1. Structure learning with deep neuronal networks 6 th Network Modeling Workshop, 6/6/2013 Patrick Michl

2. Page 26/6/2013 Patrick Michl Network Modeling Agenda Autoencoders Biological Model Validation & Implementation

3. Page 36/6/2013 Patrick Michl Network Modeling Real world data usually is high dimensional … x1x1 x2x2 DatasetModel Autoencoders

4. Page 46/6/2013 Patrick Michl Network Modeling … which makes structural analysis and modeling complicated! x1x1 x2x2 x1x1 x2x2 DatasetModel Autoencoders

5. Page 56/6/2013 Patrick Michl Network Modeling Dimensionality reduction techinques like PCA … x1x1 x2x2 PCA DatasetModel Autoencoders

6. Page 66/6/2013 Patrick Michl Network Modeling … can not preserve complex structures! x1x1 x2x2 PCA DatasetModel x1x1 x2x2 Autoencoders

7. Page 76/6/2013 Patrick Michl Network Modeling Therefore the analysis of unknown structures … x1x1 x2x2 DatasetModel Autoencoders

8. Page 86/6/2013 Patrick Michl Network Modeling … needs more considerate nonlinear techniques! x1x1 x2x2 DatasetModel x1x1 x2x2 Autoencoders

9. Page 96/6/2013 Patrick Michl Network Modeling Autoencoders are artificial neuronal networks … Autoencoder Artificial Neuronal Network Autoencoders input data X output data X‘ Perceptrons Gaussian Units

10. Page 106/6/2013 Patrick Michl Network Modeling Autoencoders are artificial neuronal networks … Autoencoder Artificial Neuronal Network Autoencoders input data X output data X‘ Perceptrons Gaussian Units Perceptron 1 0 Gauss Units R

11. Page 116/6/2013 Patrick Michl Network Modeling Autoencoders are artificial neuronal networks … Autoencoder Artificial Neuronal Network Autoencoders input data X output data X‘ Perceptrons Gaussian Units

12. Page 126/6/2013 Patrick Michl Network Modeling Autoencoder Artificial Neuronal Network Multiple hidden layers Autoencoders … with multiple hidden layers. Gaussian Units input data X output data X‘ Perceptrons (Visible layers) (Hidden layers)

13. Page 136/6/2013 Patrick Michl Network Modeling Autoencoder Artificial Neuronal Network Multiple hidden layers Autoencoders Such networks are called deep networks. Gaussian Units input data X output data X‘ Perceptrons (Visible layers) (Hidden layers)

14. Page 146/6/2013 Patrick Michl Network Modeling Autoencoder Artificial Neuronal Network Multiple hidden layers Autoencoders Such networks are called deep networks. Gaussian Units input data X output data X‘ Perceptrons (Visible layers) (Hidden layers) Definition (deep network) Deep networks are artificial neuronal networks with multiple hidden layers

15. Page 156/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders Gaussian Units input data X output data X‘ Perceptrons (Visible layers) (Hidden layers) Such networks are called deep networks. Deep network

16. Page 166/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders Autoencoders have a symmetric topology … Gaussian Units input data X output data X‘ Perceptrons (Visible layers) (Hidden layers) Deep network Symmetric topology

17. Page 176/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders … with an odd number of hidden layers. Gaussian Units input data X output data X‘ Perceptrons (Visible layers) (Hidden layers) Deep network Symmetric topology

18. Page 186/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders The small layer in the center works lika an information bottleneck input data X output data X‘ Deep network Symmetric topology Information bottleneck Bottleneck

19. Page 196/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders... that creates a low dimensional code for each sample in the input data. input data X output data X‘ Deep network Symmetric topology Information bottleneck Bottleneck

20. Page 206/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders The upper stack does the encoding … input data X output data X‘ Deep network Symmetric topology Information bottleneck Encoder

21. Page 216/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders … and the lower stack does the decoding. input data X output data X‘ Deep network Symmetric topology Information bottleneck Encoder Decoder Encoder Decoder

22. Page 226/6/2013 Patrick Michl Network Modeling Deep network Symmetric topology Information bottleneck Encoder Decoder Autoencoder Autoencoders … and the lower stack does the decoding. input data X output data X‘ Encoder Decoder Definition (deep network) Deep networks are artificial neuronal networks with multiple hidden layers Definition (autoencoder) Autoencoders are deep networks with a symmetric topology and an odd number of hiddern layers, containing a encoder, a low dimensional representation and a decoder.

