Machine learning is changing the world we live in at a break neck pace. From image recognition and generation, to the deployment of recommender systems, it seems to be breaking new ground constantly and influencing almost every aspect of our lives. In ths seminar series we ask distinguished speakers to comment on what role Bayesian statistics and Bayesian machine learning have in this rapidly changing landscape. Do we need to optimally process information or borrow strength in the big data era? Are philosophical concepts such as coherence and the likelihood principle relevant when you are running a large scale recommender system?

At Criteo, we define the word "relevance" as being products that people purchase after having been shown an ad. With AI, we focus on the causal relationship between the ads we show and the products people end up buying. Our business models are designed to align incentives across the whole chain: to maximize our profit, we need to maximize relevance and reduce waste and noise. Only a machine could perform this task a million times per second for a billion users and this machine is AI-driven. Criteo is first and foremost a technology company.

Adaptive inference – namely adaptive estimation and adaptive confidence statements – is particularly important in high of infinite dimensional models in statistics. Indeed whenever the dimension becomes high or infinite, it is important to adapt to the underlying structure of the problem. While adaptive estimation is often possible, it is often the case that adaptive and honest confidence sets do not exist. This is known as the adaptive inference paradox. And this has consequences in sequential decision making.