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.
| Perceptron : | 1.0 |
| Perceptron : | 0.42857142857142855 |
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2 Gradient Descent (50 points)
Implement a function in python: gradient descent(∇f,xinit,η) that takes the gradient of a function f as input, the starting xinit and the learning rate η. 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, xinit = 5, and η = 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.
| Gradient Descent : | [4.56719262e−05] |
| Gradient Descent : | [2.16433186e−55 5.77016976e−03] |
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