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Chap5.1-NNintro - Machine Learning Neural Networks...

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Machine Learning Srihari Neural Networks Introduction Sargur Srihari
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Machine Learning Srihari Topics 1. Introduction 1. Extending linear models 2. Feed-forward Network Functions 3. Weight-space symmetries 2. Network Training 1. Parameter Optimization 2. Local quadratic approximation 3. Use of gradient information 4. Gradient descent optimization 3. Error Backpropagation 4. The Hessian Matrix 5. Regularization in Neural Networks 6. Mixture Density Networks 7. Bayesian Neural Networks 2
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Machine Learning Srihari A Neural Network 3 Can be viewed as a generalization of linear models y k (x,w) = σ w kj (2) j = 1 M h w ji (1) i = 1 D x i + w j 0 (1) + w k 0 (2)
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Machine Learning Srihari Linear Models Linear Models for Regression and Classification have form where x is a D -dimensional vector ϕ j (x) are fixed nonlinear basis functions e.g., Gaussian, sigmoid or powers of x For Regression f is identity function For Classification f is a nonlinear activation function If f is sigmoid it is called logistic regression y (x,w) = f w j φ j (x) j = 1 M f ( a ) = 1 1 + e a Linear Regression Generalized Linear Regression
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Machine Learning Srihari Extending Linear Models Linear models have limited applicability Due to curse of dimensionality E.g., no of polynomial coeffts needed, finding means of Gaussians Extend scope by adapting basis functions ϕ j to data Become useful in large scale problems Both SVMs and Neural Networks address this limitation SVM Varying number of basis functions M centered on training data points Select subset of these during training Neural Network Number of basis functions M fixed in advance But the ϕ j have their own parameters {w ji } Adapt all parameter values during training 5 y (x,w) = f w j φ j (x) j = 1 M y k (x,w) = σ w kj (2) j = 1 M h w ji (1) i = 1 D x i + w j 0 (1) + w k 0 (2)
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