Artificial Neural Networks 2 Morten Nielsen BioSys, DTU

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

Neural network. Error estimate I1I1 I2I2 w1w1 w2w2 Linear function o

Neural networks

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)

Gradient decent (example)

Gradient decent. Example Weights are changed in the opposite direction of the gradient of the error I1I1 I2I2 w1w1 w2w2 Linear function o

What about the hidden layer?

Hidden to output layer

Input to hidden layer

Summary

Or

I i =X[0][k] H j =X[1][j] O i =X[2][i]

Can you do it your self? v 22 =1 v 12 =1 v 11 =1 v 21 =-1 w 1 =-1 w 2 =1 h2H2h2H2 h1H1h1H1 oOoO I 1 =1I 2 =1 What is the output (O) from the network? What are the  w ij and  v jk values if the target value is 0 and  =0.5?

Can you do it your self (  =0.5). Has the error decreased? v 22 =1 v 12 =1 v 11 =1 v 21 =-1 w 1 =-1 w 2 =1 h2=H2=h2=H2= h 1= H 1 = o= O= I 1 =1I 2 =1 v 22 =. v 12 = V 11 = v 21 = w1=w1= w2=w2= h2=H2=h2=H2= h1=H1=h1=H1= o= O= I 1 =1I 2 =1 Before After

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

Training and error reduction 



 Size matters

A Network contains a very large set of parameters –A network with 5 hidden neurons predicting binding for 9meric peptides has more than 9x20x5=900 weights Over fitting is a problem Stop training when test performance is optimal Neural network training years Temperature

What is going on? years Temperature  

Examples Train on 500 A0201 and 60 A0101 binding data Evaluate on 1266 A0201 peptides NH=1: PCC = 0.77 NH=5: PCC = 0.72

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

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

5 fold training Which network to choose?

5 fold training

How many folds? Cross validation is always good!, but how many folds? –Few folds -> small training data sets –Many folds -> small test data sets Example from Tuesdays exercise –560 peptides for training 50 fold (10 peptides per test set, few data to stop training) 2 fold (280 peptides per test set, few data to train) 5 fold (110 peptide per test set, 450 per training set)

Problems with 5fold cross validation Use test set to stop training, and test set performance to evaluate training –Over-fitting? If test set is small yes If test set is large no Confirm using “true” 5 fold cross validation –1/5 for evaluation –4/5 for 4 fold cross-validation

Conventional 5 fold cross validation

“True” 5 fold cross validation

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

Do hidden neurons matter? The environment matters NetMHCpan

Context matters FMIDWILDA YFAMYGEKVAHTHVDTLYVRYHYYTWAVLAYTWY 0.89 A0201 FMIDWILDA YFAMYQENMAHTDANTLYIIYRDYTWVARVYRGY 0.08 A0101 DSDGSFFLY YFAMYGEKVAHTHVDTLYVRYHYYTWAVLAYTWY 0.08 A0201 DSDGSFFLY YFAMYQENMAHTDANTLYIIYRDYTWVARVYRGY 0.85 A0101

Example

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 “true” cross-validation for small data sets And hidden neurons do matter (sometimes)

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

Predicting accuracy Can it be made differently? Reliability