81,568 research outputs found
Bayesian optimization for computationally extensive probability distributions
An efficient method for finding a better maximizer of computationally
extensive probability distributions is proposed on the basis of a Bayesian
optimization technique. A key idea of the proposed method is to use extreme
values of acquisition functions by Gaussian processes for the next training
phase, which should be located near a local maximum or a global maximum of the
probability distribution. Our Bayesian optimization technique is applied to the
posterior distribution in the effective physical model estimation, which is a
computationally extensive probability distribution. Even when the number of
sampling points on the posterior distributions is fixed to be small, the
Bayesian optimization provides a better maximizer of the posterior
distributions in comparison to those by the random search method, the steepest
descent method, or the Monte Carlo method. Furthermore, the Bayesian
optimization improves the results efficiently by combining the steepest descent
method and thus it is a powerful tool to search for a better maximizer of
computationally extensive probability distributions.Comment: 13 pages, 5 figure
A Dynamics Driven by Repeated Harmonic Perturbations
We propose an exactly soluble W*-dynamical system generated by repeated
harmonic perturbations of the one-mode quantum oscillator. In the present paper
we deal with the case of isolated system. Although dynamics is Hamiltonian and
quasi-free, it produces relaxation of initial state of the system to the steady
state in the large-time limit. The relaxation is accompanied by the entropy
production and we found explicitly the rate for it. Besides, we study evolution
of subsystems to elucidate their eventual correlations and convergence to
equilibrium state. Finally we prove a universality of the dynamics driven by
repeated harmonic perturbations in a certain short-time interaction limit
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