9,388 research outputs found
Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains
We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions
with spatio-temporal constraints from experimental spike trains. This is an
extension of two papers [10] and [4] who proposed the estimation of parameters
where only spatial constraints were taken into account. The extension we
propose allows to properly handle memory effects in spike statistics, for large
sized neural networks.Comment: 34 pages, 33 figure
Differential Entropy on Statistical Spaces
We show that the previously introduced concept of distance on statistical
spaces leads to a straightforward definition of differential entropy on these
statistical spaces. These spaces are characterized by the fact that their
points can only be localized within a certain volume and exhibit thus a feature
of fuzziness. This implies that Riemann integrability of relevant integrals is
no longer secured. Some discussion on the specialization of this formalism to
quantum states concludes the paper.Comment: 4 pages, to appear in the proceedings of the joint meeting of the 2nd
International Conference on Cybernetics and Information Technologies, Systems
and Applications (CITSA 2005) and the 11th International Conference on
Information Systems Analysis and Synthesis (ISAS 2005), to be held in
Orlando, USA, on July 14-17, 200
Differential Entropy on Statistical Spaces
We show that the previously introduced concept of distance on statistical
spaces leads to a straightforward definition of differential entropy on these
statistical spaces. These spaces are characterized by the fact that their
points can only be localized within a certain volume and exhibit thus a feature
of fuzziness. This implies that Riemann integrability of relevant integrals is
no longer secured. Some discussion on the specialization of this formalism to
quantum states concludes the paper.Comment: 4 pages, to appear in the proceedings of the joint meeting of the 2nd
International Conference on Cybernetics and Information Technologies, Systems
and Applications (CITSA 2005) and the 11th International Conference on
Information Systems Analysis and Synthesis (ISAS 2005), to be held in
Orlando, USA, on July 14-17, 200
A simple derivation and classification of common probability distributions based on information symmetry and measurement scale
Commonly observed patterns typically follow a few distinct families of
probability distributions. Over one hundred years ago, Karl Pearson provided a
systematic derivation and classification of the common continuous
distributions. His approach was phenomenological: a differential equation that
generated common distributions without any underlying conceptual basis for why
common distributions have particular forms and what explains the familial
relations. Pearson's system and its descendants remain the most popular
systematic classification of probability distributions. Here, we unify the
disparate forms of common distributions into a single system based on two
meaningful and justifiable propositions. First, distributions follow maximum
entropy subject to constraints, where maximum entropy is equivalent to minimum
information. Second, different problems associate magnitude to information in
different ways, an association we describe in terms of the relation between
information invariance and measurement scale. Our framework relates the
different continuous probability distributions through the variations in
measurement scale that change each family of maximum entropy distributions into
a distinct family.Comment: 17 pages, 0 figure
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