy
Fitting a Normal Distribution to 1,000 samples

18. 18
pomegranate can be faster than numpy
Fitting Multivariate Gaussian to 10,000,000 samples of 10
dimensions

19. 19
pomegranate uses BLAS internally

20. 20
pomegranate just merged GPU support

21. 21
pomegranate uses additive summarization
pomegranate reduces data to sufficient statistics for updates
and so only has to go datasets once (for all models).
Here is an example of the Normal Distribution sufficient
statistics

22. 22
pomegranate supports out-of-core learning
Batches from a dataset can be reduced to additive summary
statistics, enabling exact updates from data that can’t fit in memory.

23. 23
Parallelization exploits additive summaries
Extract summaries
+
+
+
+
New Parameters

24. 24
pomegranate supports semisupervised learning
Summary statistics from supervised models can be added to
summary statistics from unsupervised models to train a single model
on a mixture of labeled and unlabeled data.

25. 25
pomegranate supports semisupervised learning
Supervised Accuracy: 0.93 Semisupervised Accuracy: 0.96

26. 26
pomegranate can be faster than scipy

27. 27
pomegranate uses aggressive caching

29. 29

30. 30
Example ‘blast’ from Gossip Girl
Spotted: Lonely Boy. Can't believe the love of his life has
returned. If only she knew who he was. But everyone knows
Serena. And everyone is talking. Wonder what Blair Waldorf
thinks. Sure, they're BFF's, but we always thought Blair's
boyfriend Nate had a thing for Serena.

31. 31
How do we encode these ‘blasts’?
Better lock it down with Nate, B. Clock's ticking.
+1 Nate
-1 Blair

32. 32
How do we encode these ‘blasts’?
This just in: S and B committing a crime of fashion. Who
doesn't love a five-finger discount. Especially if it's the middle
one.
-1 Blair
-1 Serena

33. 33
Simple summations don’t work well

34. 34
Beta distributions can model uncertainty

35. 35
Beta distributions can model uncertainty

36. 36
Beta distributions can model uncertainty

37. Overview: this talk
37
Overview
Major Models/Model Stacks
1. General Mixture Models
2. Hidden Markov Models
3. Bayesian Networks
4. Bayes Classifiers
Finale: Train a mixture of HMMs in parallel

38. GMMs can model complex distributions
38

39. GMMs can model complex distributions
39
model = GeneralMixtureModel.from_samples(NormalDistribution, 2, X)

40. GMMs can model complex distributions
40

41. An exponential distribution is not right
41
model = ExponentialDistribution.from_samples(X)

42. A mixture of exponentials is better
42
model = GeneralMixtureModel.from_samples(ExponentialDistribution, 2, X)

43. Heterogeneous mixtures natively supported
43
model = GeneralMixtureModel.from_samples([ExponentialDistribution, UniformDistribution], 2, X)

44. GMMs faster than sklearn
44

45. Overview: this talk
45
Overview
Major Models/Model Stacks
1. General Mixture Models
2. Hidden Markov Models
3. Bayesian Networks
4. Bayes Classifiers
Finale: Train a mixture of HMMs in parallel

46. CG enrichment detection HMM
46
GACTACGACTCGCGCTCGCACGTCGCTCGACATCATCGACA

47. CG enrichment detection HMM
GACTACGACTCGCGCTCGCACGTCGCTCGACATCATCGACA
47

48. pomegranate HMMs are feature rich
48

49. GMM-HMM easy to define
49

50. HMMs are faster than hmmlearn
50

51. Overview: this talk
51
Overview
Major Models/Model Stacks
1. General Mixture Models
2. Hidden Markov Models
3. Bayesian Networks
4. Bayes Classifiers
Finale: Train a mixture of HMMs in parallel

52. Bayesian networks
52
Bayesian networks are powerful inference tools which define a
dependency structure between variables.
Sprinkler
Wet Grass
Rain

53. Bayesian networks
53
Sprinkler
Wet Grass
Rain
Two main difficult tasks:
(1) Inference given incomplete information
(2) Learning the dependency structure from data

54. Bayesian network inference
54
Inference is done using Belief Bropagation on a factor graph.
Messages are sent from one side to the other until convergence.
Rain
Sprinkler
Grass
Wet
R/S/GW
Factor
Grass
Wet
Rain
Sprinkler
Marginals Factors

55. Inference in a medical diagnostic network
55
BRCA 2 BRCA 1 LCT
BLOATLE LOA VOM AC
PREGLIOC

56. Inference in a medical diagnostic network
56
BRCA 2 BRCA 1 LCT
BLOATLE LOA VOM AC
PREGLIOC

57. Bayesian network structure learning
57
???
Three primary ways:
● “Search and score” / Exact
● “Constraint Learning” / PC
● Heuristics

