5,679 research outputs found
Expectation Consistent Free Energies for Approximate Inference
We propose a novel a framework for deriving approximations for intractable probabilistic models. This framework is based on a free energy (negative log marginal likelihood) and can be seen as a generalization of adaptive TAP [1, 2, 3] and expectation propagation (EP) [4, 5]. The free energy is constructed from two approximating distributions which encode different aspects of the intractable model such a single node constraints and couplings and are by construction consistent on a chosen set of moments. We test the framework on a difficult benchmark problem with binary variables on fully connected graphs and 2D grid graphs. We find good performance using sets of moments which either specify factorized nodes or a spanning tree on the nodes (structured approximation). Surprisingly, the Bethe approximation gives very inferior results even on grids.
Psychophysical identity and free energy
An approach to implementing variational Bayesian inference in biological
systems is considered, under which the thermodynamic free energy of a system
directly encodes its variational free energy. In the case of the brain, this
assumption places constraints on the neuronal encoding of generative and
recognition densities, in particular requiring a stochastic population code.
The resulting relationship between thermodynamic and variational free energies
is prefigured in mind-brain identity theses in philosophy and in the Gestalt
hypothesis of psychophysical isomorphism.Comment: 22 pages; published as a research article on 8/5/2020 in Journal of
the Royal Society Interfac
Quantum Monte Carlo for minimum energy structures
We present an efficient method to find minimum energy structures using energy
estimates from accurate quantum Monte Carlo calculations. This method involves
a stochastic process formed from the stochastic energy estimates from Monte
Carlo that can be averaged to find precise structural minima while using
inexpensive calculations with moderate statistical uncertainty. We demonstrate
the applicability of the algorithm by minimizing the energy of the H2O-OH-
complex and showing that the structural minima from quantum Monte Carlo
calculations affect the qualitative behavior of the potential energy surface
substantially.Comment: 7 pages, 4 figure
A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which
are commonly used as the building blocks for deep architectures neural
architectures. In this work, we derive a deterministic framework for the
training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer
(TAP) mean-field approximation of widely-connected systems with weak
interactions coming from spin-glass theory. While the TAP approach has been
extensively studied for fully-visible binary spin systems, our construction is
generalized to latent-variable models, as well as to arbitrarily distributed
real-valued spin systems with bounded support. In our numerical experiments, we
demonstrate the effective deterministic training of our proposed models and are
able to show interesting features of unsupervised learning which could not be
directly observed with sampling. Additionally, we demonstrate how to utilize
our TAP-based framework for leveraging trained RBMs as joint priors in
denoising problems
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