Mean field bound and GHS inequality

1984 ◽  
Vol 35 (1-2) ◽  
pp. 99-107 ◽  
Author(s):  
Hal Tasaki ◽  
Takashi Hara
Keyword(s):  
Mean Field ◽  
Ghs Inequality ◽  
Mean Field Bound

scholarly journals A Tighter Bound for Graphical Models

2001 ◽  
Vol 13 (9) ◽  
pp. 2149-2171 ◽  
Author(s):  
M. A. R. Leisink ◽  
H. J. Kappen
Keyword(s):  
Graphical Models ◽  
Mean Field ◽  
Third Order ◽  
First Order ◽  
Direct Extension ◽  
Odd Order ◽  
Order Polynomial ◽  
The Mean ◽  
Mean Field Bound ◽  
Better Than

We present a method to bound the partition function of a Boltzmann machine neural network with any odd-order polynomial. This is a direct extension of the mean-field bound, which is first order. We show that the third-order bound is strictly better than mean field. Additionally, we derive a third-order bound for the likelihood of sigmoid belief networks. Numerical experiments indicate that an error reduction of a factor of two is easily reached in the region where expansion-based approximations are useful.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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