A common problem in data science is "use this function defined over this small set to generate predictions over that larger set." Extrapolation, interpolation, statistical inference and forecasting all reduce to this problem. The Kan extension is a powerful tool in category theory that generalizes this notion. In this work we explore several applications of Kan extensions to data science. We begin by deriving simple classification and clustering algorithms as Kan extensions and experimenting with these algorithms on real data. Next, we build more complex and resilient algorithms from these simple parts.
Further Information
Right now Dan works as the Head of Machine Learning at Abnormal Security. Previously. He led the Web Ads Machine Learning team at Twitter. Before that he worked as a Staff ML Engineer at Twitter Cortex and a Senior Data Scientist at TrueMotion.
His PhD research at the University of Oxford focused on applications of Category Theory to Machine Learning (advised by Jeremy Gibbons and Cezar Ionescu). Before that he worked as a Computer Vision Researcher at the Serre Lab.
You can find out more about Dan here: https://danshiebler.com/