1. A collection of reviews about comedy movies (data D) contains the following keywords and binary labels for whether each movie was funny (+) or not funny (-). The data are shown below: for example, the cell at the intersection of "Review 1" and "laugh" indicates that the text of Review 1 contains 2 tokens of the word "laugh." Review laugh hilarious awesome dull yawn bland | Y 1 1 1 0 + 2 0 0 0 + 0 0 0 1 + 0 2 1 0 - 1 2 0 You may find it easier to complete this problem if you copy the data into a spreadsheet and use formulas for calculations, rather than doing calculations by hand. Please report all scores as log-probabilities, with 3 significant figures (10 pts (a) Assume that you have trained a Naive Bayes model on data D to detect funny vs. not funny movie reviews. Compute the model's predicted score for funny and not-funny to the following sentence S i.e. P(+S) and P(-1S)), and determine which label the model will apply to S. (4 pts) S: "This film was hilarious! I didn't yawn once. Not a single bland moment. Every minute was a laugh." (b) The counts in the original data are sparse and may lead to overfitting, e.g. a strong prior on assigning the "not funny" label to reviews that contain "yawn." What would happen if you applied smoothing? Apply add-1 smoothing and recompute the Naive Bayes model's predicted scores for S. Did the label change? (4 pts) (c) What is an additional feature that you could extract from text to improve the classification of sentences like S, and how would it help improve the classification? (2 pt]