1. A system, comprising: a discriminant identification device that includes a processor configured to: specify a discriminant function by machine learning using learning data and a learning input parameter, the discriminant function being for separating a distribution of a genuine similarity from a distribution of impostor similarity, the learning input parameter indicating a degree of the discriminant function and being set before executing the machine learning, set a plurality of discriminant functions, each of the plurality of discriminant functions being obtained by changing values of the learning input parameter and a learning output parameter, the learning output parameter being a parameter indicating a coefficient of the calculated discriminant function, acquire an error rate for each of the plurality of discriminant functions; and extract one discriminant function among the plurality of discriminant functions, the one discriminant function having the error rate which meets a predetermined error condition; and a biometric identification device coupled to the discriminant identification device and configured to perform biometric authentication using the extracted discriminant function.