Description
Problem 1 You have a set of 𝑁 training inputs 𝐱 ∈ ℝ𝑀, 𝑛 1, 2, … , 𝑁, 𝑁 ≫ 𝑀. The target outputs of the training inputs are 𝑡 ∈ ℝ, 𝑛 1, 2, … , 𝑁. Build a linear regression model to predict the target value by 𝐰 𝐱 .
Derive the closed-form solution for the weight vector 𝐰 ∈ ℝ𝑀 that minimizes the error function 𝐸 𝐰
𝐰 𝐱 𝑡 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 am le f om he no diabe e cla , and e hem 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
i a diabe e ; if 𝑡̂ 0.5 (closer to 0), cla if i a no diabe e . Run 1000 independent experiments, and calculate the prediction accuracy rate as %. Let n=40, 80, 120, 160, 200, plot the
accuracy rate versus n. Comment on the result. Attach the code at the end of the homework.
