[SOLVED] COEN240 Homework 1

Description

Problem 1 You have a set of 𝑁 training inputs 𝐱_𝑛 ∈ ℝ^𝑀, 𝑛 = 1, 2, … , 𝑁, 𝑁 ≫ 𝑀. The target outputs of the training inputs are 𝑡_𝑛 ∈ ℝ, 𝑛 = 1, 2, … , 𝑁. Build a linear regression model to predict the target value by 𝐰^𝑇𝐱_𝑛. Derive the closed-form solution for the weight vector 𝐰 ∈ ℝ^𝑀 that minimizes the error function  𝐸(𝐰) =

{𝐰^𝑇𝐱_𝑛 − 𝑡_𝑛 }².

Problem 2 The Pima Indians diabetes data set (pima-indians-diabetes.xlsx) is a data set used to diagnostically predict whether or not a patient has diabetes, based on certain diagnostic measurements included in the dataset. All patients here are females at least 21 years old of Pima Indian heritage. The dataset consists of M = 8 attributes and one target variable, Outcome (1 represents diabetes, 0 represents no diabetes). The 8 attributes include Pregnancies, Glucose, BloodPressure, BMI, insulin level, age, and so on. There are N=768 data samples.

Randomly select n samples from the “diabetes” class and n samples from the “no diabetes” class, and use them as the training samples. The remaining data samples are the test samples. Build a linear regression model as described in Problem 1 with the training set, and test your model on the test samples to predict whether or not a test patient has diabetes or not. Assume the predicted outcome of a test sample is 𝑡̂, if 𝑡̂ ≥ 0.5 (closer to 1), classify it as “diabetes”; if 𝑡̂ < 0.5 (closer to 0), classify it as “no diabetes”. Run 1000 independent experiments, and calculate the prediction accuracy rate as ^{𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛𝑠} %. Let n=40, 80, 120, 160, 200, plot the

𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑠𝑡 𝑐𝑎𝑠𝑒𝑠

accuracy rate versus n. Comment on the result. Attach the code at the end of the homework.