Mistis has been created in January 2008 and is a joint team of Inria and Laboratoire Jean Kuntzmann , a joint research unit of Centre National de Recherche Scientifique (CNRS), Institut National Polytechnique de Grenoble (G-INP) and Université Grenoble-Alpes (UGA).
The context of our work is the analysis of structured stochastic models with statistical tools. The idea underlying the concept of structure is that stochastic systems that exhibit great complexity can be accounted for by combining simple local assumptions in a coherent way. This provides a key to modelling, computation, inference and interpretation. This approach appears to be useful in a number of high impact applications including signal and image processing, neuroscience, genomics, sensors networks, etc. while the needs from these domains can in turn generate interesting theoretical developments. However, this powerful and flexible approach can still be restricted by necessary simplifying assumptions and several generic sources of complexity in data.
Our goal is to contribute to statistical modelling by offering theoretical concepts and computational tools to handle properly some of these issues that are frequent in modern data. So doing, we aim at developing innovative techniques for high scientific, societal, economic impact applications and in particular via image processing and spatial data analysis in environment, biology and medicine.
We mainly focus on two directions of research:
- How to deal with complex phenomenons, complex models and complex data. We propose to use structured models and methods allowing easy interpretations. We propose to develop model selection and approximation techniques for complex structure models and to study dimension reduction techniques based on non linear data analysis.
- The theoretical and practical behaviour of methods. We focus on approximations justifications, asymptotic behaviour and convergence analysis.
The methods we develop involve mixture models, Markov models, and more generally hidden structure models identified by stochastic algorithms on one hand, and semi and non-parametric methods on the other hand.