This paper establishes that a class of $ N $-player stochastic games with singular controls, either bounded velocity or finite variation, can both be approximated by mean field (MFGs) controls velocity. More specifically, it shows (i) the optimal control to an MFG \theta is shown \epsilon_N $-NE game velocity, = O(\frac{1}{\sqrt{N}}) $, and (ii) this (\epsilon_N + \epsilon_{\theta}) where \epsi...

We describe a new approach for estimating the posterior probability of tissue labels. Conventional likelihood models are combined with a curve length prior on boundaries, and an approximate posterior distribution on labels is sought via the Mean Field approach. Optimizing the resulting estimator by gradient descent leads to a level set style algorithm where the level set functions are the logar...

In singular statistical models, it was shown that Bayes learning is effective. However, on Bayes learning, calculation containing the Bayes posterior distribution requires huge computational costs. To overcome the problem, mean field approximation (or equally variational Bayes method) was proposed. Recently, the generalization error and stochastic complexity in mean field approximation have bee...