Tübingen is one of the stronger machine learning departments in Europe and Philipp Hennig has put two of his master's courses on YouTube along with the slides, which sit on GitHub with time-stamped links into the video at each point. That format deserves copying widely. Slides alone are a poor learning artefact because the explanation lives in the room, and video alone is a poor reference because you cannot skim it, and having each slide link to the moment it was discussed gives you both. The Probabilistic Machine Learning series is the more conventional of the two, working through inference, graphical models, Gaussian processes, approximate inference and the probabilistic reading of standard methods.
It is well done and there are alternatives, including Murphy's books if you prefer reading. The reason to come here is the other one. Numerics of Machine Learning is a genuinely unusual course and I do not know of another public series on the subject. The premise is that numerical computation, the business of solving linear systems, integrating, optimising, solving differential equations, is itself an inference problem.
Your conjugate gradient solver does not simply return the answer, it accumulates information about the solution and stops when it judges it has enough, and if you take that view seriously you can put a probability distribution over what the solver does not yet know. The consequence is that computation returns a quantified uncertainty rather than a number presented as exact. Fourteen lectures cover this through numerical linear algebra, Monte Carlo methods, Bayesian quadrature, state space models, and probabilistic solvers for differential equations. Why this matters practically rather than as an intellectual curiosity.
Almost every machine learning system rests on numerical approximation and the approximation error is invisible in the output. You fit a Gaussian process, the solver approximates a matrix inverse, and the predictive variance you report is confidently stated while quietly ignoring the error the linear algebra introduced. In most applications this is fine. In the applications where you actually need the uncertainty, which is to say scientific modelling, control, anything where a decision depends on knowing what you do not know, it stops being fine, and this course is where you learn to think about it.
It is also a genuine antidote to a bad habit the current field has encouraged, which is treating numerical behaviour as somebody else's problem handled by the library. The honest difficulty is that this is hard and the prerequisites are real. You want to be comfortable with linear algebra at the level of understanding why conjugate gradients converge the way it does, comfortable with probability, and not frightened by numerical analysis. Without that the lectures will be a wall.
It is also completely undiscovered. Search volume for these courses is effectively zero, there is no community, no Discord, nobody to ask. You will work through it alone and that suits some people and defeats others. And it is worth being clear about what this is not.
There is nothing here about transformers, language models, fine-tuning or anything with commercial application in the next quarter. Nobody will be impressed that you watched it and it will not appear on a job description. It is mathematical education for people who want to understand the machinery, and the payoff is the kind that shows up later as better instincts rather than immediately as a skill you can list. The 2022 and 2023 vintage matters less here than it would for a deep learning course, because probabilistic numerics is not moving at the pace of the LLM field and the material is closer to mathematics than to engineering practice.
It does mean nothing has been refreshed and there is no sign of an updated offering. Four point three. Excellent, generous, demanding, and for a small audience who will get a great deal from it.