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# CSE 258: Homework 1

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CSE 258: Homework 1
Instructions
Please submit your solution by the beginning of the week 3 lecture (Jan 23). Submissions should be
You will need the following files:
50,000 beer reviews : http://jmcauley.ucsd.edu/cse258/data/beer/beer_50000.json
UCI Wine Quality Dataset :
http://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv
Code examples : http://jmcauley.ucsd.edu/cse258/code/week1.py (regression) and http://jmcauley.
ucsd.edu/cse258/code/week2.py (classification)
Executing the code requires a working install of Python 2.7 or Python 3 with the scipy packages installed.
In the first two questions, we’ll see how ratings vary across different years in our dataset of 50,000 beer reviews.
These questions should be completed on the entire dataset.
1. First, let’s train a predictor that uses the year (‘review/timeStruct’/‘year’) to predict the overall rating,
i.e.,
review/overall ‘ θ0 + θ1 × year.
You may use Python libraries to do so, so long as you include the code of your solutions. What are the
fitted values of θ0 and θ1? (1 mark)
2. A simple regressor like the one above may not be very realistic—it assumes that ratings get linearly
better or linearly worse over time. Can you come up with a better representation of the year variable?
Describe your representation and write down an equation for it in terms of θ (like the equation from Q1
above). Compare the the new representation to the representation from Question 1 in terms of the Mean
Squared Error (i.e., report the MSE for both representations) (1 mark).
Next, we’ll use the UCI Wine Quality Dataset (white wine) to train a regressor with a few more features.
This data is in CSV format, and can be processed using the Python CSV library (https://docs.python.org/
3.6/library/csv.html). See https://archive.ics.uci.edu/ml/datasets/Wine+Quality for a few more
Start by splitting the data into ‘train’ and ‘test’ portions by taking the first half of the rows for training
data and the remaining rows as test data.
3. Next, train a regressor that uses the first 11 features to predict the last feature (‘quality’), i.e.,
quality = θ0 + θ1 × ‘fixed acidity’ + θ2 × ‘volatile acidity’ + θ2 × ‘citric acid’ + . . . + θ11 × ‘alcohol’.
Write down the fitted coefficients on the training data, and the MSE on the train and test data (1 mark).
4. An ablation experiment consists of removing one feature from an experiment, in order to assess the amount
of additional information that feature provides above and beyond the others. Repeat the experiment from
Question 3 for all possible ablations (i.e., removing the ‘fixed acidity’ feature only, removing ‘volatile
acidity’ only, etc.).
(a) Report the MSEs (on the test set) of all 11 ablation experiments (1 mark).
(b) Based on the test MSEs, Which features do you conclude provide the most and least additional
information beyond what is present in the 11 other features? (1 mark)
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Classification (week 2):
Finally, we’ll treat the Wine Quality task from above as a classification task. Again, split the data so that the
first half is used for training and the second half is used for testing as above.
To turn this into a classification problem, split the data so that ‘negative’ examples are those where
quality ≤ 5 and ‘positive’ examples are those where quality 5.
5. Again using the first 11 features, run an SVM classifier on the data (see the code provided in class) –
remember to train on the first half and test on the second half. What is the accuracy (percentage of
correct classifications) of the predictor on the train and test data (1 mark)?
6. (Hard) Finally, let’s fit a model using logistic regression. A code stub has been provided to perform
logistic regression using the above model on http://jmcauley.ucsd.edu/cse258/code/homework1.py
Code for the log-likelihood has been provided in the code stub (f) but code for the derivative is incomplete
(fprime)
• Complete the code stub for the derivative (fprime) (1 mark).
• What is the log-likelihood of after convergence, and what is the accuracy (on the test set) of the
resulting model? (1 mark)
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