Bruno Bauwens
m-sophistication.
Wed, 01/27/2010 - 16:01 — SomNambulAuthors: Bruno Bauwens
Subjects: Computational Complexity
AbstractThe m-sophistication of a finite binary string x is introduced as a
generalization of some parameter in the proof that complexity of complexity is
rare. A probabilistic near sufficient statistic of x is given which length is
upper bounded by the m-sophistication of x within small additive terms. This
shows that m-sophistication is lower bounded by coarse sophistication and upper
bounded by sophistication within small additive terms.Influence tests I: ideal composite hypothesis tests, and causal semimeasures.
Tue, 12/15/2009 - 16:01 — SomNambulAuthors: Bruno Bauwens
Subjects: Statistics
AbstractRatios of universal enumerable semimeasures corresponding to hypotheses are
investigated as a solution for statistical composite hypotheses testing if an
unbounded amount of computation time can be assumed.Influence testing for discrete time series is defined using generalized
structural equations. Several ideal tests are introduced, and it is argued that
when Halting information is transmitted, in some cases, instantaneous cause and
consequence can be inferred where this is not possible classically.On the equivalence between minimal sufficient statistics, minimal typical models and initial segments of the Halting sequence.
Wed, 11/25/2009 - 16:01 — SomNambulAuthors: Bruno Bauwens
Subjects: Computational Complexity
AbstractIt is shown that the length of the algorithmic minimal sufficient statistic
of a binary string x, either in a representation of a finite set, computable
semimeasure, or a computable function, has a length larger than the
computational depth of x, and can solve the Halting problem for all programs
with length shorter than the m-depth of x. It is also shown that there are
strings for which the algorithmic minimal sufficient statistics can contain a
substantial amount of information that is not Halting information.Additivity of on-line decision complexity is violated by a linear term in the length of a binary string.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Bruno Bauwens
Subjects: Information Theory
AbstractWe show that there are infinitely many binary strings z, such that the sum of
the on-line decision complexity of predicting the even bits of z given the
previous uneven bits, and the decision complexity of predicting the uneven bits
given the previous event bits, exceeds the Kolmogorov complexity of z by a
linear term in the length of z.Additivity of on-line decision complexity is violated by a linear term in the length of a binary string.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Bruno Bauwens
Subjects: Information Theory
AbstractWe show that there are infinitely many binary strings z, such that the sum of
the on-line decision complexity of predicting the even bits of z given the
previous uneven bits, and the decision complexity of predicting the uneven bits
given the previous event bits, exceeds the Kolmogorov complexity of z by a
linear term in the length of z.
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