CdSINFORMATICA

Codice646AA

CFU9

PeriodoPrimo semestre

LinguaItaliano

Students are expected to acquire: some knowledge of the main techniques and methods for the solution of numerical and optimization problems; some understanding of the connections between typical techniques of numerical analysis and optimization algorithms; tools for modeling (through numerical analysis and optimization) specific problems from the following areas: regression and parameter estimation in statistics, approximation and data fitting, machine learning, data mining, image and signal reconstruction.

The student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology. During the oral exam the student must be able to demonstrate his/her knowledge of the course material together with adequate language and proper terminology. Critical awareness of the topics will be also evaluated.

The student will learn to use software to solve some of the basic problems in optimization and linear algebra, including: linear systems and least-squares problems, constrained and non-constrained continuous optimization problems. The student will acquire some knowledge of the theoretical properties of these problems and of the functioning of these algorithms.

The final written exam will include a part in which suitable software (such as Matlab) is used to implement some of the algorithms seen during the course.

The student will learn to combine analysis and computer implementations to solve the main theoretical problems underlying data mining and machine learning.

The behaviors will be assessed during the final written and oral exam.

Undergraduate courses in calculus, linear algebra, numerical analysis (recommended) and optimization (recommended).

None.

This course prepares the student to take on the future courses involving machine learning and data analysis.

Delivery: face to face

Learning activities:

- attending lectures
- participation in seminar
- individual study
- ICT assisted study

Attendance: Advised

Teaching methods:

- Lectures
- Seminar

Il corso è tenuto in inglese, quindi si prega di fare riferimento al programma in inglese.

Linear algebra and calculus background; Unconstrained optimization and systems of equations; Direct and iterative methods for linear systems; Iterative methods for nonlinear systems; Numerical methods for unconstrained optimization; The least-squares problem; Iterative methods for computing eigenvalues; Constrained optimization and systems of equations; Lagrangian duality; Numerical methods for constrained optimization; The fast Fourier transform; Applications: regression, parameter estimation, approximation and data fitting, support vector machines, signal reconstruction; Software tools for numerical and optimization problems (Matlab, in particular).

Lecture notes by the lecturers available to students. Recommended readings: J.W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997 L.N. Trefethen, D. Bau III, Numerical Linear Algebra, SIAM, 1997 J. Nocedal, S.J. Wright, Numerical Optimization, Springer, 1999 D. Bertsekas, Nonlinear Programming, Athena, 2004 M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley, 1993

Written and oral exam.