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Optimal Estimation via Nonanticipative Rate Distortion Function and Applications to Time-Varying Gauss-Markov Processes [article]

Photios A. Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey Loyka
2017 arXiv   pre-print
We apply the developed theory to design optimal filters for time-varying multidimensional Gauss-Markov processes, subject to a mean square error fidelity constraint.  ...  In this paper, we develop finite-time horizon causal filters using the nonanticipative rate distortion theory.  ...  The nonanticipative -entropy is equivalent to Shannon's Rate Distortion Function (RDF) [3, 4] with an additional causality constraint on the optimal reproduction or estimator.  ... 
arXiv:1603.04172v3 fatcat:v25domfkqfhxtio6cfaoktljky

Optimal Estimation via Nonanticipative Rate Distortion Function and Applications to Time-Varying Gauss--Markov Processes

Photios A. Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey Loyka
2018 SIAM Journal of Control and Optimization  
Subsequently, we apply the NRDF to design optimal filters for time-varying vector-valued Gauss-Markov processes, subject to a mean-squared error (MSE) distortion.  ...  In this paper, we develop finite-time horizon causal filters for general processes taking values in Polish spaces using the nonanticipative rate distortion function (NRDF).  ...  the optimal nonanticipative reproduction conditional distribution {P * (R2) Applications of (R1) to a time-varying multidimensional fully observed Gauss-Markov process X n with MSE distortion, to derive  ... 
doi:10.1137/17m1116349 fatcat:pbbdtegerzg2feokukubbtkxfu

Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints [article]

Photios A. Stavrou, Mikael Skoglund, Takashi Tanaka
2020 arXiv   pre-print
(a) A parallel time-varying Gauss-Markov process with identically distributed spatial components that is quantized and transmitted through a noiseless channel to a minimum mean-squared error (MMSE) decoder  ...  that allocates optimally the rate-distortion for any fixed finite-time horizon.  ...  ACKNOWLEDGEMENT The authors wish to thank the Associate Editor and the anonymous reviewers for their valuable comments and suggestions. They are also indebted to Prof. T.  ... 
arXiv:1906.04217v2 fatcat:nn246dr7b5b4dh4oifqly3grru

Real Time Coding and Estimation of Linear Discrete Time System over Networks

Junyong Chen, Yang Zhou
2020 IEEE Access  
ACKNOWLEDGMENT The authors would like to thank the Editors and the Reviewers for their valuable comments and suggestions.  ...  In general, for the real time coding and estimation system, the optimal rate distortion performance is hard to establish, and to overcome the computational complexity of the real time rate distortion function  ...  REAL TIME CODING-ESTIMATION VIA STANDARD KALMAN FILTER AND LLOYD-MAX QUANTIZATION AND ITS RATE DISTORTION PERFORMANCE The information rate distortion functions for real time coding-estimation system have  ... 
doi:10.1109/access.2020.3033620 fatcat:w7w6f3lpnzdfhgvt6k5scqb6vm

Zero-Delay Rate Distortion via Filtering for Vector-Valued Gaussian Sources

Photios Stavrou, Jan Ostergaard, Charalambos Demetriou Charalambous
2018 IEEE Journal on Selected Topics in Signal Processing  
rate distortion function (RDF).  ...  We recall the realization that corresponds to the optimal "test-channel" of the Gaussian NRDF, when considering a vector Gauss-Markov source subject to a MSE distortion in the finite time horizon.  ...  in [20] considered the NRDF of the time-varying vector-valued Gauss-Markov source under a total MSE distortion fidelity, and gave a sub-optimal realization of the design coefficient in the parametric  ... 
doi:10.1109/jstsp.2018.2855046 fatcat:v2ai6txep5aodhecwqtwqttvqe

Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-Offs

Takashi Tanaka, Kwang-Ki K. Kim, Pablo A. Parrilo, Sanjoy K. Mitter
2017 IEEE Transactions on Automatic Control  
In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria.  ...  Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems.  ...  ACKNOWLEDGMENT The authors would like to thank Prof. Sekhar Tatikonda for valuable discussions.  ... 
doi:10.1109/tac.2016.2601148 fatcat:haoq5nlbx5fdfidcrzxugzkofe

Bounds on the Sum-Rate of MIMO Causal Source Coding Systems with Memory under Spatio-Temporal Distortion Constraints

Photios A. Stavrou, Jan Ostergaard, Mikael Skoglund
2020 Entropy  
To characterize the lower bounds, we use state augmentation techniques and a data processing theorem, which recovers a variant of rate distortion function as an information measure known in the literature  ...  Each user's source model is described by a multidimensional Markov source driven by additive i.i.d. noise process subject to three classes of spatio-temporal distortion constraints.  ...  At time t, the packet t is sent over a noiseless channel with rate R t . The decoder at each time t, receives t to construct an estimate y t of x t .  ... 
doi:10.3390/e22080842 pmid:33286612 fatcat:c7oawm76t5cpbbtwx4vj4t5vem

Information-Theoretic Viewpoints on Optimal Causal Coding-Decoding Problems [article]

Siva Gorantla, Todd Coleman
2011 arXiv   pre-print
We provide examples of the applicability of this framework to communication with feedback, hidden Markov models and the nonlinear filter, decentralized control, brain-machine interfaces, and queuing theory  ...  In this paper we consider an interacting two-agent sequential decision-making problem consisting of a Markov source process, a causal encoder with feedback, and a causal decoder.  ...  With Q W Gauss-Markov and P Y |X an AGN channel, "error" encoding and MMSE estimation decoding is inverse control optimal. The induced cost function is squared error. + − Zi−1 MMSE estim.  ... 
arXiv:1102.0250v1 fatcat:kjwuxv2t7rgdpcm3jfbmfteuxa

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
Finally I report numerical results of a comparison between the variant and a minimization approach using penalty functions.  ...  If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  mentioned explicitly, the feasibility set is allowed to vary in a non-standard way and the objective function is also allowed to vary.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

Abstracts of Working Papers in Economics

1997 Abstracts of Working Papers in Economics  
The same criterion is used to find optimal values of the hyperparameters in the BVAR's.  ...  For any arbitrary finite horizon, the solution is time-dependent.  ...  A stationary, ergodic Markov process determines who moves at each decision node.  ... 
doi:10.1017/s0951007900003508 fatcat:sjk3leigpvgdfeuxuh5dsgiuaa

Tutorials on Advanced Optimization Methods [article]

Wei Wei
2020 arXiv   pre-print
It discusses how to reformulate a difficult (non-convex, multi-agent, min-max) problem to a solver-compatible form (semidefinite program, mixed-integer linear program) via convexification, linearization  ...  programming, robust optimization, and equilibrium/game problems.  ...  process.  ... 
arXiv:2007.13545v1 fatcat:o5rx62tjzvfunitksen4dlci6m

PROCEEDINGS of the 2017 Symposium on Information Theory and Signal Processing in the Benelux

Richard Heusdens, Jos Weber
unpublished
We gave a finite-time horizon solution to the INRDF in log-determinant terms. This expression can be minimized using for example SDP algorithm which can optimize log-determinant terms directly.  ...  Conclusions We used the versatile scheme proposed in [1] to address the INRDF for scalar Gaussian AR(p) sources under average MSE distortion criterion.  ...  (1) , the source model is described by a (vector or scalar) Gaussian AR(p) process, where p is a positive finite integer, and the distortion measure is a square error distortion function, then, the optimal  ... 
fatcat:kn4dxrad7zf2reqejkwnvzepna