58. Bayesian network structure learning
58
???
pomegranate supports:
● “Search and score” / Exact
● “Constraint Learning” / PC
● Heuristics

59. Exact structure learning is intractable
???
59

60. Chow-Liu trees are fast approximations
60

61. pomegranate supports four algorithms
61

62. Constraint graphs merge data + knowledge
62
BRCA 2 BRCA 1 LCT
BLOATLE LOA VOM AC
PREGLIOC
genetic conditions
conditions
symptoms

63. Constraint graphs merge data + knowledge
63
genetic conditions
diseases
symptoms

64. Modeling the global stock market
64

65. Constraint graph published in PeerJ CS
65

66. Overview: this talk
66
Overview
Major Models/Model Stacks
1. General Mixture Models
2. Hidden Markov Models
3. Bayesian Networks
4. Bayes Classifiers
Finale: Train a mixture of HMMs in parallel

67. Bayes classifiers rely on Bayes’ rule
67

68. 68
Let’s build a classifier on this data

69. 69
Likelihood function alone is not good

70. 70
Priors can model class imbalance

71. 71
The posterior is a good model of the data

72. Naive Bayes assumes independent features
72

73. Naive Bayes produces ellipsoid boundaries
73model = NaiveBayes.from_samples(NormalDistribution, X, y)

74. Naive Bayes can be heterogeneous
74

75. Data can fall under different distributions
75

76. Using appropriate distributions is better
76
model = NaiveBayes.from_samples(NormalDistribution, X_train, y_train)
print "Gaussian Naive Bayes: ", (model.predict(X_test) == y_test).mean()
clf = GaussianNB().fit(X_train, y_train)
print "sklearn Gaussian Naive Bayes: ", (clf.predict(X_test) == y_test).mean()
model = NaiveBayes.from_samples([NormalDistribution, LogNormalDistribution,
ExponentialDistribution], X_train, y_train
print "Heterogeneous Naive Bayes: ", (model.predict(X_test) == y_test).mean()
Gaussian Naive Bayes: 0.798
sklearn Gaussian Naive Bayes: 0.798
Heterogeneous Naive Bayes: 0.844

77. This additional flexibility is just as fast
77

78. Bayes classifiers don’t require independence
78
naive accuracy: 0.929 bayes classifier accuracy: 0.966

79. Gaussian mixture model Bayes classifier
79

80. Creating complex Bayes classifiers is easy
80
gmm_a = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, 2, X[y == 0])
gmm_b = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, 2, X[y == 1])
model_b = BayesClassifier([gmm_a, gmm_b], weights=numpy.array([1-y.mean(), y.mean()]))

81. Creating complex Bayes classifiers is easy
81
mc_a = MarkovChain.from_samples(X[y == 0])
mc_b = MarkovChain.from_samples(X[y == 1])
model_b = BayesClassifier([mc_a, mc_b], weights=numpy.array([1-y.mean(), y.mean()]))
hmm_a = HiddenMarkovModel.from_samples(X[y == 0])
hmm_b = HiddenMarkovModel.from_samples(X[y == 1])
model_b = BayesClassifier([hmm_a, hmm_b], weights=numpy.array([1-y.mean(), y.mean()]))
bn_a = BayesianNetwork.from_samples(X[y == 0])
bn_b = BayesianNetwork.from_samples(X[y == 1])
model_b = BayesClassifier([bn_a, bn_b], weights=numpy.array([1-y.mean(), y.mean()]))

82. Overview: this talk
82
Overview
Major Models/Model Stacks
1. General Mixture Models
2. Hidden Markov Models
3. Bayesian Networks
4. Bayes Classifiers
Finale: Train a mixture of HMMs in parallel

83. Training a mixture of HMMs in parallel
83
Creating a mixture of HMMs is just as simple as passing the
HMMs into a GMM as if it were any other distribution

84. Training a mixture of HMMs in parallel
84fit(model, X, n_jobs=n)

85. Documentation available at Readthedocs
85

86. Tutorials available on github
86
https://github.com/jmschrei/pomegranate/tree/master/tutorials

87. Acknowledgements
87

88. fast and flexible probabilistic modeling in python
jmschreiber91
@jmschrei
@jmschreiber91
Jacob Schreiber
PhD student, Paul G. Allen School of
Computer Science, University of
Washington, Seattle WA
Maxwell Libbrecht
Postdoc, Department of Genome Sciences,
University of Washington, Seattle WA
Assistant Professor, Simon Fraser University,
Vancouver BC
noble.gs.washington.edu/~maxwl/