New version page

Berkeley CS 188 - Naive Bayes

This preview shows page 1 out of 3 pages.

View Full Document
View Full Document

End of preview. Want to read all 3 pages?

Upload your study docs or become a GradeBuddy member to access this document.

View Full Document
Unformatted text preview:

CS 188Fall 2019 Section Handout 11 Solutions1 Naive BayesIn this question, we will train a Naive Bayes classifier to predict class labels Y as a function of input featuresA and B. Y , A, and B are all binary variables, with domains 0 and 1. We are given 10 training points fromwhich we will estimate our distribution.A 1 1 1 1 0 1 0 1 1 1B 1 0 0 1 1 1 1 0 1 1Y 1 1 0 0 0 1 1 0 0 0(a) What are the maximum likelihood estimates for the tables P (Y ), P (A|Y ), and P (B|Y )?Y P (Y )0 3/51 2/5A Y P (A|Y )0 0 1/61 0 5/60 1 1/41 1 3/4B Y P (B|Y )0 0 1/31 0 2/30 1 1/41 1 3/4(b) Consider a new data point (A = 1, B = 1). What label would this classifier assign to this sample?P (Y = 0, A = 1, B = 1) = P (Y = 0)P (A = 1|Y = 0)P (B = 1|Y = 0) (1)= (3/5)(5/6)(2/3) (2)= 1/3 (3)P (Y = 1, A = 1, B = 1) = P (Y = 1)P (A = 1|Y = 1)P (B = 1|Y = 1) (4)= (2/5)(3/4)(3/4) (5)= 9/40 (6)(7)Our classifier will predict label 0.(c) Let’s use Laplace Smoothing to smooth out our distribution. Compute the new distribution for P (A|Y )given Laplace Smoothing with k = 2.1A Y P (A|Y )0 0 3/101 0 7/100 1 3/81 1 5/82 PerceptronYou want to predict if movies will be profitable based on their screenplays. You hire two critics A and B to reada script you have and rate it on a scale of 1 to 4. The critics are not perfect; here are five data points includingthe critics’ scores and the performance of the movie:# Movie Name A B Profit?1 Pellet Power 1 1 -2 Ghosts! 3 2 +3 Pac is Bac 2 4 +4 Not a Pizza 3 4 +5 Endless Maze 2 3 -AB(a) First, you would like to examine the linear separability of the data. Plot the data on the 2D plane above;label profitable movies with + and non-profitable movies with − and determine if the data are linearlyseparable. The data are linearly separable.(b) Now you decide to use a perceptron to classify your data. Suppose you directly use the scores given aboveas features, together with a bias feature. That is f0= 1, f1= score given by A and f2= score given byB.Run one pass through the data with the perceptron algorithm, filling out the table below. Go throughthe data points in order, e.g. using data point #1 at step 1.step Weights Score Correct?1 [-1, 0, 0] −1 · 1 + 0 · 1 + 0 · 1 = −1 yes2 [-1, 0, 0] −1 · 1 + 0 · 3 + 0 · 2 = −1 no3 [0, 3, 2] 0 · 1 + 3 · 2 + 2 · 4 = 14 yes4 [0, 3, 2] 0 · 1 + 3 · 3 + 2 · 4 = 17 yes5 [0, 3, 2] 0 · 1 + 3 · 2 + 2 · 3 = 12 noFinal weights: [-1, 1, -1](c) Have weights been learned that separate the data? With the current weights, points will be classified aspositive if −1 · 1 + 1 · A + −1 · B ≥ 0, or A − B ≥ 1. So we will have incorrect predictions for data points 3:−1 · 1 + 1 · 2 + −1 · 4 = −3 < 0and 4:−1 · 1 + 1 · 3 + −1 · 4 = −2 < 0Note that although point 2 has w · f = 0, it will be classified as positive (since we classify as positive ifw · f ≥ 0).(d) More generally, irrespective of the training data, you want to know if your features are powerful enoughto allow you to handle a range of scenarios. Circle the scenarios for which a perceptron using the featuresabove can indeed perfectly classify movies which are profitable according to the given rules:2(a) Your reviewers are awesome: if the total of their scores is more than 8, then the movie will definitelybe profitable, and otherwise it won’t be. Can classify (consider weights [−8, 1, 1])(b) Your reviewers are art critics. Your movie will be profitable if and only if each reviewer gives eithera score of 2 or a score of 3. Cannot classify(c) Your reviewers have weird but different tastes. Your movie will be profitable if and only if bothreviewers agree. Cannot


View Full Document
Loading Unlocking...
Login

Join to view Naive Bayes and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Naive Bayes and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?