ML Algorithms

1 . Linear Regression In this problem, we will implement least squares linear regression to predict density of wine based on its acidity. a) Implement batch gradient descent method for optimizing J(θ). Choose an appropriate learning rate and the stopping criteria (as a function of the change in the value of J(θ)). You can initialize the parameters as θ = ~0 (the vector of all zeros). Do not forget to include the intercept term. Report your learning rate, stopping criteria and the final set of parameters obtained by your algorithm 2. Sampling and Stochastic Gradient Descent In this problem, we will introduce the idea of sampling by adding Gaussian noise to the prediction of a hypothesis and generate synthetic training data. Consider a given hypothesis hθ (i.e. known θ0, θ1, θ2) for a data point x = " x0 x1 x2 # . Note that x0 = 1 is the intercept term. y = hθ(x) = θ0 + θ1x1 + θ2x2 Adding Gaussian noise, equation becomes y = θ0 + θ1x1 + θ2x2 +  where  ∼ N (0, σ2 ) 3. Logistic Regression 4. Gaussian Discrmimant Analysis In this problem, we will implement GDA for separating out salmons from Alaska and Canada. Each salmon is represented by two attributes x1 and x2 depicting growth ring diameters in 1) fresh water, 2) marine water, respectively. File [login to view URL] stores the two attribute values with one entry on each row. File [login to view URL] contains the target values (y (i) ’s ∈ {Alaska, Canada}) on respective rows. More details and documents will share upon confirmation