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Course 2021-2022 a.y.

30554 - MATHEMATICAL MODELLING IN MACHINE LEARNING

BAI
Department of Decision Sciences

Course taught in English

Go to class group/s: 27

BAI (8 credits - II sem. - OB  |  4 credits FIS/02  |  4 credits MAT/06)
Course Director:
RICCARDO ZECCHINA

Classes: 27 (II sem.)
Instructors:
Class 27: RICCARDO ZECCHINA


Suggested background knowledge

For a productive and effective learning experience, it is recommended a preliminary knowledge of linear algebra, programming in Python, basic probability and statistics, calculus and convex optimization


Mission & Content Summary
MISSION

Machine learning is a rapidly evolving field. It is also becoming more and more central to many sciences and applications in which data play a role. The purpose of this course is to give the fundamental principles and methods of modern machine learning, from its probabilistic foundations to its modelling and computational aspects.

CONTENT SUMMARY
  • Explain and understand the fundamental mathematical and modeling theories underlying machine learning (ML) methods.
  • Define the basic ML models and explain the main differences between them through increasing levels of complexity: regression, classification, clustering, dimensionality reduction and different computational approaches to learning.
  • Acquire the basic knowledge of information theory which is relevant for learnaing.
  • Implement and apply machine learning methods through programming platforms.
  • Evaluate results through cross-validation  and rigorous tests when possible.
  • Optimize key tradeoffs such as overfitting and computational cost. 

Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...

 

  • Rigorously understand the methodological underpinnings of different machine learning models.
  • Understand their limitations and open problems.
  • Be familiar with the programming techniques required for efficient implementation of the different algorithms that characterize ML.
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...

 

1) Understand to associated the appropriate  mathematical framework to the different ML techniques.

 

2) Depending on the type of problem, the students are expected to be able to identify the appropriate ML models and implement the different  machine learning algorithms. Basic examples are:

  • Regression
  • Classification algorithms (from K-NN, to Decisions Trees and Forests, to  Neural Networks)
  • Clustering (e.g. K-means, hierarchical and  spectral approaches)
  • Dimensionality reduction (e.g. PCA)
  • Implement and apply machine learning algorithm to real-world problems, and rigorously evaluate their performance using cross-validation.
  • Optimize the main trade-offs such as overfitting, and computational cost vs accuracy.
  • Experience common pitfalls and how to overcome them.

 


Teaching methods
  • Face-to-face lectures
  • Exercises (exercises, database, software etc.)
  • Individual assignments
  • Group assignments
DETAILS

Face-to-face lecture will be devoted to the understanding of the mathematical foundations and computational problems associated to the different ML methods, and to the software implementation of the algorithms.

 

Exercises, individual and gruop assignments have the scope of make the students familiarize with the application of   machine learning methods to real-world problems.  Students will be also asked to  critically evaluate performance and to

optimize their programs.

 


Assessment methods
  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
  •   x x
  • Individual assignment (report, exercise, presentation, project work etc.)
  •     x
  • Group assignment (report, exercise, presentation, project work etc.)
  •     x
    ATTENDING AND NOT ATTENDING STUDENTS

    Scope of the written exam is to check the understanding of the mathematical and computational problems at the root of modern ML.

    Individual and group assigmnets will relate to the capability of dealing with real world problems and the software implementation  of the different algorithms.

     

    Grading scheme:

    General written exam: 80% of the final grade.

    Each partial: 40%

    Group project: 20%


    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS

    Textbooks:

     

    - S. Shalev-Shwartz and S. Ben-David: Understanding Machine Learning - From Theory to Algorithms

    - G. Strang: Linear Algebra and Learning from Data

    - C. Bishop: Pattern Recognition and Machine Learning

     

    Handouts will be provided for each lecture.

    Last change 29/06/2021 00:39