CE40 - Mathématiques

Hidden Semi Markov Models: Inference, Control and Applications – HSMM-INCA

Submission summary

Most dynamic processes cannot be directly observed and Hidden Markov Models are a natural framework to model the relations between the observable and non-observable components. The extension to Hidden Semi Markov Models (HSMM) enables to relax assumptions on the distribution of the hidden variables, known to be inappropriate in several domains (speech recognition, activity recognition, disease dynamics with latency, earthquake prediction). HSMM are now very popular tools, however new theoretical and algorithmic advances are required to tackle more challenging real life problems with complex observations, interleaved dynamics, and complex management constraints. This concerns in particular understanding and controlling disease spread, and biodiversity conservation, two social issues Science needs to make progress on during coming decades. In these domains (but not only), the following Applied Challenges are crucial questions: (AC1) disentangling the influence of the local history and the regional neighbourhood in spatio-temporal phenomena like disease spread, or species dynamics (relevant also for earthquakes, bio geography, soil pollution...); (AC2) inferring transmission chains, or who infected whom, in a broad sense, like in epidemiology but also in animals migration routes; and finally (AC3) managing these processes in a learning-while managing approach where knowledge acquisition and control actions have taken jointly (as in medicine, conservation, invasive species control...). Motivated by these three Applied Challenges, we propose to extend the HSMM framework and the associated tools in three directions: complex single chain HSMM, multi chain HSMM and controlled HSMM. Even for a single chain HSMM, when observations are complex (censored, hybrid) or when the model parameters depend on covariables, current inference tools reach their limits. Multi-chains HSMM, i.e. several interacting hidden chains, is the natural framework to take into account spatial interactions or dynamics on networks, but the theoretical foundations have not been studied and efficient algorithmic tools for reasoning are rare. Controlled HSMM are usually studied from a theoretical point of view but operational algorithms for designing optimal control strategies are still missing. These issues can only be tackled via a strong collaboration between researchers from the fields of probability, computational statistics and decision, with an expertise on the applied challenges. Our consortium gather such scientists. We will make new developments to tackle both the theoretical and algorithmic issues raised by single, multi-chain HSMM and controlled HSMM. Algorithmic developments will go hand by hand with theoretical results for a solid understanding of the algorithms outputs. Furthermore, we will also demonstrate on concrete applications in ecology, epidemiology, medicine and seismology, how these methodological tools can improve the way to address questions AC1 to AC3. This relies on five cases study our consortium has already a solid experience on, and established collaborations.
In conclusion, the strength and originality of our project is in the continuum from theory, to algorithms and towards applications. Our developments will serve as a reference and open perspectives for future works on complex HSMM, and we have the ambition to contribute actively to the creation of a French community on the topic of Hidden Processes and their applications.

Project coordination

Nathalie Peyrard (Mathématiques et Informatique Appliquées Toulouse)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

MIAT Mathématiques et Informatique Appliquées Toulouse
LMAC LABORATOIRE DE MATHEMATIQUES APPLIQUEES DE COMPIEGNE
IMAG Institut Montpelliérain Alexander Grothendieck
LMRS LABORATOIRE DE MATHEMATIQUES RAPHAEL SALEM

Help of the ANR 395,765 euros
Beginning and duration of the scientific project: December 2021 - 48 Months

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