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Oberwolfach Reports, 2006
The workshop Free Probability Theory , organised by Philippe Biane (Paris), Roland Speicher (Kingston), and Dan Voiculescu (Berkeley) was held March 27th–April 2nd, 2005. This meeting was well attended with over 50 participants with broad geographic representation from Austria, Canada ...
Philippe Biane +2 more
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The workshop Free Probability Theory , organised by Philippe Biane (Paris), Roland Speicher (Kingston), and Dan Voiculescu (Berkeley) was held March 27th–April 2nd, 2005. This meeting was well attended with over 50 participants with broad geographic representation from Austria, Canada ...
Philippe Biane +2 more
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Distribution-Free Probability Density Forecast Through Deep Neural Networks
IEEE Transactions on Neural Networks and Learning Systems, 2020Probability density forecast offers the whole distributions of forecasting targets, which brings greater flexibility and practicability than the other probabilistic forecast models such as prediction interval (PI) and quantile forecast. However, existing
Tianyu Hu +4 more
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Expectation Propagation for Approximate Inference: Free Probability Framework
International Symposium on Information Theory, 2018We study asymptotic properties of expectation propagation (EP) - a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate Gaussian approximation
Burak Çakmak, M. Opper
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Oberwolfach Reports, 2016
The workshop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory.
Alice Guionnet +2 more
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The workshop brought together leading experts, as well as promising young researchers, in areas related to recent developments in free probability theory. Some particular emphasis was on the relation of free probability with random matrix theory.
Alice Guionnet +2 more
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Limit theorems in bi-free probability theory
Probability theory and related fields, 2017In this paper additive bi-free convolution is defined for general Borel probability measures, and the limiting distributions for sums of bi-free pairs of self-adjoint commuting random variables in an infinitesimal triangular array are determined.
Takahiro Hasebe +2 more
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AXIOMS FOR TYPE-FREE SUBJECTIVE PROBABILITY
The Review of Symbolic Logic, 2023AbstractWe formulate and explore two basic axiomatic systems of type-free subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial ...
CEZARY CIEŚLIŃSKI +2 more
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Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2004
We introduce and study a notion of Λ-freeness, which generalises both freeness and independence in the context of noncommutative probability. In particular, we extend Voiculescu's construction of the free product of representations of unital *-algebras. A central limit theorem is also proved.
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We introduce and study a notion of Λ-freeness, which generalises both freeness and independence in the context of noncommutative probability. In particular, we extend Voiculescu's construction of the free product of representations of unital *-algebras. A central limit theorem is also proved.
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2017
AbstractFree probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion ...
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AbstractFree probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion ...
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Free Probability and Random Matrices
, 2014The concept of freeness was introduced by Voiculescu in the context of operator algebras. Later it was observed that it is also relevant for large random matrices.
R. Speicher
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