Causality and directed information in communication, gambling and estimation.
Abstract In this talk we will present a fundamental role that directed information and causal conditioning has in communication with feedback, gambling with causal side information and estimation.We will begin by defining and establishing some key properties of the notions of causal conditioning and directed information. These properties will be seen to be natural counterparts, for the case where feedback is present, of the well-known properties of regular conditioning and mutual information.We will then use these notions to derive a sequence of upper and lower bounds on the capacity of any Finite State Channel (FSC) with time-invariantfeedback, and to identify a large class of FSCs for which the bounds coincide to yield the capacity.Applications of these multi-letter capacity expressions will be discussed. In particular we will show a framework for the computation of capacity of unifilar channels. We will also detail how the framework can lead to closed form analytical solutions, such as in the case of the trapdoor/chemical channel.Further, will show which of the capacity results for FSCs can be extended to FS-MACs and which can not. We will show how, among other things, this extension leads to the identification of a large class of FS-MACs for which feedback does not enlarge thecapacity region, and for which source-channel separation holds.Finally, we will discuss recent application of directed informationand causal conditioningin fields other than communication such as horse-race gambling,stock investment and estimation.The talk is based on research carried out in collaborations with Paul Cuff, Andrea Goldsmith, Young-Han Kim, Jun Chen, BrookeShrader, Benjamin Van-Roy and Tsachy Weissman.
Biography:Haim Permuter received his B.Sc. (summa cum laude) from Ben-GurionUniversity (BGU) and Ph.D. from Stanford University, both in inElectrical Engineering, in 1997 and 2008, respectively. Between1997-2004, he served as a scientific research officer in an R&D unitin the Israeli Defense Forces. In summer 2002 he worked for IBM,Almaden research center, and automn he was research visitor atStanford. He is a recipient of several awards including EshkolFellowship, Wolf Award, Fulbright Fellowship, Stanford GraduateFellowship, and Allon Fellowship. Recently, Haim joined the facultyof Electrical Engineering Department at BGU.