Problem 1
Consider a linear regression model with the hypothetical relation 𝑦 = 𝛽𝑇𝑥.
a) Given one practical example which can be well modeled by such a linear model. Clearly define the predictors and the response. Explain why.
b) Given one practical example which cannot be well modeled by such a linear model. Clearly define the predictors and the response. Explain why not.
c) Given one practical example which can be approximately modeled by such a linear model, with possibly significant error sometimes. Clearly define the predictors and the response. Explain why.
Problem 2
Suppose that we use smart meters to infer the usage of home appliances.
(a) What data does a smart meter measure?
(b) Why we need to retrieve “signatures” from the data rather than directly using the original data for the inference?
(c) Suppose that we use a linear function
𝐺𝑘(𝑥) = 𝛽𝑇𝑥 − 𝛾𝑘
to determine whether appliance 𝑘 is “on” or “off”. That is, we classify appliance 𝑘 to be “on” if and only if 𝐺𝑘(𝑥) > 0. Use 1-2 sentences to describe how to obtain the coefficients 𝛽 via linear regression.
(d) Does the linear regression approach in part (c) always work for general classification problems? Why or why not?
Problem 3
Answer the following questions on neural networks. a) What is a deep neural network?
b) Why this class of machine learning algorithms are called “neural networks”?
c) What is an activation function?
d) (bonus) Suppose that you are using a neural network (NN) for an engineering task. How would you determine the structure of the NN?
