1. An introduction to machine learning and probabilistic graphical models Kevin Murphy MIT AI Lab Presented at Intel’s workshop on “Machine learning for the life sciences”, Berkeley, CA, 3 November 2003

3. Supervised learning yes no N Small Arrow Red Y Small Star Blue Y Small Square Blue Y Big Torus Blue Output Size Shape Color F(x1, x2, x3) -> t Learn to approximate function from a training set of (x,t) pairs

4. Supervised learning Learner Training data Hypothesis Testing data Prediction N S A R Y S S B Y S S B Y B T B T X3 X2 X1 ? S C Y ? S A B T X3 X2 X1 N Y T

5. Key issue: generalization yes no ? ? Can’t just memorize the training set (overfitting)

7. Perceptron (neural net with no hidden layers) Linearly separable data

8. Which separating hyperplane?

9. The linear separator with the largest margin is the best one to pick margin

10. What if the data is not linearly separable?

11. Kernel trick kernel Kernel implicitly maps from 2D to 3D, making problem linearly separable x 1 x 2 z 1 z 2 z 3

13. Boosting Simple classifiers (weak learners) can have their performance boosted by taking weighted combinations Boosting maximizes the margin

18. Hierarchical clustering

19. Principal Component Analysis (PCA) PCA seeks a projection that best represents the data in a least-squares sense. PCA reduces the dimensionality of feature space by restricting attention to those directions along which the scatter of the cloud is greatest.

20. Discovering nonlinear manifolds

21. Combining supervised and unsupervised learning

22. Discovering rules (data mining) Find the most frequent patterns (association rules) Num in household = 1 ^ num children = 0 => language = English Language = English ^ Income < $40k ^ Married = false ^ num children = 0 => education {college, grad school} HS MD PhD MA Educ. $30k $80k $20k $10k Income Retired Doctor Student Student Occup. 60 M F 30 M M 24 S F 22 S M Age Married Sex

24. Discovering networks ? From data visualization to causal discovery

28. Qualitative level: Boolean Networks

31. Simple probabilistic model: linear regression Y Y =  +  X + noise Deterministic (functional) relationship X

32. Simple probabilistic model: linear regression Y Y =  +  X + noise Deterministic (functional) relationship X “ Learning” = estimating parameters  ,  ,  from (x,y) pairs. Can be estimate by least squares Is the empirical mean Is the residual variance

33. Piecewise linear regression Latent “switch” variable – hidden process at work

35. Classes of graphical models Probabilistic models Graphical models Directed Undirected Bayes nets MRFs DBNs

41. Viterbi decoding Y 1 Y 3 X 1 X 2 X 3 Y 2 Compute most probable explanation (MPE) of observed data Hidden Markov Model (HMM) “ Tomato” hidden observed

42. Inference: computational issues Easy Hard Chains Trees Grids Dense, loopy graphs PCWP CO HRBP HREKG HRSAT ERRCAUTER HR HISTORY CATECHOL SAO2 EXPCO2 ARTCO2 VENTALV VENTLUNG VENITUBE DISCONNECT MINVOLSET VENTMACH KINKEDTUBE INTUBATION PULMEMBOLUS PAP SHUNT MINOVL PVSAT PRESS INSUFFANESTH TPR LVFAILURE ERRBLOWOUTPUT STROEVOLUME LVEDVOLUME HYPOVOLEMIA CVP BP

43. Inference: computational issues Easy Hard Chains Trees Grids Dense, loopy graphs Many difference inference algorithms, both exact and approximate PCWP CO HRBP HREKG HRSAT ERRCAUTER HR HISTORY CATECHOL SAO2 EXPCO2 ARTCO2 VENTALV VENTLUNG VENITUBE DISCONNECT MINVOLSET VENTMACH KINKEDTUBE INTUBATION PULMEMBOLUS PAP SHUNT MINOVL PVSAT PRESS INSUFFANESTH TPR LVFAILURE ERRBLOWOUTPUT STROEVOLUME LVEDVOLUME HYPOVOLEMIA CVP BP

48. Score ­b ased Learning E B A E B A E B A Search for a structure that maximizes the score Define scoring function that evaluates how well a structure matches the data E, B, A <Y,N,N> <Y,Y,Y> <N,N,Y> <N,Y,Y> . . <N,Y,Y>

52. Problems with local search S(G|D) Easy to get stuck in local optima “ truth” you

53. Problems with local search II Picking a single best model can be misleading E R B A C P(G|D)

58. Discovering latent variables a) 17 parameters b) 59 parameters There are some techniques for automatically detecting the possible presence of latent variables

63. Learning from relational data Can we learn concepts from a set of relations between objects, instead of/ in addition to just their attributes?

65. ILP for learning protein folding: input yes no TotalLength(D2mhr, 118) ^ NumberHelices(D2mhr, 6) ^ … 100 conjuncts describing structure of each pos/neg example

68. The future of machine learning for bioinformatics? Oracle

70. The end

71. Decision trees blue? big? oval? no no yes yes

72. Decision trees blue? big? oval? no no yes yes + Handles mixed variables + Handles missing data + Efficient for large data sets + Handles irrelevant attributes + Easy to understand - Predictive power

73. Feedforward neural network input Hidden layer Output Weights on each arc Sigmoid function at each node

74. Feedforward neural network input Hidden layer Output - Handles mixed variables - Handles missing data - Efficient for large data sets - Handles irrelevant attributes - Easy to understand + Predicts poorly

76. Nearest Neighbor ? - Handles mixed variables - Handles missing data - Efficient for large data sets - Handles irrelevant attributes - Easy to understand + Predictive power

79. Replace all inner products with kernels Kernel function

87. Instances of graphical models Probabilistic models Graphical models Directed Undirected Bayes nets MRFs DBNs Hidden Markov Model (HMM) Naïve Bayes classifier Mixtures of experts Kalman filter model Ising model