2 research outputs found
The NLMS algorithm with time-variant optimum stepsize derived from a Bayesian network perspective
In this article, we derive a new stepsize adaptation for the normalized least
mean square algorithm (NLMS) by describing the task of linear acoustic echo
cancellation from a Bayesian network perspective. Similar to the well-known
Kalman filter equations, we model the acoustic wave propagation from the
loudspeaker to the microphone by a latent state vector and define a linear
observation equation (to model the relation between the state vector and the
observation) as well as a linear process equation (to model the temporal
progress of the state vector). Based on additional assumptions on the
statistics of the random variables in observation and process equation, we
apply the expectation-maximization (EM) algorithm to derive an NLMS-like filter
adaptation. By exploiting the conditional independence rules for Bayesian
networks, we reveal that the resulting EM-NLMS algorithm has a stepsize update
equivalent to the optimal-stepsize calculation proposed by Yamamoto and
Kitayama in 1982, which has been adopted in many textbooks. As main difference,
the instantaneous stepsize value is estimated in the M step of the EM algorithm
(instead of being approximated by artificially extending the acoustic echo
path). The EM-NLMS algorithm is experimentally verified for synthesized
scenarios with both, white noise and male speech as input signal.Comment: 4 pages, 1 page of reference
Marginal and simultaneous predictive classification using stratified graphical models
An inductive probabilistic classification rule must generally obey the
principles of Bayesian predictive inference, such that all observed and
unobserved stochastic quantities are jointly modeled and the parameter
uncertainty is fully acknowledged through the posterior predictive
distribution. Several such rules have been recently considered and their
asymptotic behavior has been characterized under the assumption that the
observed features or variables used for building a classifier are conditionally
independent given a simultaneous labeling of both the training samples and
those from an unknown origin. Here we extend the theoretical results to
predictive classifiers acknowledging feature dependencies either through
graphical models or sparser alternatives defined as stratified graphical
models. We also show through experimentation with both synthetic and real data
that the predictive classifiers based on stratified graphical models have
consistently best accuracy compared with the predictive classifiers based on
either conditionally independent features or on ordinary graphical models.Comment: 18 pages, 5 figure