The objective of this course is to provide the principles of advanced (supervised and unsupervised) machine learning algorithms, and explain their interest when applying them to address learning tasks using visual, auditory or textual data, as well as multi-modal combinations.

In a very broad acceptation, shape and topology optimization is about finding the best domain (which may represent, depending on applications, a mechanical structure, a fluid channel,…) with respect to a given performance criterion (e.g. robustness, weight, etc.), under some constraints (e.g. of a geometric nature).

This interdisciplinary course is designed for students with a computer science or mathematical background, offering them an opening to bioinformatics and to bioinformatics and computational biology.

This course consists on a cycle of seminars given by different industrials and on a projet related to the manipulation of real data.

The course is structured in two parts, treated respectively and independently by Sylvein Meignen and Kévin Polisano. The first part is devoted to differential calculus and its applications in image restoration and edge detection. The second part is dedicated to the construction and practical use of the wavelet transform. Wavelets are basis functions widely used in a large variety of fields: signal and image processing, data compression, smoothing/denoising data, numerical schemes for partial differential equations, scientific visualization, etc. Connections between the two parts will be made on the aspects of denoising, edge detection and graph analysis.

Statistical learning is about the construction and study of systems that can automatically learn from data.

In this course, we will introduce parallel programming paradigms to the students in the context of applied mathematics.

Numerical simulation is ubiquitous in today's world. Initially confined to well-mastered physical problems, it has spread to all fields (oceanography, biology, ecology, etc.), the aim being to make forecasts of the systems under study.

The main aim of this course is to provide the principles and tools to understand and master learning models based on probabilities and causality.

Understanding of fundamental notions in Machine Learning (inference, ERM and SRM principles, generalization bounds, classical learning models, unsupervised learning, semi-supervised learning.