2. (25 points) Consider the following experiment on perceptron learning for random training sets of dimension 10 : - Generate an 11-dimensional weight vector w, where the first dimension is 0 and the other 10 dimensions are sampled independently at random from the uniform (0,1) distribution (the first dimension will serve as the threshold and we set it to 0 for convenience). - Generate a random training set with 100 examples, where each dimension of each training example is sampled independently at random from the uniform {1,1} distribution. The examples are all classified in accordance with w. - Run the perceptron learning algorithm, starting with a zero weight vector, on the training set you just generated. Keep track of the number of iterations it takes to learn a hypothesis that correctly separates the training data. Write code in Python to perform the above experiment and then repeat it 1000 times (note that you're generating a new w and a new training set each time). (a) Plot a histogram of the number of iterations the algorithm takes to learn a linear separator; you should submit this with your writeup. (b) How does the number of iterations compare with the bound on the number of iterations derived in part (e) of the previous problem? Note that this bound will be different for each instantiation of w and training set so in order to answer this question, you will need to analyze the distribution of differences between the bound and the number of iterations. Plot and submit a histogram of the log of this difference. Discuss your interpretation of these results