Inference of interactions between players based on asynchronously updated evolutionary game data

The interactions between players of the prisoner's dilemma game are inferred using observed game data.All participants play the game with their counterparts and gain corresponding rewards during each round of the game.The strategies of each player are updated asynchronously during the game.Two inference methods of the interactions between players are derived with naive mean-field(n MF)approximation and maximum log-likelihood estimation(MLE),respectively.Two methods are tested numerically also for fully connected asymmetric Sherrington-Kirkpatrick models,varying the data length,asymmetric degree,payoff,and system noise(coupling strength).We find that the mean square error of reconstruction for the MLE method is inversely proportional to the data length and typically half(benefit from the extra information of update times)of that by n MF.Both methods are robust to the asymmetric degree but work better for large payoffs.Compared with MLE,n MF is more sensitive to the strength of couplings and prefers weak couplings.

Inverse Ising techniques to infer underlying mechanisms from data

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.