Teaching
My teaching is divided into two main areas:
(1) Probability, statistics, and their applications. Basic teaching of probability in I-MARO-005 (random variable, continuous/discrete distributions, etc.) and statistics in I-MARO-007 (confidence intervals, hypothesis testing, etc.). For civil engineering in architecture, these two courses are combined into one course (I-MARO-012). These concepts, along with other new ones (e.g. Markov chains, and matrix and tensor factorizations which generalize PCA), are applied to practical problems in the course 'Models and methods in Data Science' (MARO-015).
(2) Optimization: introduction to linear optimization with the simplex method, duality, branch and bound (I-MARO-035), project of modeling and solving an industrial problem (I-MARO-017), introduction to first-order methods for solving large-scale problems, including optimization of neural network parameters (I-MARO-303), and advanced topics in convex optimization (I-MARO-232).
Research
I am interested in linear dimension reduction techniques and low-rank matrix approximations (in particular nonnegative matrix factorization). I also work on the development of efficient optimization algorithms for continuous optimization problems (e.g., in imaging, data analysis and machine learning). See https://sites.google.com/site/nicolasgillis for more details.
Keywords: optimization, data analysis, machine learning, matrix theory and linear numerical algebra, image analysis, hyperspectral imaging, algorithmic complexity, signal processing