CSC 4780/6780 Homework 07

Description

This homework is due at 11:59 pm on Sunday, Oct 9. It must be uploaded to iCollege by then. No credit will be given for late submissions. A solution will be released by noon on Monday, Oct 10.

it is always a good idea to get this done and turn it in early. You can turn it in as many times as you like { iCollege will only keep the last submission. If, for some reason, you are unable to upload your solution, email it to me before the deadline.

• Logistic Regression

Many data science problems require us to give a “Yes” or “No” answer. One of the common methods we use is logistic regression. In this exercise you are going to split a data set into a training set and testing set. You will t the model to the training set and test it with the test set. You will toy with the threshold to get di erent levels of recall and precision.

1.1 Explore the data

You are given framingham.csv which is a real data set from a famous study on coronary heart disease: https://en.wikipedia.org/wiki/Framingham_Heart_Study

Create a program called chd explore.py that:

• Reads framingham.csv into a pandas data frame.

• Uses pandas profiling.ProfileReport to make a report.

• Save the report to data report.html

Open data report.html in a browser and look at the data. You are trying to predict TenYearCHD, whether the person will have coronary heart disease event in the next 10 years.

1.2 Split the data

Create another program called chd split.py that

• Reads farmingham.csv into a data frame.

• (You know from the report that some of the rows are missing values. ) Drops rows with missing values.

• Uses sklearn.model selection.train test split to divide the dataframe into two dataframes: the test data frame will be a randomly chosen 20% of the rows, the train data frame will have the rest.

• Save the data frames into test.csv and train.csv.

1.3 Fit the model to the training data

Create another program called chd train.py that

• Reads train.csv into a data frame.

• Divides it into two numpy arrays: Y is TenYearCHD, X is the other columns.

• Uses sklearn.preprocessing.StandardScaler to standardize the columns of X.

• Uses sklearn.linear model.LogisticRegression to t the data.

• Prints out the accuracy of the model on the training data.

• Saves the scaler and the logistic regression model to a single pickle le called classifier.pkl.

1.4 Test the model on the testing data

Create another program called chd test.py that

• Con gure a logger.

• Reads test.csv into a data frame.

• Divide it into numpy arrays X and Y , as above.

• Loads the scaler and logistic regression model from classifier.pkl.

• Apply the scaler to X so that it is scaled exactly as the training data was.

• Print the accuracy of the model on the testing data.

• Use sklearn.metrics.confusion matrix to print a confusion matrix.

• Try 40 thresholds between 0 and 1. For each one, use the logger to print:

{ The threshold { The accuracy { The recall score

{ The precision score { The F1 score

Like this: INFO@14:49:15: Threshold=0.220 Accuracy=0.776 Recall=0.50 Precision=0.32 F1 = 0.393

• Make another confusion matrix using the threshold that gave you the best F1 score.

• Create a graph of the recall and precision vs. threshold as threshold.png

• Softmax

The softmax function makes several di erent kinds of multi-class classi ers possible. We need to understand softmax.

Make a LaTeX document called Softmax.tex. In that le, answer the following questions. Turn in Softmax.pdf

2.1 Compute a softmax

What is the softmax of the vector [5; 3; 0; 1]? (Hint: the answer is also a vector.)

2.2 6780 Students only: Compute the Jacobian of the softmax

This one is for the graduate students! Undergrads should read it, but chuckle and move on.

If you have a function f : Rⁿ ! R^m, we can think of that as m functions f₁ : Rⁿ ! R, f₁2Rⁿ ! R,

: : :, f_m : Rⁿ ! R.

The Jacobian of f, then, is the matrix

2		@f1		@f1	: : : @f1		3
	@x1			@x2	: : : @xn
6	@x1			@x2		@xn	7
		@f2		@f2		@f2
6							7

• ::: ::: ::: ::: 7

45

	@fm		@fm	: : :	@fm
	@x1		@x2		@xn
What is the jacobian of the softmax function at [5; 3; 0;					1]?

• Criteria for success

If your name is Fred Jones, you will turn in a zip le called HW06 Jones Fred.zip of a directory called HW06 Jones Fred. It will contain:

• chd explore.py

• chd split.py

• chd train.py

• chd test.py

• framingham.csv

• train.csv

• test.csv

• classifier.pkl

• threshold.png

• data report.html

• Softmax.pdf

Be sure to format your python code with black before you submit it.

We will run your code like this:

cd HW07_Jones_Fred

python3 chd_explore.py

python3 chd_split.py

python3 chd_train.py

python3 chd_test.py

threshold.png should look something like this:

(But, of course, your test/train split is random and probably di erent from mine. So yours will look a little di erent.)

Do this work by yourself. Stackover ow is OK. A hint from another student is OK. Looking at another student’s code is not OK.

The template les for the python programs have import statements. Do not use any frameworks not in those import statements.

• Reading

You should have read through the cross validation section of Chapter 11 : Machine Learning for Classi cation.

Here’s a good video on Logistic Regression: https://youtu.be/yIYKR4sgzI8

Here’s a video from the same guy on Cross Validation https://youtu.be/fSytzGwwBVw

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