Perform the answers with python code.

In this assignment, you are given the following 3 datasets. Each dataset has a training and a test file. Specifically, these files are:

dataset 1: train-100-10.csv dataset 2: train-100-100.csv dataset 3: train-1000-100.csv

test-100-10.csv test-100-100.csv test-1000-100.csv

Start the experiment by creating 3 additional training files from the train-1000-100.csv by taking the first 50, 100, and 150 instances respectively. Call them: train-50(1000)- 100.csv, train-100(1000)-100.csv, train-150(1000)-100.csv. The corresponding test file for these dataset would be test-1000-100.csv and no modification is needed.

Implement L2 regularized linear regression algorithm with ranging from 0 to 150 (integers only). For each of the 6 dataset, plot both the training set MSE and the test set MSE as a function of (x-axis) in one graph.

(a) For each dataset, which value gives the least test set MSE?

(b) For each of datasets 100-100, 50(1000)-100, 100(1000)-100, provide an additional

graph with ranging from 1 to 150.

(c) Explain why = 0 (i.e., no regularization) gives abnormally large MSEs for those

three datasets in (b).

From the plots in question 1, we can tell which value of is best for each dataset once we know the test data and its labels. This is not realistic in real world applications. In this part, we use cross validation (CV) to set the value for . Implement the 10-fold CV technique discussed in class (pseudo code given in Appendix A) to select the best value from the training set.

1

(a) Using CV technique, what is the best choice of value and the corresponding test set MSE for each of the six datasets?

(b) How do the values for and MSE obtained from CV compare to the choice of and MSE in question 1(a)?

(c) What are the drawbacks of CV?

(d) What are the factors affecting the performance of CV?

3. Fix = 1, 25, 150. For each of these values, plot a learning curve for the algorithm using the dataset 1000-100.csv.

Note: a learning curve plots the performance (i.e., test set MSE) as a function of the size of the training set. To produce the curve, you need to draw random subsets (of increasing sizes) and record performance (MSE) on the corresponding test set when training on these subsets. In order to get smooth curves, you should repeat the process at least 10 times and average the results.