Enrollment year
2020/2021
Academic discipline
MAT/05 (MATHEMATICAL ANALYSIS)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Curriculum
PERCORSO COMUNE
Period
2nd semester (01/03/2021 - 11/06/2021)
Lesson hours
24 lesson hours
Prerequisites
Courses of Mathematical Analysis and Numerical Analysis
Learning outcomes
This course will review the theory and applications of Data Analysis, illustrating the main results and the applications of the theory to practical problems.
Course contents
- Recap of geometry, linear algebra, probability in high dimensional spaces.
- Gaussians in high dimensions. Data fitting on a sperichal Gaussian.
- Singular Value Decomposition (SVD)
- Best rank-k approximations
- Application of SVD: principal component analysis (PCA), mixed clustering of sperical gaussians, max-cut problem
- Overfitting and uniform convergence.Occam's razor
- Learning of decision trees. Support Vector Machines (SVM) and VC dimension.
- Clustering: k-means, k-center,spectral clustering, recursive clustering and sparse cuts, graph partitioning and communities search.
Teaching methods
Lectures and lab
Reccomended or required readings
Avrim Blum, John Hopcroft, Ravindran Kannan. “Foundations of Data Science”. Cambridge University Press, Jan 23, 2020
Assessment methods
Final project, presentation and oral exam
Sustainable development goals - Agenda 2030
Università di Pavia - Offerta formativa