information theory

We discuss new information-based Uncertainty Quantification (UQ) methods cable to assess and improve the predictive ability of computational models in applications ranging from materials design, optimizing catalysts and fuel cells to risk assessment in subsurface flows. These models are typically multi-scale and involve any available data, e.g. from electronic structure calculations or observational/experiment data.

This presentation explores information theory and statistics themes in two or three topics with which I have been involved, selected from among the the following topics: penalized likelihood concentration and risk bounds derivable from the information theory properties of penalized likelihood; greedy algorithms for vertex selection for projection onto convex hulls (and associated algorithms for term selection in regression); provably fast capacity-achieving codes for communication in the presence of Gaussian noise; information-theoretic characterization of minimax risk as

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There are several relationships between the Information theory and Convex Geometry that have been highlighted in the late 80's, notably through the work of Costa, Cover, Dembo and Thomas. In this talk, we will review some of these relationships and discuss recent developments surrounding them.