• Provide the student with the statistical foundations to understand the regulators in Machine Learning.
  To introduce the ideas and uses of Extreme Value Theory and its comparison with other classic results.

• Invite the student to some applications of statistics and probability to Finance and Data Science

• Provide the student with the necessary language to translate fluently:

  • The problems of data science to the mathematical language used in machine learning.

  • The algorithms exposed in the literature -either in scientific articles or textbooks- to the specific problems.

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Syllabus

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The syllabus is focused on three main objectives, each one corresponding to one of the following topics:

• Introduce the formal and axiomatic study of regularization in Bayesian statistics under the pretext of practicing rigorous mathematical reasoning from simple examples and then advancing in more complicated aspects of the theory.

• Invite the student to study Bayesian methods similar to the Monte Carlo simulation in order to be able to compare and study them in detail.

• Begin the systematic study of Extreme Value Theory with a view to its

  financial applications and their simulation algorithms.

 

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1. Regularization and statistics

• Statistical tools

• Maximum likelihood and Machine Learning 3. Formal definition of overfitting

• Regularizers in

• Linear and logistic regressions

• Neural Networks

• Geometric interpretation and PCA

2. Bayesian sampling methods

• Markov chains

• Law of large numbers and ergodicity theorems

• Monte Carlo

• Metropolis Hastling

• Gibbs Sampling

• Global optimization

• Propp-Wilson

• Algorithm speed and comparisons

3. Introduction to Extreme value theory

Intuition and comparison
Gaussian distribution in EVT
Law of large numbers in EVT 4. Applications to Risk theory

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