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Talk Abstract

Universal Modeling and Coding

Universal Modeling and Coding

Universal models are an outgrowth of the ideas rooted in universal
coding, stochastic complexity, and modeling by the shortest
code length or the *MDL* principle, which themselves are
modifications of algorithmic complexity, as introduced by Solomonoff.
Much like algorithmic complexity, which permits the definition
of a universal probability model, albeit a noncomputable one,
stochastic complexity can be used to define a computable model,
which is universal for a class of probability measures. Although
it can fully learn to imitate these models from their samples
only asymptotically, we can prove for many classes of models
that asymptotically no "estimate" of the data-generating machinery
can perform better than the universal model, which then may
be regarded as the ultimate "estimator".

In reality, such a foundation for statistics does not require the data, let alone the parameters, to be a sample from any population. The selected probability models are just a convenient way via the Kraft inequality to describe good codes without need to resort to the (false) claim that any of them has generated the data. The central issue then becomes model fitting rather than estimation, in which the elusive model complexity plays a natural and essential part. This brings advantages well beyond the reach of the traditional techniques, especially in complex modeling problems.

This talk will outline algorithms for universal density and
regression models as well as a new way to do universal coding.

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