This course is designed to equip students with an in-depth understanding and hands-on proficiency in machine learning, with a specific focus on techniques that complement contemporary deep learning methods. Throughout the course, students will start by quickly revisiting linear in parameters models with a focus on their Bayesian interpretation, followed by an examination of these models from a Gaussian process perspective. Additionally, we will explore the theory of regularization within reproducing kernel Hilbert spaces (RKHSs). To ensure a seamless transition into topics related to RKHSs, we will also provide an essential foundation in the context of real and functional analysis. Moreover, the course will encompass the practical applications of mathematical optimization in the realm of machine learning and a thorough examination of the algorithmic aspects of regularization techniques applicable to semi-supervised and unsupervised learning problems. By the end of this course, students will gain a comprehensive grasp of Bayesian machine learning concepts, an understanding of the theory underpinning RKHS, and proficiency in optimization techniques relevant to various facets of machine learning.

Prerequisites
- Prerequisite mathematical knowledge encompasses linear algebra, multivariate calculus, and probability theory.
-This course requires a foundational understanding of basic programming concepts and undergraduate-level machine learning.
- Python will serve as the programming environment for coursework, so a degree of familiarity with Python is assumed.

Midterm exam (30%), coursework (30%), Final project (40%)

Carl Edward Rasmussen and Christopher K. I. Williams, Gaussian Processes for Machine Learning, MIT Press

01 Linear in parameters models and Bayesian linear regression
02 Gaussian process models 1
03 Gaussian process models 2
04 Basic real and functional analysis 1
05 Basic real and functional analysis 2
06 Kernel methods and regularization techniques 1
07 Kernel methods and regularization techniques 2
08 Midterm exam
09 Kernel methods and regularization techniques 3
10 Optimization in machine learning 1
11 Optimization in machine learning 2
12 Semi-supervised and unsupervised learning 1
13 Semi-supervised and unsupervised learning 2
14 Selected Topics in Machine Learning 1
15 Selected Topics in Machine Learning 2
16 Final project

On-site lectures