scholarly journals Properties of Bethe Free Energies and Message Passing in Gaussian Models

2011 ◽  
Vol 41 ◽  
pp. 1-24 ◽  
Author(s):  
B. Cseke ◽  
T. Heskes
Keyword(s):  
Free Energy ◽  
Message Passing ◽  
Probabilistic Models ◽  
Mean Field ◽  
Necessary Condition ◽  
Free Energies ◽  
Gaussian Models ◽  
Message Passing Algorithm ◽  
Bethe Free Energy ◽  
The Moment

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Bethe free energy and establish a necessary condition for the lower bound to be bounded from below. It turns out that the condition is identical to the pairwise normalizability condition, which is known to be a sufficient condition for the convergence of the message passing algorithm. We show that stable fixed points of the Gaussian message passing algorithm are local minima of the Gaussian Bethe free energy. By a counterexample, we disprove the conjecture stating that the unboundedness of the free energy implies the divergence of the message passing algorithm.

scholarly journals Cooperative Localization for Mobile Networks: A Distributed Belief Propagation–Mean Field Message Passing Algorithm

2016 ◽  
Vol 23 (6) ◽  
pp. 828-832 ◽  
Author(s):  
Burak Cakmak ◽  
Daniel N. Urup ◽  
Florian Meyer ◽  
Troels Pedersen ◽  
Bernard H. Fleury ◽  
...  
Keyword(s):  
Mobile Networks ◽  
Message Passing ◽  
Belief Propagation ◽  
Mean Field ◽  
Cooperative Localization ◽  
Message Passing Algorithm

SEMICLASSICAL SHELL STRUCTURE OF MOMENTS OF INERTIA IN DEFORMED FERMI SYSTEMS

2010 ◽  
Vol 19 (04) ◽  
pp. 735-746 ◽  
Author(s):  
A. G. MAGNER ◽  
A. M. GZHEBINSKY ◽  
A. S. SITDIKOV ◽  
A. A. KHAMZIN ◽  
J. BARTEL
Keyword(s):  
Free Energy ◽  
Shell Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Moment Of Inertia ◽  
Mean Field Approximation ◽  
Perfect Agreement ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
The Moment

The collective moment of inertia is derived analytically within the cranking model in the adiabatic mean-field approximation at finite temperature. Using the nonperturbative periodic-orbit theory the semiclassical shell-structure components of the collective moment of inertia are obtained for any potential well. Their relation to the free-energy shell corrections are found semiclassically as being given through the shell-structure components of the rigid-body moment of inertia of the statistically equilibrium rotation in terms of short periodic orbits. Shell effects in the moment of inertia disappear exponentially with increasing temperature. For the case of the harmonic-oscillator potential one observes a perfect agreement between semiclassical and quantum shell-structure components of the free energy and the moment of inertia for several critical bifurcation deformations and several temperatures.

scholarly journals Variational Message Passing and Local Constraint Manipulation in Factor Graphs

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 807
Author(s):  
İsmail Şenöz ◽  
Thijs van de Laar ◽  
Dmitry Bagaev ◽  
Bert de de Vries
Keyword(s):  
Free Energy ◽  
Latent Variables ◽  
Message Passing ◽  
Factor Graph ◽  
Estimation Accuracy ◽  
Attractive Alternative ◽  
Factor Graphs ◽  
Data Set ◽  
Bethe Free Energy ◽  
Model Evidence

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.

scholarly journals A Threshold-Based Max-log-MPA Low Complexity Multiuser Detection Algorithm

Sensors ◽  
2020 ◽  
Vol 20 (4) ◽  
pp. 1016
Author(s):  
Guanghua Zhang ◽  
Zonglin Gu ◽  
Qiannan Zhao ◽  
Jingqiu Ren ◽  
Weidang Lu
Keyword(s):  
Computational Complexity ◽  
Multiuser Detection ◽  
Message Passing ◽  
Multiple Access ◽  
Low Complexity ◽  
Detection Algorithm ◽  
Necessary Condition ◽  
Threshold Condition ◽  
Message Passing Algorithm ◽  
The Stability

Sparse Code Multiple Access (SCMA) technology is a new multiple access scheme based on non-orthogonal spread spectrum technology, which was proposed by Huawei in 2014. In the algorithm application of this technology, the original Message Passing Algorithm (MPA) has slow convergence speed and high algorithm complexity. The threshold-based MPA has a high Bit Error Ratio (BER) when the threshold is low. In the Maximum logarithm Message Passing Algorithm (Max-log-MPA), the approximation method is used, which will cause some messages to be lost and the detection performance to be poor. Therefore, in order to solve the above problems, a Threshold-Based Max-log-MPA (T-Max-log-MPA) low complexity multiuser detection algorithm is proposed in this paper. The Maximum logarithm (Max-log) algorithm is combined with threshold setting, and the stability of user nodes is considered as a necessary condition for decision in the algorithm. Before message updating, the user information nodes are judged whether the necessary conditions for the stability of the user node have been met, and then the threshold is determined. Only users who meet the threshold condition and pass the necessary condition of user node stability can be decoded in advance. In the whole process, the logarithm domain MPA algorithm is used to convert an exp operation and a multiplication operation into a maximum value and addition operation. The simulation results show that the proposed algorithm can effectively reduce the computational complexity while ensuring the BER, and with the increase of signal-to-noise ratio, the effect of the Computational Complexity Reduction Ratio (CCRR) is more obvious.

scholarly journals Chemically Interpretable Graph Interaction Network for Prediction of Pharmacokinetic Properties of Drug-Like Molecules

