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 engineers and architects, these two courses are combined into one course, I-MARO-012. These concepts, along with other new ones (e.g., Markov chains), are applied to practical problems in the MARO-015 course.
(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 optimization for civil architectural engineers (I-MARO-222), and introduction to first-order methods for solving large-scale problems, including optimization of neural network parameters (I-MARO-303).
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