As a problem in data science the inverse Ising(or Potts)problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising(or Potts)model from samples drawn from that distribution.The algorithmic and co...As a problem in data science the inverse Ising(or Potts)problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising(or Potts)model from samples drawn from that distribution.The algorithmic and computational interest stems from the fact that this inference task cannot be carried out efficiently by the maximum likelihood criterion,since the normalizing constant of the distribution(the partition function)cannot be calculated exactly and efficiently.The practical interest on the other hand flows from several outstanding applications,of which the most well known has been predicting spatial contacts in protein structures from tables of homologous protein sequences.Most applications to date have been to data that has been produced by a dynamical process which,as far as it is known,cannot be expected to satisfy detailed balance.There is therefore no a priori reason to expect the distribution to be of the Gibbs-Boltzmann type,and no a priori reason to expect that inverse Ising(or Potts)techniques should yield useful information.In this review we discuss two types of problems where progress nevertheless can be made.We find that depending on model parameters there are phases where,in fact,the distribution is close to Gibbs-Boltzmann distribution,a non-equilibrium nature of the under-lying dynamics notwithstanding.We also discuss the relation between inferred Ising model parameters and parameters of the underlying dynamics.展开更多
基金the National Natural Science Foundation of China(Grant No.11705097)the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20170895)+1 种基金the Jiangsu Government Scholarship for Overseas Studies of 2018 and Scientific Research Foundation of Nanjing University of Posts and Telecommunications,China(Grant No.NY217013)the Foundation for Polish Science through TEAM-NET Project(Grant No.POIR.04.04.00-00-17C1/18-00).
文摘As a problem in data science the inverse Ising(or Potts)problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising(or Potts)model from samples drawn from that distribution.The algorithmic and computational interest stems from the fact that this inference task cannot be carried out efficiently by the maximum likelihood criterion,since the normalizing constant of the distribution(the partition function)cannot be calculated exactly and efficiently.The practical interest on the other hand flows from several outstanding applications,of which the most well known has been predicting spatial contacts in protein structures from tables of homologous protein sequences.Most applications to date have been to data that has been produced by a dynamical process which,as far as it is known,cannot be expected to satisfy detailed balance.There is therefore no a priori reason to expect the distribution to be of the Gibbs-Boltzmann type,and no a priori reason to expect that inverse Ising(or Potts)techniques should yield useful information.In this review we discuss two types of problems where progress nevertheless can be made.We find that depending on model parameters there are phases where,in fact,the distribution is close to Gibbs-Boltzmann distribution,a non-equilibrium nature of the under-lying dynamics notwithstanding.We also discuss the relation between inferred Ising model parameters and parameters of the underlying dynamics.