2020 ◽  
Vol 34 (01) ◽  
pp. 873-880 ◽  
Author(s):  
Yashaswi Pathak ◽  
Siddhartha Laghuvarapu ◽  
Sarvesh Mehta ◽  
U. Deva Priyakumar
Keyword(s):  
Neural Network ◽  
Free Energy ◽  
Message Passing ◽  
Solvation Free Energy ◽  
The Body ◽  
Free Energies ◽  
Pharmacokinetic Properties ◽  
Interaction Map ◽  
Solvent Molecules ◽  
Solvation Free Energies

Solubility of drug molecules is related to pharmacokinetic properties such as absorption and distribution, which affects the amount of drug that is available in the body for its action. Computational or experimental evaluation of solvation free energies of drug-like molecules/solute that quantify solubilities is an arduous task and hence development of reliable computationally tractable models is sought after in drug discovery tasks in pharmaceutical industry. Here, we report a novel method based on graph neural network to predict solvation free energies. Previous studies considered only the solute for solvation free energy prediction and ignored the nature of the solvent, limiting their practical applicability. The proposed model is an end-to-end framework comprising three phases namely, message passing, interaction and prediction phases. In the first phase, message passing neural network was used to compute inter-atomic interaction within both solute and solvent molecules represented as molecular graphs. In the interaction phase, features from the preceding step is used to calculate a solute-solvent interaction map, since the solvation free energy depends on how (un)favorable the solute and solvent molecules interact with each other. The calculated interaction map that captures the solute-solvent interactions along with the features from the message passing phase is used to predict the solvation free energies in the final phase. The model predicts solvation free energies involving a large number of solvents with high accuracy. We also show that the interaction map captures the electronic and steric factors that govern the solubility of drug-like molecules and hence is chemically interpretable.

scholarly journals Chemically Interpretable Graph Interaction Network for Prediction of Pharmacokinetic Properties of Drug-like Molecules

2019 ◽  
Author(s):  
Yashaswi Pathak ◽  
Siddhartha Laghuvarapu ◽  
Sarvesh Mehta ◽  
U. Deva Priyakumar
Keyword(s):  
Neural Network ◽  
Free Energy ◽  
Message Passing ◽  
Solvation Free Energy ◽  
The Body ◽  
Free Energies ◽  
Pharmacokinetic Properties ◽  
Interaction Map ◽  
Solvent Molecules ◽  
Solvation Free Energies

<div>Solubility of drug molecules is related to pharmacokinetic properties such as absorption and distribution, which affects the amount of drug that is available in the body for its action. Computational or experimental evaluation of solvation free energies of drug-like molecules/solute that quantify solubilities is an arduous task and hence development of reliable computationally tractable models is sought after in drug discovery tasks in pharmaceutical industry. Here, we report a novel method based on graph neural network to predict solvation free energies. Previous studies considered only the solute for solvation free energy prediction and ignored the nature of the solvent, limiting their practical applicability. The proposed model is an end-to-end framework comprising three phases namely, message passing, interaction and prediction phases. In the first phase, message passing neural network was used to compute inter-atomic interaction within both solute and solvent molecules represented as molecular graphs. In the interaction phase, features from the preceding step is used to calculate a solute-solvent interaction map, since the solvation free energy depends on how (un)favorable the solute and solvent molecules interact with each other. The calculated interaction map that captures the solute-solvent interactions along with the features from the message passing phase is used to predict the solvation free energies in the final phase. The model predicts solvation free energies involving a large number of solvents within the limits of chemical accuracy. We also show that the interaction map captures the electronic and steric factors that govern the solubility of drug-like molecules and hence is chemically interpretable.</div>

scholarly journals Chemically Interpretable Graph Interaction Network for Prediction of Pharmacokinetic Properties of Drug-like Molecules

2019 ◽  
Author(s):  
Yashaswi Pathak ◽  
Siddhartha Laghuvarapu ◽  
Sarvesh Mehta ◽  
U. Deva Priyakumar
Keyword(s):  
Neural Network ◽  
Free Energy ◽  
Message Passing ◽  
Solvation Free Energy ◽  
The Body ◽  
Free Energies ◽  
Pharmacokinetic Properties ◽  
Interaction Map ◽  
Solvent Molecules ◽  
Solvation Free Energies

<div>Solubility of drug molecules is related to pharmacokinetic properties such as absorption and distribution, which affects the amount of drug that is available in the body for its action. Computational or experimental evaluation of solvation free energies of drug-like molecules/solute that quantify solubilities is an arduous task and hence development of reliable computationally tractable models is sought after in drug discovery tasks in pharmaceutical industry. Here, we report a novel method based on graph neural network to predict solvation free energies. Previous studies considered only the solute for solvation free energy prediction and ignored the nature of the solvent, limiting their practical applicability. The proposed model is an end-to-end framework comprising three phases namely, message passing, interaction and prediction phases. In the first phase, message passing neural network was used to compute inter-atomic interaction within both solute and solvent molecules represented as molecular graphs. In the interaction phase, features from the preceding step is used to calculate a solute-solvent interaction map, since the solvation free energy depends on how (un)favorable the solute and solvent molecules interact with each other. The calculated interaction map that captures the solute-solvent interactions along with the features from the message passing phase is used to predict the solvation free energies in the final phase. The model predicts solvation free energies involving a large number of solvents within the limits of chemical accuracy. We also show that the interaction map captures the electronic and steric factors that govern the solubility of drug-like molecules and hence is chemically interpretable.</div>

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