2022-05642 - Investigating model miss specification in simulation based inference
Contract type : Internship
Level of qualifications required : Master's or equivalent
Fonction : Internship ResearchContext
This is a M2 internship taking place at the Statify team from Inria Grenoble. The team specializes in the statistical modeling of systems involving data with a complex structure. Most applications are in brain imaging (or neuroimaging), personalized medicine, environmental risk analysis and geosciences. Statify is a scientific project centered on statistics and aims towards strong methodological developments for general applications in data science. During the internship, we also intend having interactions with colleagues from the MIND team at Inria Saclay as well from the Lander associated team between Statify and certain australian universities.Assignment
In this internship, we will investigate and better understand the effects of model miss specification in the approximation of posterior distributions with SBI. The intern will begin his work with getting acquainted to the modern tools from SBI (e.g. normalizing flows, automatic differentiation, probabilistic programming, sending batches of simulations to clusters of computers) and then investigate the effects model miss specifications in simple toy models. He will then focus on understanding and implementing the ideas proposed in 2 and 3 so to get a better sense of their contributions as well as limitations. The intern is then expected to work in close collaboration with its tutors so to explore the viability of some their recent theoretical developments on the topic and compare the results with those in the literature.Main activities
Bayesian inference is a powerful framework for inverse problems. It yields a posterior probability density function over the space of parameter that could have generated a given observed data. Unfortunately, using a Bayesian framework within modern complex models is, in general, a difficult task, because their likelihood functions are often intractable. A modern approach for bypassing such obstacle is to use simulation-based inference (SBI) methods, where one learns an approximation to the posterior distribution based on several simulations over different parameters 1.
Although SBI has been validated and illustrated in many toyish and/or strictly controlled examples, there remains a considerable gap between theory and actual experimental data. One of the main difficulties comes from the well known fact that “all models are wrong” and, therefore, the simulations used to approximate the posterior distribution often don't exactly match the data that one can obtain in an experiment. This fundamental aspect of SBI known as model miss specification and has not been properly studied in most of recent SBI literature. Two exceptions are 2 and 3.
1 Kyle Cranmer, Johann Brehmer, and Gilles Louppe. The frontier of simulation-based inference. Proceedings of the National Academy of Sciences, 117(48):30055–30062, 2020.
2 David T. Frazier, Christian Robert, and Judith Rousseau. Model Misspecification in ABC: Consequences and Diagnostics. Journal of the Royal Statistical Society: Series B, 2019.
3 Daniel Ward, Patrick Cannon, Mark Beaumont, Matteo Fasiolo, and Sebastian M Schmon. Robust neural posterior estimation and statistical model criticism, 2022.Skills
Strong mathematical background, specially advances concepts in probability and statistics.
Good working knowledge in Python programming; experience with a deep learning library (e.g. pyTorch or tensorflow) will be a plus.
Language: good English skills both written and spoken.
Relational skills: good team working skills
Theme/Domain : Optimization, machine learning and statistical methods Scientific computing (BAP E)
Town/city : Montbonnot
Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact.Instruction to apply
Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.
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