Data Science

General goals: The aim of the course is to introduce students to the theory and applications of optimization techniques for machine learning problems. Also, students are expected to acquire knowledge about standard models used in machine learning, such as Deep Neural Networks and Support Vector Machines. Specific goals: The course will put a special emphasis on convex optimization techniques which play a key role in data sciences. The objective of this course is to provide basic tools and methods at the core of modern nonlinear convex optimization. Starting from the gradient descent method we will cover some state of the art algorithms, including proximal gradient methods, accelerated methods, stochastic subgradient method and randomized block-coordinate descent methods, which are nowadays very popular techniques to solve machine learning and inverse problems. The course will also cover topics in statistics in high dimension which is the typical scenario in machine learning problems. Knowledge and understanding: the student will learn about (1) mathematical formulation of the machine learning problem, (2) the latest optimization algorithms for solving machine learning problems and extract information from data (3) understanding the theory of convergence of such algorithms (4) develop computational skills for handling several important problems in data science. Applying knowledge and understanding: through several examples from applied sciences and lab sessions, the student will appreciate the importance of optimization techniques and will understand which algorithm is most appropriate to use in each context. Critical and judgmental skills: the student will be able to tackle with rigor a number of significant optimization problems and algorithms so as to become fully aware of the technicalities and main ideas behind the various approaches. This will stimulate the student's independent judgment. Communication skills: by studying the theoretical and practical aspects of optimization techniques the student will learn gradually to communicate with rigor and clarity. She will also learn that a proper understanding of the mathematical aspects of data science is one of the main skills to achieve effective communication. Learning skills: students will have the chance to have additional details on some specific topics.