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We develop an elementary mean field approach for fully asymmetric kineticIsing models, which can be applied to a single instance of the problem. In thecase of the asymmetric SK model this method gives the exact values of the localmagnetizations and the exact relation between equal-time and time-delayedcorrelations. It can also be used to solve efficiently the inverse problem,i.e. determine the couplings and local fields from a set of patterns, also incases where the fields and couplings are time-dependent. This approachgeneralizes some recent attempts to solve this dynamical inference problem,which were valid in the limit of weak coupling. It provides the exact solutionto the problem also in strongly coupled problems. This mean field inference canalso be used as an efficient approximate method to infer the couplings andfields in problems which are not infinite range, for instance in dilutedasymmetric spin glasses.

Exact mean field inference in asymmetric kinetic Ising systems