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Datamining & Neural Networks

Session 3

PCA & ARD

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• Regularization on cost-function : βED + αEW e.g EW=1/2*||w||2

• three levels of inference

1. Infer model parameters w ; α, β fixed 2. Infer α, β ; given the model params 3. comparison of different models

• Evidence-based framework of MacKay for

estimation of hyperparameters : interpretation of • α as 1/σ2

W

• β as 1/σ2 D

• approx. of evidence factor yields update formula’s for hyperparameters

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ARD

• one hyperparam per input of your NN

• Goal: detection of most relevant inputs in

the Bayesian framework

N N α1 α2 α3 Costfunction = βED + α1(Σwi12)+α 2(Σwi22)+…

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ARD in practice

1.

Define NN model

2.

Optimize weights

3.

Optimize

α, β , -- given weights

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Exercise 2

• Demev1 (Evidence-based framework)

• Demard (ARD)

• Ionosphere dataset: 33 inputs, appr. 350

datapoints.

– make classification NN (cfr. also session 2, ex. 3) – perform ARD, rank inputs

– select subset of inputs based on α’s

– make new NN with this subset of inputs – compare performance with first NN

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