The field of adaptive signal processing experienced dramatic
growth due to the proliferation of new and exciting applications
ranging from Internet, wireless communications to multimedia and
quantitative finance. Adaptive systems have become an integral part of
information and telecommunications industries as a result of advances
in device technology. As the range of environments that these signal
processing applications are expected to work are increasing, there is
now a greater need for adaptive algorithms that can operate
efficiently in the presence of a wide range of environmental
uncertainties and volatility with relatively low computational
complexity. In this context, there exist significant practical and
theoretical difficulties to adaptive signal processing, since there is
usually no or little knowledge about the statistical properties of the
underlying signals or systems involved. Furthermore, the classical
robust methods that are resilient to such challenges are overly
conservative and usually static such that they provide profoundly
inferior results on the average, deeming them practically useless.
In order to provide robust adaptive methods that also perform
satisfactorily in real life applications, we introduce a completely
radical approach to adaptive signal processing. In this project,
we aim to design adaptive methods that are mathematically guaranteed
to work uniformly for all possible signals without any explicit or
implicit statistical assumptions on the underlying signals or
systems. In this sense, this is the first approach to build
adaptive systems that can operate effectively in the presence of large
degrees of environmental variability and uncertainty without
sacrificing performance. This radical approach would provide the
required tools in data prediction, pattern estimation, attribute
derivation and adaptive data modeling to deal with the open-ended and
frequently changing conditions of real life applications.
Sample publications on this topic include:
-- M. A. Donmez, S. S. Kozat, ``Steady-state MSE Analysis of Convexly Constrained Mixture Methods,'' IEEE Transactions on Signal Processing, vol. 60, iss. 6, 3314-3321, 2012.
-- S. S. Kozat, A. T. Erdogan, A. C. Singer, A. H. Sayed, ``A Transient Analysis of Affine Mixtures," IEEE Transactions on Signal Processing, vol. 59, iss. 1, 6227-6232, 2011.
-- H. Ozkan, A. Akman and S. S. Kozat, ``A Novel Training Algorithm for HMMs with Partial and Noisy Access to States,'' Signal Processing, vol. 94, pp. 490-497, January 2014.
-- S. S. Kozat, A. T. Erdogan, A. C. Singer, A. H. Sayed, ``A Transient Analysis of Affine Mixtures," IEEE Transactions on Signal Processing, vol. 59, iss. 1, 6227-6232, 2011.
-- S. S. Kozat, A. C. Singer, A. T. Erdogan, A. H. Sayed, ``Unbiased Model Combinations for Adaptive Filtering," IEEE Transactions on Signal Processing, vol. 58, pp. 4421-4427, Aug. 2010.
FIGURE: A tree based adaptive prediction method for deterministic nonlinear filtering.