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# hw4_solution - column is the index for the data points the...

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CS 6375 Machine Learning, 2009 Spring Homework 4: Total points: 80 Part I. Written problems. 45 points. 1. Gradient descent. [10 pts] Consider a different kind of computing unit for a neural network. Rather than a sigmoid function, it will use a Gaussian. That is, given an input vector x (augmented with x 0 =1) and a weight vector β , the output of the unit will be 2 ) ( ), ( z e z g where x g o = = β Derive a gradient descent training rule for a single Gaussian unit. Sol: 2 2 ) ( ' z ze z g = . Using the following notation, the gradient-descent training rule is T x in β ) ( in g o = o t Err j in j j x e in Err × × × × 2 2 η β β 2. Neural network and back propagation [15 pts] For the following network with initial weights, show the weights after an example ((1,1), 1) is presented. Assume learning rate is 0.05, and no momentum. Sigmoid function is used in the nodes.

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3. Cross validation (CV). [10 pts] The following table shows the training data for a binary classification task, where the first
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Unformatted text preview: column is the index for the data points, the second one shows the value for the feature (just one attribute) and the last column gives the class label. We will use nearest neighbor classifier for this problem. sample Attribute 1 Class table 1 -0.1 - 2 0.7 - 3 1.0 + 4 1.6 + 5 2.0 + 6 2.5 - 7 3.2 + 8 3.5 - 9 4.1 + 10 4.9 + (a) What is the 5-fold CV error of 1-NN on this data set? Split the data like this: I: instance 1, 2; II: 3, 4; III: 5, 6; IV: 7, 8; V: 9, 10. The error rate for each of the folds is: 1, 0.5, 0.5, 1, 1, respectively. The average error rate is thus 0.8. (b) What is the 2-fold CV error of 3-NN on this data set? Use the first 5 data points in the first subset, and the last 5 points in the other subset. The error rate for the two folds is 0.6, 0.4. The average error rate is 0.5....
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