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Computable Bayesian Compression for Uniformly Discretizable Statistical Models
Lukasz Debowski
In: ALT 2009, Porto, Portugal(2009).
AbstractSupplementing Vovk and V’yugin’s ‘if’ statement, we show
that Bayesian compression provides the best enumerable compression for
parameter-typical data if and only if the parameter is Martin-L¨of random
with respect to the prior. The result is derived for uniformly discretizable
statistical models, introduced here. They feature the crucial property
that given a discretized parameter, we can compute how much data is
needed to learn its value with little uncertainty. Exponential families and
certain nonparametric models are shown to be uniformly discretizable. [Edit]
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