Fundamentals of Probabilistic data mining - WMM9MO17
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Number of hours
Lectures : 15.0
Tutorials : -
Laboratory works : 4.5
Projects : -
Internship : -
Written tests : -
ECTS : 3.0
Officials :Xavier ALAMEDA-PINEDA
This lecture introduces fundamental concepts and associated numerical methods in model-based clustering, classification and models with latent structure. We will also discuss probabilistic graphical models with latent variables in general, the expectation maximisation algorithm and its variational Bayes formulation. Overall we will discuss Gaussian mixture models, hidden Markov models, probabilistic PCA, linear dynamical systems, and more complex models that are combinations of these ones, and that require variational expectation-maximisation algorithms. If time allows, we will discuss the link with variational auto-encoders.
Model-based clustering, classification and models with latent structure are particularly relevant to model random vectors, sequences or graphs, to account for data heterogeneity, and to present general principles in statistical modelling. The following topics are addressed:
Principles of probabilistic data mining and generative models; models with latent variables Probabilistic graphical models Mixture models and clustering PCA and probabilistic PCA Generative models for series and graphs : hidden Markov models Linear dynamical systems. Variational EM algorithm.
Fundamental principles in probability theory (conditioning) and statistics (maximum likelihood estimator and its usual asymptotic properties). Constrained optimization, Lagrange multipliers.
3-hours written exam (E) and one report on practicals and research work (P) Authorized documents: handwritten notes only.
The exam is given in english only
The course exists in the following branches:
Curriculum - Master 2 in Applied Mathematics - Semester 9 (this course is given in english only )
Curriculum - Master 2 in Computer Science - Semester 9 (this course is given in english only )