Geometric Statistics & Statistical learning from and on graphs
Additional Info
- ECTS credits: 6
- University: University of Nice - Sophia Antipolis
- Semester: 3
- Lecturer 1: Khazhgali Kozhasov
- Lecturer 2: Marco Cornelli
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Topics:
Geometric Statistics by Prof. Khazhgali Kozhasov
Statistical concepts like principal component analysis, (empirical) mean or covariance (matrix) are inherent to data and probability distributions living in linear spaces. Geometric statistics aims at providing tools for analysing data that populate (possibly) non-linear spaces such as manifolds. As the notion of metric is essential for this goal, Riemanniangeometry provides a solid ground for the theory. In the course we are going to introduce necessary geometric results, give essentials on probability distributions and then discuss “nonlinear” generalizations of some classical concepts from statistics. The exposition will be accompanied by numerous examples with a view towards applications. Familiarity with calculus on manifolds or basic differential geometry is recommended.
Statistical learning from and on graphs by Prof. Marco Cornelli
This course explores in detail some areas in machine/statistical learning that either use graphs in order to learn from data leaving in Euclidean spaces (e.g. Bayesian networks, spectral clustering) or directly model graph data (e.g. social network analysis, graph neural networks). In all model based approaches that we consider, maximum likelihood inference is adopted for the numerical estimation of the model parameters, with an important focus on EM and variational EM algorithms. Both R and Python will be employed to illustrate some implementations/applications of the proposed approaches and allow the student to become acquainted with the related libraries.
