Say we added a higher order product term x1x2 with a new

Question

Problems - For the following problems, use these weights:

w₁ = 0.75

w₂ = 0.45

w₀ = 0.5

With this sample:

x₁ = 2

x₂ = 0.6

1. In a linear regression model, what would the output be?

2. In a perceptron, what would the output be? (Positive class or negative class?)

3. In a logistic regression model, what would the output be (in terms of a posterior probability)?

4. Say we added a higher order product term, x₁*x₂ with a new weight w₃ = 0.25. Compute the posterior probability of a logistic regression model.

5. Say that the above sample is a new sample with y^t = 1 and r^t = 0. Using the stochastic update rule with learning rate η = 0.1, what are the updated weights w₁, w₂, and w₀?

6. After completing the programming assignment, adjust the l2 regularization on the not MIST logistic regression model. Try values 1, 0.1, 0.01, and 0. Which produces the lowest error? Why do you think this is the case?

The answers must include the work to get to solutions.