EECS 445 ML - University of Michigan_ Introduction to Machine Learning-Homework 3 Plus Solutions.

EECS 445 ML - University of Michigan_ Introduction to Machine Learning-Homework 3 Plus Solutions. EECS 445, Winter 2020 – Homework 3, Due: Tues. 4/7 at 11:59pm 1 UNIVERSITY OF MICHIGAN Department of Electrical Engineering and Computer Science EECS 445 — Introduction to Machine Learning Wint er 2020 Homework 3, Due: Tues. 4/7 at 11:59pm Submission: Please upload your completed assignment by 11:59pm Tuesday, April 7th to Gradescope. 1 Neural Networks [8 pts] Sahas was inspired by Noa’s findings in Project 2. He is now interested in determining the price of a dish is based on two inputs Size and Tastiness. Sahas eats ten different dishes and records their mass in kilograms and tastiness on a continuous scale of 1-10. Then he records the price of the dish. The following is the neural network he sets up to perform this regression task. We will use the Sigmoid activation function on each hidden neuron and use squared loss to evaluate our model. All of the current weights are given below. The tables are organized such that the row designates which input the weight is from and the column indicates which output the weight is to. For example weight w (1) 21 is found in the x1 row and the h(2) 2 column. Table 1: Layer 1 Weights EECS 445, Winter 2020 – Homework 3, Due: Tues. 4/7 at 11:59pm 2 Table 2: Layer 2 Weights a Note: w(l) ji is the weight for lth fully connected layer, connecting unit j with input i. We are currently in the process of training our neural network and randomly sample the data point {x¯ = [1, 5]t, y = 4} (a) [2 pt] What is the output of our neural network given this datapoint? (b) [1 pt] Next, compute the loss between the expected output and our prediction. (c) [5 pts] Since we are still training this network, we now need @L @w(l) ij for all i, j and l to perform an SGD update. Compute @L @w(1) 12 , @L @w(2) 12 , @L @w(3) 12 EECS 445, Winter 2020 – Homework 3, Due: Tues. 4/7 at 11:59pm 3 EECS 445, Winter 2020 – Homework 3, Due: Tues. 4/7 at 11:59pm 4 2 Food Clusters [15 pts] Thanks to all of your hard work in Project 2, Noa has a way to easily sort through all of her food options. Unfortunately, in her excitement to finally choose, Noa misplaced the labels of her images so you have promised to create her an unsupervised algorithm for categorizing the food. Like the autoencoder in Project 2, we will attempt to identify structure in the data without training on labels. You will be implementing the k-means clustering algorithm as well as a variant of the algorithm, k-means++, which has the additional property of encouraging good cluster centroid initializations. These are simple yet powerful unsupervised methods for grouping similar examples within a dataset. You will write your code in clustering and . (a) [1 pt] Why are poor centroid initializations often a problem? (b) [1 pt] Implement the function Pnce() in the file clustering . This function takes as arguments two Point objects and retur