18 research outputs found
Loop Calculus for Non-Binary Alphabets using Concepts from Information Geometry
The Bethe approximation is a well-known approximation of the partition
function used in statistical physics. Recently, an equality relating the
partition function and its Bethe approximation was obtained for graphical
models with binary variables by Chertkov and Chernyak. In this equality, the
multiplicative error in the Bethe approximation is represented as a weighted
sum over all generalized loops in the graphical model. In this paper, the
equality is generalized to graphical models with non-binary alphabet using
concepts from information geometry.Comment: 18 pages, 4 figures, submitted to IEEE Trans. Inf. Theor
The DLR Hierarchy of Approximate Inference
We propose a hierarchy for approximate inference based on the Dobrushin,
Lanford, Ruelle (DLR) equations. This hierarchy includes existing algorithms,
such as belief propagation, and also motivates novel algorithms such as
factorized neighbors (FN) algorithms and variants of mean field (MF)
algorithms. In particular, we show that extrema of the Bethe free energy
correspond to approximate solutions of the DLR equations. In addition, we
demonstrate a close connection between these approximate algorithms and Gibbs
sampling. Finally, we compare and contrast various of the algorithms in the DLR
hierarchy on spin-glass problems. The experiments show that algorithms higher
up in the hierarchy give more accurate results when they converge but tend to
be less stable.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty
in Artificial Intelligence (UAI2005
Some interesting observations on the free energy principle
Biehl et al (2020) present some interesting observations on an early
formulation of the free energy principle in (Friston, 2013). We use these
observations to scaffold a discussion of the technical arguments that
underwrite the free energy principle. This discussion focuses on solenoidal
coupling between various (subsets of) states in sparsely coupled systems that
possess a Markov blanket - and the distinction between exact and approximate
Bayesian inference, implied by the ensuing Bayesian mechanics.Comment: A response to a technical critique [arXiv:2001.06408] of the free
energy principle as presented in "Life as we know it
Approximate inference techniques with expectation constraints
Contains fulltext :
100937.pdf (preprint version ) (Open Access
Statistical modelling of higher-order correlations in pools of neural activity
Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2^N-1)-dimensional model for a population with N neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.Instituto de Física de Líquidos y Sistemas BiológicosInstituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica
Statistical modelling of higher-order correlations in pools of neural activity
Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable statistical models to describe the response variability of the recorded spike trains. Using the information geometry framework, it is possible to estimate higher-order correlations by assigning one interaction parameter to each degree of correlation, leading to a (2^N-1)-dimensional model for a population with N neurons. However, this model suffers greatly from a combinatorial explosion, and the number of parameters to be estimated from the available sample size constitutes the main intractability reason of this approach. To quantify the extent of higher than pairwise spike correlations in pools of multiunit activity, we use an information-geometric approach within the framework of the extended central limit theorem considering all possible contributions from higher-order spike correlations. The identification of a deformation parameter allows us to provide a statistical characterisation of the amount of higher-order correlations in the case of a very large neural ensemble, significantly reducing the number of parameters, avoiding the sampling problem, and inferring the underlying dynamical properties of the network within pools of multiunit neural activity.Instituto de Física de Líquidos y Sistemas BiológicosInstituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica
Path integrals, particular kinds, and strange things
This paper describes a path integral formulation of the free energy
principle. The ensuing account expresses the paths or trajectories that a
particle takes as it evolves over time. The main results are a method or
principle of least action that can be used to emulate the behaviour of
particles in open exchange with their external milieu. Particles are defined by
a particular partition, in which internal states are individuated from external
states by active and sensory blanket states. The variational principle at hand
allows one to interpret internal dynamics - of certain kinds of particles - as
inferring external states that are hidden behind blanket states. We consider
different kinds of particles, and to what extent they can be imbued with an
elementary form of inference or sentience. Specifically, we consider the
distinction between dissipative and conservative particles, inert and active
particles and, finally, ordinary and strange particles. Strange particles (look
as if they) infer their own actions, endowing them with apparent autonomy or
agency. In short - of the kinds of particles afforded by a particular partition
- strange kinds may be apt for describing sentient behaviour.Comment: 31 pages (excluding references), 6 figure