Chap5.7-BayesianNeuralNetworks

Chap5.7-BayesianNeuralNetworks - Machine Learning Srihari...

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Machine Learning Srihari Bayesian Neural Networks Sargur Srihari [email protected] 1
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Machine Learning Srihari Topics discussed here 1. Why Bayesian? 2. Difficulty of exact Bayesian treatment and need for approximation 3. Two approximate approaches Variational Laplace (one discussed here) 4. Bayesian neural network for regression Posterior parameter distribution Hyper-parameter optimization 5. Bayesian neural network for classification 2
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Machine Learning Srihari Why Bayesian? More complex models fit data better but generalize poorly Linear with two free parameters, quadratic with three, cubic with four? Occam ʼ s razor says that unnecessarily complex models should not be preferred to simpler ones Neural networks are popular but notoriously lack objective grounding Bayesian approach allows different models to be compared (no of hidden units) 3
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Machine Learning Srihari Classical and Bayesian neural networks Classical neural networks use maximum likelihood To determine network parameters (weights and biases) Regularized maximum likelihood is MAP (maximum a posteriori) Regularizer is the logarithm of prior parameter distribution Bayesian treatment marginalizes over distribution of parameters in order to make prediction 4
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Machine Learning Srihari Need for Approximation in Bayesian treatment In simple linear regression problem, under assumption of Gaussian noise Posterior is Gaussian and evaluated exactly
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