sp21final

DATA 100 Final-Exam Spring 2021 Final-Exam INSTRUCTIONS This is your exam. Complete it either at exam.cs61a.org or, if that doesn’t work, by emailing course sta ff with your solutions before the exam deadline. This exam is intended for the student with email address <EMAILADDRESS> . If this is not your email address, notify course sta ff immediately, as each exam is di ff erent. Do not distribute this exam PDF even after the exam ends, as some students may be taking the exam in a di ff erent time zone. For questions with circular bubbles , you should select exactly one choice. # You must choose either this option # Or this one, but not both! For questions with square checkboxes , you may select multiple choices. 2 You could select this choice. 2 You could select this one too! You may start your exam now. Your exam is due at <DEADLINE> Pacific Time. Go to the next page to begin.

Exam generated for <EMAILADDRESS> 3 1. (7.0 points) (a) (2.0 pt) Recall the tips dataset that we worked with on assignments in the past, which includes data about the tip on a restaurant bill as well as the day of week and the sex of the individual. The plot below attempts to examine patterns between the tip as a percentage of the bill and the sex of the individual by the day of week (DOW) Select the best reason below for why the data visualization is misleading or poorly constructed. # the y -axis should be log transformed # the clustering of bars doesn’t allow a key comparison to be made # the plot su ff ers from overplotting # the bars for each day of week should be stacked on top of each other (e.g. the bar for “Thur” would have a total height of approximately 0.3)

Exam generated for <EMAILADDRESS> 5 # #

Exam generated for <EMAILADDRESS> 6 # # (c) (3.0 points) We have read in some data as the dataframe df . Consider a subset of df below, which contains some information on the background of various individuals in the US.

Exam generated for <EMAILADDRESS> 8 ii. (1.0 pt) Suppose we want to understand the relationship between weeks_worked_1999 and the sex of the individual. We run the following code to generate a plot: df2 = df.groupby("zip_code").mean().reset_index() sns.lineplot("zip_code", "log_earn_1999", data=df2) Select the reason below for why this plot would represent a bad data visualization. # treats a categorical variable as a continuous variable # treats a continuous variable as a categorical variable # represents a density with a feature other than area # does not show the relationship between the variables of interest

Exam generated for <EMAILADDRESS> 9 2. (9.0 points) (a) (4.0 points) Recall that a random forest is created from a number of decision trees, with each decision tree created from a bootstrapped version of the original training set. One hyperparameter of a random forest is the number of decision trees we train to create the random forest. Define T to be the number of decision trees used to create the random forest. Let’s say we have two candidate values for T : var 1 and var 2 . We want to perform var 3 - fold cross-validation to determine the optimal value of T . Assume var 1 , var 2 , and var 3 are integers. i. (2.0 pt) In this cross-validation process, how many random forests will we train? Your answer should be in terms of var 1 , var 2 , and/or var 3 and should be an integer. ii. (2.0 pt) In this cross-validation process, how many decision trees will we train? Your answer should be in terms of var 1 , var 2 , and/or var 3 and should be an integer.

Exam generated for <EMAILADDRESS> 11 3. (14.0 points) We are trying to train a decision tree for a classification task where 0 is the negative class and 1 is the positive class. We are given 8 data points each in pairs of ( x 1 , x 2 ) features. (a) (3.0 pt) x 1 x 2 y 3 4 1 2 1 0 1 3 1 5 9 0 9 6 1 7 2 1 4 7 0 8 8 1 What is the entropy at the root of the tree? Round to 4 decimal places. (b) (2.0 pt) What is the gini inpurity at the root of the tree? Note that the formula for gini impurity is 1 - P c i =1 p 2 i where p i is the fraction of items labelled with class i and c is the total number of classes.

Exam generated for <EMAILADDRESS> 12 (c) (4.0 pt) Suppose we decide to split the root node with the rule x i ≥ β where i = 1 or 2. Which of the following minimizes the weighted entropy of the two resulting child nodes. # x 1 ≥ 6 # x 1 ≥ 3 . 5 # x 2 ≥ 5 # x 2 ≥ 3 . 5 # x 2 ≥ 6 . 5 (d) (2.0 points) We have decided to create a food recommendation system using a decision tree! We would like to run our decision tree to see what food it recommends in certain scenarios. If you have trouble reading the above tree, please go to this link: https://i.imgur.com/9Z40cYP.png i. (1.0 pt) Bob wants to eat some unhealthy food, specifically at a fast food restaurant. When asked what he’s in the mood for, he replies with “Mediterranean”. Which of the following restaurants could the decision tree recommend for Bob? # Chipotle # Taco Bell # Dyars Cuisine # IBs Burgers ii. (1.0 pt) Larry would like to eat some unhealthy food as well! However, he got a salary bonus from his job so he does not want to eat at a fast food restaurant. When asked how much he would like to pay, he replies with “I have no preference”. Which of the following restaurants could the decision tree recommend for Larry? 2 Olive Garden 2 Cheesecake Factory 2 Super Dupers Burger 2 Flemings Prime Steakhouse

