AI-Fun with ELLIS Seminar | Jack Liell-Cock: Compositional imprecise probability
| Dates: | 13 November 2024 |
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| Times: | 11:00 - 12:00 |
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| What is it: | Seminar |
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| Organiser: | Faculty of Science and Engineering |
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| Who is it for: | University staff, External researchers, Alumni, Current University students |
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| Speaker: | Jack Liell-Cock |
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The Manchester Centre for AI Fundamentals and Manchester's ELLIS Unit are co-hosting a series of seminars featuring expert researchers working in the fundamentals of AI.
Jack Liell-Cock is a PhD student at Keble College, Oxford, under the supervision of Jeremy Gibbons and Sam Staton.
Title: Compositional imprecise probability
Abstract:
Imprecise probability concerns uncertainty about which probability distributions to use. It has applications in robust statistics and AI safety. Imprecise probability can be modelled in various ways, such as by convex sets of probability distributions.
We look at programming language models for imprecise probability. Our desiderata are that we would like our model to support all kinds of composition, categorical and monoidal; in other words, guided by dataflow diagrams. Another equivalent perspective is that we would like a model of synthetic probability in the sense of Markov categories.
The leading monad-based approach to imprecise probability is not fully compositional because the monad involved is not commutative, meaning it does not have a proper monoidal structure. In this work, we provide a new fully compositional account. The key idea is to name the non-deterministic choices. To manage the renamings and disjointness of names, we use graded monads. We show that the resulting compositional model is maximal and relate it with the earlier monad approach, proving that we obtain tighter bounds on the uncertainty.
Speaker
Jack Liell-Cock
Role: Researcher
Organisation: University of Oxford
Travel and Contact Information
Find event
Lecture Theatre 1.4
Kilburn Building
Manchester
