T. A. Fritz

Tobias Fritz, Tomáš Gonda, Antonio Lorenzin et al.

Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like conditional probability and almost sure equality, as well as proofs of fundamental results such as the Hewitt--Savage 0/1 Law, the de Finetti Theorem and the Ergodic Decomposition Theorem. In this work, we develop additional relevant notions from probability theory in the setting of Markov categories. This comprises improved versions of previously introduced definitions of absolute continuity and supports, as well as a detailed study of idempotents and idempotent splitting in Markov categories. Our main result on idempotent splitting is that every idempotent measurable Markov kernel between standard Borel spaces splits across another standard Borel space, and we derive this as an instance of a general categorical criterion for idempotent splitting in Markov categories.

Vadim Liventsev, Tobias Fritz

Reinforcement Learning in Healthcare is typically concerned with narrow self-contained tasks such as sepsis prediction or anesthesia control. However, previous research has demonstrated the potential of generalist models (the prime example being Large Language Models) to outperform task-specific approaches due to their capability for implicit transfer learning. To enable training of foundation models for Healthcare as well as leverage the capabilities of state of the art Transformer architectures, we propose the paradigm of Healthcare as Sequence Modeling, in which interaction between the patient and the healthcare provider is represented as an event stream and tasks like diagnosis and treatment selection are modeled as prediction of future events in the stream. To explore this paradigm experimentally we develop MIMIC-SEQ, a sequence modeling benchmark derived by translating heterogenous clinical records from MIMIC-IV dataset into a uniform event stream format, train a baseline model and explore its capabilities.