Artificiel Neural Networks 2 Morten Nielsen Department of Systems Biology , DTU

1. Artificiel Neural Networks 2Morten NielsenDepartment of Systems Biology,DTU

2. Outline • Optimization procedures • Gradient decent (this you already know) • Network training • back propagation • cross-validation • Over-fitting • examples

3. Neural network. Error estimate Linear function I1 I2 w1 w2 o

4. Neural networks

5. Gradient decent (from wekipedia) Gradient descent is based on the observation that if the real-valued function F(x) is defined and differentiable in a neighborhood of a point a, then F(x) decreases fastest if one goes from a in the direction of the negative gradient of F at a. It follows that, if for  > 0 a small enough number, then F(b)<F(a)

6. Gradient decent (example)

7. Gradient decent (example)

8. Gradient decent. Example Weights are changed in the opposite direction of the gradient of the error Linear function I1 I2 w1 w2 o

9. Network architecture Ik Input layer vjk hj Hidden layer Hj wj o Output layer O

10. What about the hidden layer?

11. Hidden to output layer

12. Hidden to output layer

13. Hidden to output layer

14. Input to hidden layer

15. Input to hidden layer

16. Summary

17. Or

18. Or Ii=X[0][k] Hj=X[1][j] Oi=X[2][i]

19. Can you do it your self? I1=1 I2=1 v21=-1 v12=1 v11=1 v22=1 h1 H1 h2 H2 w2=1 w1=-1 o O What is the output (O) from the network? What are the wij and vjk values if the target value is 0 and =0.5?

20. Can you do it your self (=0.5). Has the error decreased? After Before I1=1 I2=1 I1=1 I2=1 v21=-1 v12=1 v21= v12= v11=1 v22=1 V11= v22=. h2= H2= h1= H1= h1= H1= h2= H2= w2=1 w1=-1 w2= w1= o= O= o= O=

21. Can you do it your self? I1=1 I2=1 v21=-1 v12=1 v11=1 v22=1 h2=0 H2=0.5 h1=2 H1=0.88 w2=1 w1=-1 o=-0.38 O=0.41 • What is the output (O) from the network? • What are the wij and vjk values if the target value is 0?

22. Can you do it your self (=0.5). Has the error decreased? I1=1 I2=1 I1=1 I2=1 v21=-1 v12=1 v12=1.005 v21=-1.01 v11=1 v22=1 v22=.0.99 v11=1.005 h2=0 H2=0.5 h1=2 H1=0.88 h1=2.01 H1=0.882 h2=-0.02 H2=0.495 w2=1 w1=-1 w2=0.975 w1=-1.043 o=-0.38 O=0.41 o=-0.44 O=0.39

23. Sequence encoding • Change in weight is linearly dependent on input value • “True” sparse encoding is therefore highly inefficient • Sparse is most often encoded as • +1/-1 or 0.9/0.05

24. Sequence encoding - rescaling • Rescaling the input values If the input (o or h) is too large or too small, g´ is Zero and the weight are not changed. Optimal performance is when o,h are close to 0.5

25. Training and error reduction 

26. Training and error reduction 

27. Training and error reduction Size matters 

28. Example

29. Neural network training. Cross validation Cross validation Train on 4/5 of data Test on 1/5 => Produce 5 different neural networks each with a different prediction focus

30. Neural network training curve Maximum test set performance Most cable of generalizing

31. 5 fold training Which network to choose?

32. 5 fold training

33. Conventional 5 fold cross validation

34. “Nested”5 fold cross validation

35. When to be careful • When data is scarce, the performance obtained used “conventional” versus “Nested”cross validation can be very large • When data is abundant the difference is small, and “nested”cross validation might even be higher than “conventional” cross validation due to the ensemble aspect of the “nested”cross validation approach

36. NetMHCpan Do hidden neurons matter? • The environment matters

37. Context matters • FMIDWILDA YFAMYGEKVAHTHVDTLYVRYHYYTWAVLAYTWY 0.89 A0201 • FMIDWILDA YFAMYQENMAHTDANTLYIIYRDYTWVARVYRGY 0.08 A0101 • DSDGSFFLY YFAMYGEKVAHTHVDTLYVRYHYYTWAVLAYTWY 0.08 A0201 • DSDGSFFLY YFAMYQENMAHTDANTLYIIYRDYTWVARVYRGY 0.85 A0101

38. Example

39. Summary • Gradient decent is used to determine the updates for the synapses in the neural network • Some relatively simple math defines the gradients • Networks without hidden layers can be solved on the back of an envelope (SMM exercise) • Hidden layers are a bit more complex, but still ok • Always train networks using a test set to stop training • Be careful when reporting predictive performance • Use “nested”cross-validation for small data sets • And hidden neurons do matter (sometimes)

40. And some more stuff for the long cold winter nights • Can it might be made differently?

41. Predicting accuracy • Can it be made differently? Reliability

42. Making sense of ANN weights • Identification of position specific receptor ligand interactions by use of artificial neural network decomposition. An investigation of interactions in the MHC:peptide system Master thesis by FrederikOtzen Bagger

43. Making sense of ANN weights

44. Making sense of ANN weights

45. Making sense of ANN weights

46. Making sense of ANN weights

47. Making sense of ANN weights

48. Making sense of ANN weights

49. Deep learning http://www.slideshare.net/hammawan/deep-neural-networks

50. NN with 2 hidden layers