Learning with Kan Extensions
Abstract: A common problem in machine learning 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 applications of the Kan extension to machine learning problems. We begin by deriving a simple classification algorithm as a Kan extension and experimenting with this algorithm on real data. Next, we use the Kan extension to derive a procedure for learning clustering algorithms from labels and explore the performance of this procedure on real data.
Although the Kan extension is usually defined in terms of categories and functors, this paper assumes no knowledge of category theory. We hope this will enable a wider audience to learn more about this powerful mathematical tool.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Sivan_Sabato1
Submission Number: 300
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