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Exercise 7

Due Wednesday October 23 2019.

Some files are provided that you need below: E7.zip. As usual, you may not write any loops in your code.

Dog Rates Significance

One last statistics question: when we looked at Pup Inflation in Exercise 2, we drew a fit line across the data, but didn't really ask the question at hand: have the ratings given by this Twitter account been changing over time?

Revisit your dog-rates.ipynb from exercise 2 and append some more useful results. Output the p-value from the regression for the question is the slope different from zero?. Also plot a histogram of the residuals (observed values minus predicted values). [Note the question about this below.]

CPU Temperature Regression

Let's revisit another question from the past. When we looked at CPU temperature values in Exercise 3, we made a prediction for the next temperature: could we have done better?

There was more data in my original data set. I actually collected CPU usage percent (at the moment the sample was taken), the system load (one minute average), fan speed (RPM), and CPU temperature. Also, data was collected every 10 seconds: the Exercise 3 data set was subsampled down to once per minute. Surely we could have made a better CPU temperature in the next time step prediction with more data.

For this question, I have provided the expanded data set as sysinfo.csv.

Create a program regress_cpu.py based on the provided regress_cpu_hint.py. Things you need to do:

  • Fill in the 'next_temp' column in the DataFrame when it's read. This should be the temperature at time t+1, which is what we want to predict. Hint.
  • Create a scikit-learn linear regression model and fit it to the training data. Hint, also do not fit an intercept (since there's nowhere to put it in the Kalman filter).
  • Update the transition matrix for the Kalman filter to actually use the new-and-improved predictions for temperature.

Have a look at the output and note the questions below. When you submit, the output should be the one line from the output_regression function provided in the hint.

Colour Words

With previous classes, I have collected data mapping colours (specifically RGB colours you saw on-screen) to colour words. When creating the experiment, I gave options for the English basic colour terms.

The result has been a nice data set: almost 4000 data points that we can try to learn with. It is included this week as colour-data.csv.

Let's actually use it for its intended purpose: training a classifier.

Create a program colour_bayes.py. You should take the name of the CSV file on the command line: the provided colour_bayes_hint.py does this and contains some code to nicely visualize the output.

Start by getting the data: read the CSV with Pandas. Extract the X values (the R, G, B columns) into a NumPy array and normalize them to the 01 range (by dividing by 255: the tools we use will be looking for RGB values 01). Also extract the colour words as y values.

Partition your data into training and validation sets using train_test_split.

Now we're ready to actually do something: create a naïve Bayes classifier and train it. Use the default priors for the model: they are set from the frequency in the input, which seems as sensible as anything else.

Have a look at the accuracy score on the validation data to see how you did. Print the accuracy score for this model.

The score doesn't tell much of a story: call plot_predictions from the hint to see a plot of colours (left) and predicted colour categories (right).

Colour Words and Colour Distances

The naïve Bayes approach implicitly assumes that distances in the input space make sense: distances between training X and new colour values are assumed to be comparable. That wasn't a great assumption: distances between colours in RGB colour space aren't especially useful.

Possibly our inputs are wrong: the LAB colour space is much more perceptually uniform. Let's convert the RGB colours we have been working with to LAB colours, and train on that. The skimage.color module has a function for the conversion we need. (You may have to install scikit-image, depending on your original setup).

We can create a pipeline model where the first step is a transformer that converts from RGB to LAB, and the second is a Gaussian classifier, exactly as before.

There is no built-in transformer that does the colour space conversion, but if you write a function that converts your X to LAB colours, you can create a FunctionTransformer to do the work.

The skimage.color functions assume you have a 2D image of pixel colors: you will have to a little NumPy reshaping in your function to make it all work. Reshape the array of colours to an image \(1\times n\) (which is a .reshape(1,-1,3)), convert to LAB, and then reshape back to an array of colour values (.reshape(-1,3)).

Have a look at the accuracy value for this model as well. When finished, your colour_bayes.py should print two lines: the first and second accuracy score. Please do not have a plt.show() in your code when you submit: it makes marking a pain.

Questions

Answer these questions in a file answers.txt.

  1. Looking at your dog-rates.ipynb, do you think the residual are close-enough to being normal to look at the OLS p-value? Can you reasonably conclude that the ratings are increasing?
  2. Do you think that the new better prediction is letting the Kalman filter do a better job capturing the true signal in the noise?

Submitting

Submit your files through CourSys for Exercise 7.

Updated Mon Aug. 26 2019, 11:25 by ggbaker.