# 91255 - Statistical and Mathematical Methods for Artificial Intelligence

### Course Unit Page

• Teacher Elena Loli Piccolomini

• Credits 6

• SSD SECS-S/01

• Language English

• Campus of Bologna

• Degree Programme Second cycle degree programme (LM) in Artificial Intelligence (cod. 9063)

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda. ## 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.

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