Exam generated for <EMAILADDRESS> 14 4. (16.0 points) (a) (3.0 pt) Suppose we are modeling the number of calls to MangoBot food delivery service per minute. We believe that there are likely more calls around lunch time. Which of the following feature encodings of the time of day (0.0 to 24.0, exclusive of both ends) would capture this assumption? Select all that apply. 2 time_of_day ** 2 2 np.log(12 * time_of_day) 2 1-np.cos(np.pi * time_of_day / 12) 2 np.exp(-(time_of_day - 12) ** 2) (b) (4.0 pt) Recall that in a binary classification task, we want our data to become linearly separable so that we can maximize the performance of our classifier. In many cases, however, our data are not directly linearly separable. As a result, we want to apply some transformation to our data so they will become linearly separable afterwards. For the following dataset, select all transformations that can make the data linearly separable. 2 ( x 1 , x 2 ) ! ( x 2 1 , x 2 ) 2 ( x 1 , x 2 ) ! ( x 1 , x 2 2 ) 2 ( x 1 , x 2 ) ! ( x 2 1 , x 2 2 ) 2 ( x 1 , x 2 ) ! ( x 2 2 , x 2 1 )

Exam generated for <EMAILADDRESS> 15 (c) (3.0 pt) One way to transform textual data into features is to count the frequencies for all of the words in the text. Consider the following preprocessing steps: i. Remove all punctuations ( . , , , : , . . . ). ii. Remove all stopwords ( did , the , . . . ). Note that stopwords do not include words that negate things such as no , not , . . . iii. Lower case the sentence, and keep words that only consist of letters a - z . iv. Encode the sentence as a vector containing the frequencies for all the unique words in the text. Suppose we use the frequency vector from the steps above as our feature to train a logistic regression model that predicts the sentiment of a sentence (positive, negative). In 1-2 sentences, describe a case where our model would fail and make a false prediction. Your answer must be specific to the preprocessing steps and includes an example sentence to earn credits .

Exam generated for <EMAILADDRESS> 17 5. (9.0 points) Suppose we are modelling some response using our data X . For a given observation we have 3 features, x 1 , x 2 , x 3 . Note that the subscript does not refer to the first, second, and third observations, respectively. For a given data point x , we come up with a model of the form f ✓ ( x ) = ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 . We use the squared error function, denoted L ( y, ˆ y ) , to calculate the error for each observation and additionally use L2 regularization, denoted R ( ✓ ) , with penalty λ . You may assume that λ > 0 . Thus our objective function is of the form L ( y, ˆ y ) + λ R ( ✓ ) . (a) (3.0 pt) For a single observation x having response y and features x 1 , x 2 , x 3 , compute the gradient to be used in gradient descent: # - 2  ( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 ))( x 1 + ✓ 2 x 2 + 2 ✓ 1 x 3 ) - λ✓ 1 ( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 ))( ✓ 1 x 2 ) - λ✓ 2 #  2( x 1 + ✓ 2 x 2 + 2 ✓ 1 x 3 - y )( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 ) + 2 λ✓ 1 2( ✓ 1 x 2 - y )( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 ) + 2 λ✓ 2 #  - 2( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 ))( x 1 + ✓ 2 x 2 + 2 ✓ 1 x 3 ) - 2( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 ))( ✓ 1 x 2 ) # 2 2 4 ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 - y )( ✓ 1 ) + λ✓ 1 ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 - y )( ✓ 1 ✓ 2 ) + λ✓ 1 ✓ 2 ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 - y )( ✓ 2 1 ) + λ✓ 2 1 3 5 # 2 4 ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 - y ) 2 ( ✓ 1 ) ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 - y ) 2 ( ✓ 2 ) ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 - y ) 2 ( ✓ 3 ) 3 5 # 2 4 ( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 )) + λ R ( ✓ 1 ) ( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 )) + λ R ( ✓ 2 ) ( y - ( ✓ 1 x 1 + ✓ 1 ✓ 2 x 2 + ✓ 2 1 x 3 )) 3 5 (b) (2.0 pt) Suppose that you and your friend are implementing gradient descent. Just for fun, your friend chooses a negative learning rate ↵ and asks you to fix their code. Which of the following expressions will always result in the same update as the conventional gradient descent algorithm? You may assume that the gradient r is correctly computed and you do not need to worry about the magnitude of ↵ . 2 ✓ ( t +1) = ✓ ( t ) - ↵ r 2 ✓ ( t +1) = ✓ ( t ) + ↵ r 2 ✓ ( t +1) = ✓ ( t ) - | ↵ | r 2 ✓ ( t +1) = ✓ ( t ) + | ↵ | r 2 None of the above (c) (4.0 points)

Exam generated for <EMAILADDRESS> 18 i. (2.0 pt) We seek to optimize a given loss function using stochastic gradient descent where 1 < batch size < n , where n is the total number of data points, We initialize all model parameters as 0 and use a constant learning rate ⌘ ( t ) = ↵ . Based on the contour plot below, which of the following will most likely result in better minimization of the loss function: # Fewer iterations # Greater learning rate # Smaller batch size # Greater batch size

Exam generated for <EMAILADDRESS> 20 6. (6.0 points)

Exam generated for <EMAILADDRESS> 21 (a) (6.0 pt) Leif wants to do a study on the number of flowers in people’s gardens. He collects data on 100 di ff erent gardens, classifying each of them into three di ff erent sizes: ‘small’, ‘medium’, and ‘large’, and counts every flower in each person’s garden. The following is the first five rows of the data he collected: Leif then asks you to construct the following table using the data he collected. The table represents the total flowers in each category. For example, there are 1700 Hyacinths in “large” gardens. Write code below such that the above table is generated. Assume the data Leif collected is placed in a Pandas DataFrame assigned to the variable inputdf . The resulting table should be named outputdf . Please follow the template below (you must use pd.pivot_table ). outputdf = pd.pivot_table(_______________________________________________)