23. Page 236/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders Autoencoders can be used to reduce the dimension of data … input data X output data X‘ Problem: dimensionality of data Idea: 1.Train autoencoder to minimize the distance between input X and output X‘ 2.Encode X to low dimensional code Y 3.Decode low dimensional code Y to output X‘ 4.Output X‘ is low dimensional

24. Page 246/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders … if we can train them! input data X output data X‘ Problem: dimensionality of data Idea: 1.Train autoencoder to minimize the distance between input X and output X‘ 2.Encode X to low dimensional code Y 3.Decode low dimensional code Y to output X‘ 4.Output X‘ is low dimensional

25. Page 256/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders In feedforward ANNs backpropagation is a good approach. input data X output data X‘ Training Backpropagation

26. Page 266/6/2013 Patrick Michl Network Modeling Backpropagation Autoencoder Autoencoders input data X output data X‘ Training Definition (autoencoder) Backpropagation (1)The distance (error) between current output X‘ and wanted output Y is computed. This gives a error function In feedforward ANNs backpropagation is a good approach.

27. Page 276/6/2013 Patrick Michl Network Modeling Backpropagation Autoencoder Autoencoders In feedforward ANNs backpropagation is the choice input data X output data X‘ Training Definition (autoencoder) Backpropagation (1)The distance (error) between current output X‘ and wanted output Y is computed. This gives a error function Example (linear neuronal unit with two inputs)

28. Page 286/6/2013 Patrick Michl Network Modeling Backpropagation Autoencoder Autoencoders input data X output data X‘ Training Definition (autoencoder) Backpropagation In feedforward ANNs backpropagation is a good approach.

29. Page 296/6/2013 Patrick Michl Network Modeling Backpropagation Autoencoder Autoencoders In feedforward ANNs backpropagation is the choice input data X output data X‘ Training Definition (autoencoder) Backpropagation

30. Page 306/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders … the problem are the multiple hidden layers! input data X output data X‘ Training Backpropagation Problem: Deep Network

31. Page 316/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation is known to be slow far away from the output layer … Backpropagation Problem: Deep Network Very slow training

32. Page 326/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training … and can converge to poor local minima. Backpropagation Problem: Deep Network Very slow training Maybe bad solution

33. Page 336/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution The task is to initialize the parameters close to a good solution!

34. Page 346/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution Pretraining Therefore the training of autoencoders has a pretraining phase …

35. Page 356/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution Pretraining Restricted Boltzmann Machines … which uses Restricted Boltzmann Machines (RBMs)

36. Page 366/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution Pretraining Restricted Boltzmann Machines … which uses Restricted Boltzmann Machines (RBMs) Restricted Boltzmann Machine RBMs are Markov Random Fields

37. Page 376/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution Pretraining Restricted Boltzmann Machines … which uses Restricted Boltzmann Machines (RBMs) Restricted Boltzmann Machine RBMs are Markov Random Fields Markov Random Field Every unit influences every neighbor The coupling is undirected Motivation (Ising Model) A set of magnetic dipoles (spins) is arranged in a graph (lattice) where neighbors are coupled with a given strengt

38. Page 386/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution Pretraining Restricted Boltzmann Machines … which uses Restricted Boltzmann Machines (RBMs) Restricted Boltzmann Machine RBMs are Markov Random Fields Bipartite topology: visible (v), hidden (h) Use local energy to calculate the probabilities of values Training: contrastive divergency (Gibbs Sampling)

39. Page 396/6/2013 Patrick Michl Network Modeling Autoencoder Autoencoders input data X output data X‘ Training Backpropagation Problem: Deep Network Very slow training Maybe bad solution Idea: Initialize close to a good solution Pretraining Restricted Boltzmann Machines … which uses Restricted Boltzmann Machines (RBMs) Restricted Boltzmann Machine Gibbs Sampling

40. Page 406/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder The top layer RBM transforms real value data into binary codes. Top Training

41. Page 416/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Top Therefore visible units are modeled with gaussians to encode data … Training

42. Page 426/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Top … and many hidden units with simoids to encode dependencies Training

43. Page 436/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Top The objective function is the sum of the local energies. Local Energy Training

44. Page 446/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Reduction The next RBM layer maps the dependency encoding… Training

45. Page 456/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Reduction … from the upper layer … Training

46. Page 466/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Reduction … to a smaller number of simoids … Training

47. Page 476/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Reduction … which can be trained faster than the top layer Local Energy Training

48. Page 486/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Unrolling The symmetric topology allows us to skip further training. Training

