2,434 research outputs found
Optimal design of an unsupervised adaptive classifier with unknown priors
An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained
Direct-form adaptive equalization for underwater acoustic communication
Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2012Adaptive equalization is an important aspect of communication systems in various
environments. It is particularly important in underwater acoustic communication
systems, as the channel has a long delay spread and is subject to the effects of time-
varying multipath fading and Doppler spreading.
The design of the adaptation algorithm has a profound influence on the performance of the system. In this thesis, we explore this aspect of the system. The
emphasis of the work presented is on applying concepts from inference and decision
theory and information theory to provide an approach to deriving and analyzing
adaptation algorithms. Limited work has been done so far on rigorously devising
adaptation algorithms to suit a particular situation, and the aim of this thesis is to
concretize such efforts and possibly to provide a mathematical basis for expanding it
to other applications.
We derive an algorithm for the adaptation of the coefficients of an equalizer when
the receiver has limited or no information about the transmitted symbols, which we
term the Soft-Decision Directed Recursive Least Squares algorithm. We will demonstrate connections between the Expectation-Maximization (EM) algorithm and the
Recursive Least Squares algorithm, and show how to derive a computationally efficient, purely recursive algorithm from the optimal EM algorithm.
Then, we use our understanding of Markov processes to analyze the performance
of the RLS algorithm in hard-decision directed mode, as well as of the Soft-Decision
Directed RLS algorithm. We demonstrate scenarios in which the adaptation procedures fail catastrophically, and discuss why this happens. The lessons from the
analysis guide us on the choice of models for the adaptation procedure. We then
demonstrate how to use the algorithm derived in a practical system for underwater
communication using turbo equalization. As the algorithm naturally incorporates
soft information into the adaptation process, it becomes easy to fit it into a turbo
equalization framework. We thus provide an instance of how to use the information of a turbo equalizer in an adaptation procedure, which has not been very well explored in the past. Experimental data is used to prove the value of the algorithm in
a practical context.Support from the agencies
that funded this research- the Academic Programs Office at WHOI and the Office of
Naval Research (through ONR Grant #N00014-07-10738 and #N00014-10-10259)
Linear MMSE-Optimal Turbo Equalization Using Context Trees
Formulations of the turbo equalization approach to iterative equalization and
decoding vary greatly when channel knowledge is either partially or completely
unknown. Maximum aposteriori probability (MAP) and minimum mean square error
(MMSE) approaches leverage channel knowledge to make explicit use of soft
information (priors over the transmitted data bits) in a manner that is
distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside
an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization
methods either estimate the channel or use a direct adaptation equalizer in
which estimates of the transmitted data are formed from an expressly linear
function of the received data and soft information, with this latter
formulation being most common. We study a class of direct adaptation turbo
equalizers that are both adaptive and nonlinear functions of the soft
information from the decoder. We introduce piecewise linear models based on
context trees that can adaptively approximate the nonlinear dependence of the
equalizer on the soft information such that it can choose both the partition
regions as well as the locally linear equalizer coefficients in each region
independently, with computational complexity that remains of the order of a
traditional direct adaptive linear equalizer. This approach is guaranteed to
asymptotically achieve the performance of the best piecewise linear equalizer
and we quantify the MSE performance of the resulting algorithm and the
convergence of its MSE to that of the linear minimum MSE estimator as the depth
of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin
Joint Structure Learning of Multiple Non-Exchangeable Networks
Several methods have recently been developed for joint structure learning of
multiple (related) graphical models or networks. These methods treat individual
networks as exchangeable, such that each pair of networks are equally
encouraged to have similar structures. However, in many practical applications,
exchangeability in this sense may not hold, as some pairs of networks may be
more closely related than others, for example due to group and sub-group
structure in the data. Here we present a novel Bayesian formulation that
generalises joint structure learning beyond the exchangeable case. In addition
to a general framework for joint learning, we (i) provide a novel default prior
over the joint structure space that requires no user input; (ii) allow for
latent networks; (iii) give an efficient, exact algorithm for the case of time
series data and dynamic Bayesian networks. We present empirical results on
non-exchangeable populations, including a real data example from biology, where
cell-line-specific networks are related according to genomic features.Comment: To appear in Proceedings of the Seventeenth International Conference
on Artificial Intelligence and Statistics (AISTATS
Joint estimation of multiple related biological networks
Graphical models are widely used to make inferences concerning interplay in
multivariate systems. In many applications, data are collected from multiple
related but nonidentical units whose underlying networks may differ but are
likely to share features. Here we present a hierarchical Bayesian formulation
for joint estimation of multiple networks in this nonidentically distributed
setting. The approach is general: given a suitable class of graphical models,
it uses an exchangeability assumption on networks to provide a corresponding
joint formulation. Motivated by emerging experimental designs in molecular
biology, we focus on time-course data with interventions, using dynamic
Bayesian networks as the graphical models. We introduce a computationally
efficient, deterministic algorithm for exact joint inference in this setting.
We provide an upper bound on the gains that joint estimation offers relative to
separate estimation for each network and empirical results that support and
extend the theory, including an extensive simulation study and an application
to proteomic data from human cancer cell lines. Finally, we describe
approximations that are still more computationally efficient than the exact
algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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