====== Assignment: EM Algorithm ======
==== For Prior Estimation & Prior Shift Compensation ====

**📅 Deadline:** 8.1.2025 21:59

**🏦 Points:** 5
===== Task Description =====
In this assignment, you are tasked with implementing the EM algorithm for estimating class prior on unlabeled test data. Afterwards, you must use the estimated prior to account for prior shift in the plugin Bayes classifier. You can find the complete description of the assignment in the Assignment {{ :courses:be4m33ssu:homeworks:hw_assignment_em_prior_shift.pdf | }}. 

You are provided with a {{ :courses:be4m33ssu:homeworks:hw_em_prior_shift_template_11_12_2024.zip |template}} containing the following files:

  * **main.py**: This file includes the functions **e_step**, **m_step**, **compute_test_priors**, **bayes_classifier_with_prior_shift** 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/em|BRUTE]].

Your objective is to implement the function **e_step** which estimates p_{test}(y|x), the function **m_step** which estimates p_{test}(y), the function **compute_test_priors** which runs the EM algorithm to estimate p_{test}(y), and the function **bayes_classifier_with_prior_shift** which implements the plugin-bayes classifier adapted to the prior shift. All of these 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>


<note important>
The expected runtime of the evaluation is about 7 minutes. 

Go make yourself a coffee while you wait.
</note>

<note warning>
The Bayes classifier test might fail on your machine, but still be correct. So far, we observed it in code of 1 student. It is caused by having different versions of Scikit-Learn. Jakub
</note>

===== Further Reading =====
https://arxiv.org/abs/2106.11695
===== 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:
  EM Algorithm - E Step:
    e_step: Test OK
    
  EM Algorithm - M Step:
    m_step: Test OK
  
  EM Algorithm - Estimated priors:
    estimated_test_prior: Test OK
  
  Bayes Classifier:
    risks bayes_classifier: Test OK
    
  Without prior compensation; Loss: 0.13
  With prior compensation; Loss: 0.09
  Improvement:  0.04


----

== Test Case 2 ==

  python main.py test-cases/public/instances/instance_2.json --plot
Expected output:
  EM Algorithm - E Step:
    e_step: Test OK
    
  EM Algorithm - M Step:
    m_step: Test OK
  
  EM Algorithm - Estimated priors:
    estimated_test_prior: Test OK
  
  Bayes Classifier:
    risks bayes_classifier: Test OK
    
  Without prior compensation; Loss: 0.43
  With prior compensation; Loss: 0.37
  Improvement:  0.06


----

== Test Case 3 ==

  python main.py test-cases/public/instances/instance_3.json --plot
Expected output:  
  EM Algorithm - E Step:
    e_step: Test OK
    
  EM Algorithm - M Step:
    m_step: Test OK
  
  EM Algorithm - Estimated priors:
    estimated_test_prior: Test OK
  
  Bayes Classifier:
    risks bayes_classifier: Test OK
    
  Without prior compensation; Loss: 0.13
  With prior compensation; Loss: 0.1
  Improvement:  0.03
===== 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! 😊