49. Page 496/6/2013 Patrick Michl Network Modeling Autoencoders Autoencoder Unrolling The symmetric topology allows us to skip further training. Training

50. Page 506/6/2013 Patrick Michl Network Modeling After pretraining backpropagation usually finds good solutions Autoencoders Autoencoder Training Pretraining Top RBM (GRBM) Reduction RBMs Unrolling Finetuning Backpropagation

51. Page 516/6/2013 Patrick Michl Network Modeling The algorithmic complexity of RBM training depends on the network size Autoencoders Autoencoder Training Complexity: O(inw) i: number of iterations n: number of nodes w: number of weights Memory Complexity: O(w)

52. Page 526/6/2013 Patrick Michl Network Modeling Agenda Autoencoders Biological Model Validation & Implementation

53. Page 536/6/2013 Patrick Michl Network Modeling Network Modeling Restricted Boltzmann Machines (RBM) How to model the topological structure? SETF

54. Page 546/6/2013 Patrick Michl Network Modeling We define S and E as visible data Layer … S E TF Network Modeling Restricted Boltzmann Machines (RBM)

55. Page 556/6/2013 Patrick Michl Network Modeling SE TF Network Modeling Restricted Boltzmann Machines (RBM) We identify S and E with the visible layer …

56. Page 566/6/2013 Patrick Michl Network Modeling SE … and the TFs with the hidden layer in a RBM TF Network Modeling Restricted Boltzmann Machines (RBM)

57. Page 576/6/2013 Patrick Michl Network Modeling SE The training of the RBM gives us a model TF Network Modeling Restricted Boltzmann Machines (RBM)

58. Page 586/6/2013 Patrick Michl Network Modeling Agenda Autoencoder Biological Model Implementation & Results

59. Page 596/6/2013 Patrick Michl Network Modeling Results Validation of the results Needs information about the true regulation Needs information about the descriptive power of the data

60. Page 606/6/2013 Patrick Michl Network Modeling Results Validation of the results Needs information about the true regulation Needs information about the descriptive power of the data Without this infomation validation can only be done, using artificial datasets!

61. Page 616/6/2013 Patrick Michl Network Modeling Results Artificial datasets We simulate data in three steps:

62. Page 626/6/2013 Patrick Michl Network Modeling Results Artificial datasets We simulate data in three steps Step 1 Choose number of Genes (E+S) and create random bimodal distributed data

63. Page 636/6/2013 Patrick Michl Network Modeling Results Artificial datasets We simulate data in three steps Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Step 2 Manipulate data in a fixed order

64. Page 646/6/2013 Patrick Michl Network Modeling Results Artificial datasets We simulate data in three steps Step 1 Choose number of Genes (E+S) and create random bimodal distributed data Step 2 Manipulate data in a fixed order Step 3 Add noise to manipulated data and normalize data

65. Page 656/6/2013 Patrick Michl Network Modeling Simulation Results

66. Page 666/6/2013 Patrick Michl Network Modeling Simulation Results Step 2 Manipulate data

67. Page 676/6/2013 Patrick Michl Network Modeling Simulation Results

68. Page 686/6/2013 Patrick Michl Network Modeling Results We analyse the data X with an RBM

69. Page 696/6/2013 Patrick Michl Network Modeling Results We train an autoencoder with 9 hidden layers and 165 nodes: Layer 1 & 9: 32 hidden units Layer 2 & 8: 24 hidden units Layer 3 & 7: 16 hidden units Layer 4 & 6: 8 hidden units Layer 5: 5 hidden units input data X output data X‘

70. Page 706/6/2013 Patrick Michl Network Modeling Results We transform the data from X to X‘ And reduce the dimensionality

71. Page 716/6/2013 Patrick Michl Network Modeling Results We analyse the transformed data X‘ with an RBM

72. Page 726/6/2013 Patrick Michl Network Modeling Results Lets compare the models

73. Page 736/6/2013 Patrick Michl Network Modeling Results Another Example with more nodes and larger autoencoder

74. Page 746/6/2013 Patrick Michl Network Modeling Conclusion Autoencoders can improve modeling significantly by reducing the dimensionality of data Autoencoders preserve complex structures in their multilayer perceptron network. Analysing those networks (for example with knockout tests) could give more structural information The drawback are high computational costs Since the field of deep learning is getting more popular (Face recognition / Voice recognition, Image transformation). Many new improvements in facing the computational costs have been made.

75. Page 756/6/2013 Patrick Michl Network Modeling Acknowledgement eilsLABS Prof. Dr. Rainer König Prof. Dr. Roland Eils Network Modeling Group