====== Assignment: Maximum Likelihood ======

**📅 Deadline:** 1.1.2025 21:59

**🏦 Points:** 4
===== Task Description =====
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 {{ :courses:be4m33ssu:homeworks:hw_assignment_ml_plugin.pdf | PDF}}.

You are provided with a {{ :courses:be4m33ssu:homeworks:hw_maximum_likelihood_template_03_12_2024.zip |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 [[https://cw.felk.cvut.cz/brute/student/course/BE4M33SSU/mle|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**.

<note important>
All python files must be stored in the root of the .zip sent for submission.
</note>

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

----


== Test Case 1 ==
  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 ...


----

== Test Case 2 ==

  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 ...


----

== Test Case 3 ==

  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


<note>Note that this test case is not 2 dimensional. Therefore, we do not visualize it. </note>

===== Submission Guidelines =====
  * 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! 😊