Assignment: Maximum Likelihood

📅 Deadline: 1.1.2025 21:59

🏦 Points: 4

In this assignment, you are tasked with implementing a maximum-likelihood estimator for a Gaussian mixture model, computing the plugin Bayes classifier and estimating the conditional risk of the prediction. You can find the complete description of the assignment in the Assignment PDF.

You are provided with a template containing the following files:

• main.py: This file includes the functions MLE_parameters, bayes_classifier that you are required to implement.
• utils.py: Contains helper functions for loading and saving data, and visualizations. You do not need to modify this file.
• test-cases: A folder containing public test cases to help you verify your implementation before submitting to BRUTE.

Your objective is to implement the function MLE_parameters, which estimates the parameters of the Gaussian mixture, and the function bayes_classifier which implements the plugin-bayes classifier. Both functions can be found in main.py.

After completing your implementation, you can test your solution using the following commands before submitting it to BRUTE:

python main.py test-cases/public/instances/instance_1.json --plot

Expected output:

Visualizing Gaussian Mixture ...

Maximum Likelihood Estimate:
  class_priors: Test OK
  class_centroids: Test OK
  shared_covariance_matrix: Test OK
  
Bayes Classifier:
  predictions: Test OK
  risks: Test OK
  
Visualizing Conditional Risk ...

python main.py test-cases/public/instances/instance_2.json --plot

Expected output:

Visualizing Gaussian Mixture ...

Maximum Likelihood Estimate:
  class_priors: Test OK
  class_centroids: Test OK
  shared_covariance_matrix: Test OK
  
Bayes Classifier:
  predictions: Test OK
  risks: Test OK
  
Visualizing Conditional Risk ...

python main.py test-cases/public/instances/instance_3.json

Expected output:

Maximum Likelihood Estimate:
  class_priors: Test OK
  class_centroids: Test OK
  shared_covariance_matrix: Test OK
  
Bayes Classifier:
  predictions: Test OK
  risks: Test OK

• Submit the completed code as a .zip via BRUTE.
• All python files must be stored in the root of the .zip sent for submission.
• Make sure your implementation passes the test cases provided above. Good luck! 😊