Matthijs Vákár does research into the software foundations of machine learning. He is particularly interested in:
- probabilistic programming languages: These are languages for use in computational statistics and probabilistic machine learning. The idea is to specify a probabilistic model as a program and to let the compiler perform inference in the model with respect to some data set (meaning e.g. full Bayesian inference, or maximum likelihood estimation) using a general purpose algorithm. The dream is to separate the task of modeling (which requires domain expertise and is often done by people who are not professional programmers) from the intricate algorithmic task of implementing an inference algorithm. This division of labour should hopefully lead to better science and better machine learning applications.
- differential programming languages: These are languages in which all programs are differentiable in the sense that they can be made to calculate not only a value but also one or more derivatives of the value with respect to their inputs. This is often done using a combination of algebraic identities for the derivatives of language primitives and the chain rule for the derivative of compound expressions (a technique commonly known as automatic differentiation). One reason to care about such languages is that they are crucial (in the backend) for the efficient implementation of probabilistic programming languages. Indeed, the optimization and Monte-Carlo integration tasks that inference usually boils down to tend to be most practically solvable using algorithms that require derivative information.
Matthijs is a developer for the Stan language, a state-of-the-art probabilistic programming language (which relies on differentiation in the backend) for which he wrote a large part of the compiler. Stan is used by 10,000s of people across branches of academia and industry for domain-specific statistical modelling and inference as well as probabilistic machine learning.
Example MSc thesis topics he can supervise are listed here. Feel free to get in touch to discuss options!
Current PhD students: