We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a direc...We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.展开更多
The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large r...The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square(rms)deviations from data,i.e.,0.949μN and 1.272μN for odd-neutron nuclei and odd-proton nuclei,respectively.By including the dependence of the nuclear spin and Schmidt magnetic moment,the machine-learning approach precisely describes the magnetic moments of odd-A uclei with rms deviations of 0.036μN for odd-neutron nuclei and 0.061μN for odd-proton nuclei.Furthermore,the evolution of magnetic moments along isotopic chains,including the staggering and sudden jump trend,which are difficult to describe using nuclear models,have been well reproduced by the Bayesian neural network(BNN)approach.The magnetic moments of doubly closed-shell±1 nuclei,for example,isoscalar and isovector magnetic moments,have been well studied and compared with the corresponding non-relativistic and relativistic calculations.展开更多
Extensional approach vs. intensional approach is taxonomy of tackling uncertainty. In this paper,we compare these two approaches. Extensional systems are computational convenient but semantically sloppy,while intensio...Extensional approach vs. intensional approach is taxonomy of tackling uncertainty. In this paper,we compare these two approaches. Extensional systems are computational convenient but semantically sloppy,while intensional systems are semantically clear but computational clumsy. The trade-off between sematic clarity and computational efficiency has been the main issue of concern.展开更多
文摘We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.
基金Supported by the National Natural Science Foundation of China(11675063,11875070,11205068)the Open fund for Discipline Construction,Institute of Physical Science and Information Technology,Anhui University。
文摘The Bayesian neural network approach has been employed to improve the nuclear magnetic moment predictions of odd-A nuclei.The Schmidt magnetic moment obtained from the extreme single-particle shell model makes large root-mean-square(rms)deviations from data,i.e.,0.949μN and 1.272μN for odd-neutron nuclei and odd-proton nuclei,respectively.By including the dependence of the nuclear spin and Schmidt magnetic moment,the machine-learning approach precisely describes the magnetic moments of odd-A uclei with rms deviations of 0.036μN for odd-neutron nuclei and 0.061μN for odd-proton nuclei.Furthermore,the evolution of magnetic moments along isotopic chains,including the staggering and sudden jump trend,which are difficult to describe using nuclear models,have been well reproduced by the Bayesian neural network(BNN)approach.The magnetic moments of doubly closed-shell±1 nuclei,for example,isoscalar and isovector magnetic moments,have been well studied and compared with the corresponding non-relativistic and relativistic calculations.
文摘Extensional approach vs. intensional approach is taxonomy of tackling uncertainty. In this paper,we compare these two approaches. Extensional systems are computational convenient but semantically sloppy,while intensional systems are semantically clear but computational clumsy. The trade-off between sematic clarity and computational efficiency has been the main issue of concern.
