CMI Special Lecture
Series on Information, Control and Statistical
Mechanics
Sanjoy Mitter,
MIT
The theory of Stochastic control with Partial Observations when extended to
stochastic systems with unknown parameters provides a comprehensive view of
control when systems can be described using Markov Processes. Conceptually,
this theory can be extended to stochastic systems, which have both a
temporal and spatial dimension by describing them in terms of Markov Random
Fields. The statistical mechanics of Gibbs Measures, which has a rich
theoretical underpinning (See for example, H. O. Georgii: Gibbs Measures and
Phase Transitions: de Gruy, 1988) can be effectively used for mathematical
modeling of such spatiotemporal stochastic systems. Viewed thus, Shannon's
Information theory would be interpreted as the stochastic control with a
nonclassical information pattern of a statistical mechanical system on the
integers in thermodynamic limit. The coding and decoding problem for the
reliable transmission of messages over a noisy channel can be transported to
the study of a Spin glass in an asymptotic regime. These ideas are discussed
in the first lecture from a high level viewpoint.
In the next two lectures, I discuss the interconnections that exist between
Path estimation for nonlinear stochastic systems, Information theory and
Nonequilibrium Statistical Mechanics. The fundamental idea is to view
Bayesian Inference as minimization of an appropriately defined Free Energy.
This Free Energy minimization is then given an informationtheoretic
interpretation. To illustrate these ideas in a concrete setting, I discuss
the Kalman Filter for Gaussian Processes as a Statistical Mechanical System.
(1) Friday January 14 2005, 4:00pm, Jorgensen 74
(2) Tuesday January 18 2005, 4:00pm, Moore 070
(3) Monday January 24 2005, 1:00pm, Moore 070
(4) Tuesday January 25 2005, 4:00pm, Moore 070
(1) Mitter, S.K. and Newton, N. A Variational Approach to Nonlinear Estimation SIAM Jrn. on Control, Volume 42, Number 5 (2004), pp. 18131833. (pdf)
(2) Mitter, S.K. and Newton, N.J. Information and Entropy Flow in the KalmanBucy Filter to appear in J. of Stat. Phys., January 2005. (pdf)
(3) Mitter, S.K., and Tatikonda, S., Control over Noisy Channels IEEE Trans. on Auto. Control, Volume: 49 , Issue: 7 , July 2004, Pages:1196  1201. (pdf)
(4) Mitter, S.K., and Tatikonda, S., Control under Communication Constraints IEEE Trans. on Auto. Control, Volume: 49 , Issue: 7 , July 2004, Pages:1056  1068. (pdf)
(5) Tatikonda, S., Sahai, A. and Mitter, S.K. Stochastic Linear Control Over a Communication Channel IEEE Trans. on Auto Control, Special Issue on Networked Control Systems, Volume: 49 , Issue: 9 , Sept. 2004, Pages:1549  1561. (pdf)
(6) Borkar, V.S., Mitter, S.K. and Tatikonda, S. Optimal Sequential Vector Quantization of Markov Sources SIAM J. Control Optim., {\bf 40}, 135148; proceedings of the 1998 IEEE Int'l Sym on Inf Th. (pdf)
(7) Mitter, S.K. Control with Limited Information: the Role of Systems Theory and Information Theory ISIT 2000 Plenary Talk, IEEE Information Theory Society Newsletter, 50, pgs.123; Eur. Jrn. Control, Vol. 7, pp. 122131. (pdf)
(8) Markov Control Problems Under Communication Constraints, by Borkar,
V.S.,Tatikonda, S. and Mitter, S.K.,
Comm. Inf. Sys. Vol. 1., No. 1., 2001, pp. 1532. (pdf)

