The document provides an overview of machine learning concepts and applications in bioinformatics. It discusses key topics like supervised vs unsupervised learning, classification vs regression, linear vs non-linear models, and examples of machine learning algorithms like naive Bayes, neural networks, and support vector machines. Specific examples mentioned include using these algorithms for protein function prediction, gene finding, and predicting RNA binding sites in proteins.

25. Linear vs. Non-linear

27. Measuring Performance

31. Sample Learning Scenario – Protein Function Prediction

34. Bayes Theorem P(A) = prior probability P(A|B) = posterior probability

35. Bayes Theorem Applied to Classification

36. Naïve Bayes Algorithm                  n n n n c P c x X x X x X P c P c x X x X x X P x X c P x X c P 2 2 1 1 2 2 1 1 ) 0 ( ) 0 | ,..., , ( ) 1 ( ) 1 | ,..., , ( ) | 0 ( ) | 1 (

37. Naïve Bayes Algorithm Assign c =1 if

38. Example ARG 6 T S K K K R Q R G S R p(X 1 = T | c = 1) p(X 2 = S | c = 1) … p(X 1 = T | c = 0) p(X 2 = S | c = 0) … ≥ θ

39. Predictions for Ribosomal protein L15 PDB ID 1JJ2:K Actual Predicted

41. Biological Neurons Dendrites receive inputs, Axon gives output Image from Christos Stergiou and Dimitrios Siganos http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html

42. Artificial Neuron – “Perceptron” Image from Christos Stergiou and Dimitrios Siganos http://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/cs11/report.html

43. The perceptron X1 X2 XN w1 w2 wN T Input Threshold Unit Output The perceptron classifies the input vector X into two categories. If the weights and threshold T are not known in advance, the perceptron must be trained . Ideally, the perceptron must be trained to return the correct answer on all training examples, and perform well on examples it has never seen. The training set must contain both type of data (i.e. with “1” and “0” output).

45. The perceptron Training a perceptron: Find the weights W that minimizes the error function: P: number of training data X i : training vectors F(W.X i ): output of the perceptron t(X i ) : target value for X i Use steepest descent: - compute gradient: - update weight vector: - iterate (e: learning rate)

46. Biological Neural Network Image from http://en.wikipedia.org/wiki/Biological_neural_network

47. Artificial Neural Network A complete neural network is a set of perceptrons interconnected such that the outputs of some units becomes the inputs of other units. Many topologies are possible! Neural networks are trained just like perceptron, by minimizing an error function:

48. Support Vector Machines - SVMs Image from http://en.wikipedia.org/wiki/Support_vector_machine

49. SVM finds the maximum margin hyperplane Image from http://en.wikipedia.org/wiki/Support_vector_machine

50. Kernel Function

51. Kernel Function