1 Perceptron (50 points)

File name: perceptron.py

Implement a function in python:

perceptron_train(X,Y)

that takes training data as input and outputs the weights w, and the bias b of the perceptron. Your function should handle any real-valued features, with feature vectors in any dimension, and binary labels. Write-Up: describe your implementation concisely.

Implement a function in python:

perceptron_test(X_test, Y_test, w, b)

that takes testing data, the perceptron weights and bias as input and returns the accuracy on the testing data. Write-Up: describe your implementation concisely.

You should get the following output for the perceptron when you run the test script.

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2 Gradient Descent (50 points)

Implement a function in python: gradient descent(f,x_init,) that takes the gradient of a function f as input, the starting x_init and the learning rate . The output of gradient descent is the value of x that minimizes f. f will be in the form of a function, so that you can calculate the gradient at a particular point. That is f is a function with one input x and it outputs the value of the gradient at that point. If we are working with 1D variables, then x= (x₁). If x is 2D then x= (x₁,x₂) and so on. x should be a 1D numpy array. Write-Up: describe your implementation concisely.

If you test your function using f(x) = x², x_init = 5, and = 0.1. f = 2x. You should get a final x of 4.56719262e 05 or something very small like that. It should take 52 steps. Note, I am not checking for

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gradient equal to 0. I am checking that the magnitude of the gradient is less than some very small value,

0.0001.

For testing purposes: I will test your program with various f.

You should get the following output for the gradient descent when you run the test script.

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