42,495 research outputs found
A Deterministic Analysis of an Online Convex Mixture of Expert Algorithms
Cataloged from PDF version of article.We analyze an online learning algorithm that adaptively
combines outputs of two constituent algorithms (or the
experts) running in parallel to model an unknown desired signal.
This online learning algorithm is shown to achieve (and in some
cases outperform) the mean-square error (MSE) performance of
the best constituent algorithm in the mixture in the steady-state.
However, the MSE analysis of this algorithm in the literature
uses approximations and relies on statistical models on the
underlying signals and systems. Hence, such an analysis may not
be useful or valid for signals generated by various real life systems
that show high degrees of nonstationarity, limit cycles and, in
many cases, that are even chaotic. In this paper, we produce
results in an individual sequence manner. In particular, we relate
the time-accumulated squared estimation error of this online
algorithm at any time over any interval to the time-accumulated
squared estimation error of the optimal convex mixture of the
constituent algorithms directly tuned to the underlying signal
in a deterministic sense without any statistical assumptions. In
this sense, our analysis provides the transient, steady-state and
tracking behavior of this algorithm in a strong sense without any
approximations in the derivations or statistical assumptions on
the underlying signals such that our results are guaranteed to
hold. We illustrate the introduced results through examples. © 2012 IEEE
Universal Codes from Switching Strategies
We discuss algorithms for combining sequential prediction strategies, a task
which can be viewed as a natural generalisation of the concept of universal
coding. We describe a graphical language based on Hidden Markov Models for
defining prediction strategies, and we provide both existing and new models as
examples. The models include efficient, parameterless models for switching
between the input strategies over time, including a model for the case where
switches tend to occur in clusters, and finally a new model for the scenario
where the prediction strategies have a known relationship, and where jumps are
typically between strongly related ones. This last model is relevant for coding
time series data where parameter drift is expected. As theoretical ontributions
we introduce an interpolation construction that is useful in the development
and analysis of new algorithms, and we establish a new sophisticated lemma for
analysing the individual sequence regret of parameterised models
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