1. A speech recognition system comprising: acoustic analysis means for acoustically analyzing input speech and calculating feature vectors; a calculating section for calculating, based on the feature vectors, output values of adaptive discriminant functions in relation to the feature vectors by using the adaptive discriminant functions having adaptive discriminant function parameters that are transformed to be adapted to the state of the variation of the factors that affect the input speech; a determining section for determining a speech recognition result based on a calculation result of said calculating section, wherein the adaptive discriminant function parameters are obtained by applying to adaptation functions, universal discriminant function parameters, which are independent of a state of the variation of the factors, and adaptation parameters for the recognition, and wherein the adaptation parameters for the recognition maximizes a probabilistic likelihood of the adaptive discriminate function parameters in relation to adaptation learning speech signal samples for the recognition under the state of the variation of the factors, the universal discriminant function parameters being obtained by a learning method which comprises: determining, under the condition of using the adaptation functions, adaptation parameters for learning the probabilistic likelihood in relation to learning samples under the state of the variation of a plurality of factors without changing determined universal discriminant function parameters; determining, based on the probabilistic likelihood, universal discriminant function parameters in relation to the learning without changing the determined adaptation parameters for learning; judging, in a process of alternately performing said determining operations repeatedly, whether said learning method is to be discontinued; and using the obtained universal discriminant function parameters as trained values in a case where said learning method is discontinued after performing said judging operations.