91255 - Statistical and Mathematical Methods for Artificial Intelligence

Academic Year 2019/2020

Learning outcomes

At the end of the course, the student masters the basic mathematical and statistical methods needed to acquire skills in artificial intelligence foundations, theories and applications.

Course contents

1. Elements of linear algebra.

• vectorial calculus, linear mappings, normed spaces, orthogonal projections.
• matrix calculus, matrix norms, special matrices.
• Singular Values Decomposition, Principal Component Analysis.
• Eigenvalues and eigenvectors.
• Laboratory exercises in Matlab or Phyton.

    2. Elements of multivariate analysis 

• Gradient, Jacobian, Hessian. Taylor theorem.
• Convex functions and sets.

    3. Multivariate optimization

• Linear least squares.
• Extrema of multivariate functions. Optimality conditions.
• Descent methods. Gradient type methods and Newton type methods.
• Regularization.
• Basis concepts of stochastic optimization.
• Laboratory exercises in Matlab or Phyton.

    4. Elements of probability and statistics.

• Probability and Bayes theorem.
• Random variables. Continuous and discrete distributions of random variables. Normal and Poisson distributions. 
• Independent and dependent variables. Covariance and correlation.
• Estimates: Maximum Likelihood and Maximum a Posteriori estimates.
• Cross entropy and Kullback-Leibler divergence.
• Laboratory exercises in Matlab or Phyton.

Readings/Bibliography

Notes from the teacher

Teaching methods

Lectures and laboratory exercises.

The class attendance is highly recommended for the learning and for the exam preparation.

Assessment methods

It is mandatory to complete the  homework assigned in the Laboratory lessons to have the exam.

The exam consists in a written test and a brief oral discussion about the assigned homeworks.

The final score is the sum of:

• the score of the written test (maximum 22/30)
• the score of the exercises (maximum 10/30)

If the final score is greater than 30, the laude is assigned.

Teaching tools

Slides and program files from the teacher.

Office hours

See the website of Elena Loli Piccolomini