1. A speech recognition apparatus comprising: a first storing unit configured to store a first acoustic model invariable regardless of speaker and environment; a second storing unit configured to store second acoustic models that vary in accordance with at least either one of a specific speaker and a specific environment; a third storing unit configured to store a classification model that has shared parameters with the first acoustic model and non-shared parameters with the first acoustic model to classify the second acoustic models into different groups; a first recognizing unit configured to calculate a first likelihood with regard to the input speech by applying the first acoustic model to the input speech and obtain calculation result on the shared parameter and a plurality of candidate words that have relatively large values as the first likelihood; a calculating unit configured to calculate a second likelihood for each of the groups with regard to the input speech by use of the calculation result on the shared parameters and the non-shared parameters of the classification model; a selecting unit configured to select a group that has a largest value for the second likelihood from among the groups; and a second recognizing unit configured to recognize the input speech by applying a second acoustic model that belongs to the selected group onto the input speech to calculate a third likelihood for each of the candidate words and obtain as the recognition result a candidate word that has a largest value as the third likelihood, wherein: the first acoustic model and the classification model are hidden Markov models that have, as output probability distributions, mixed normal distributions in which a plurality of normal distributions are weighted in accordance with weighting factors and combined together, the shared parameters include a shared mean vector and a shared variance-covariance matrix to calculate a shared output probability distribution which is one of the output probability distributions of the classification model, the calculating unit obtains a first normal distribution as the calculation result from the first speech recognizing unit, multiplies the first normal distribution by a weighting factor to calculate the shared output probability distribution, calculates a second normal distribution by use of a non-shared mean vector and a non-shared variance-covariance matrix contained in the non-shared parameters and a feature of the input speech, multiplies the second normal distribution by a weighting factor to calculate a non-shared output probability distribution, and multiplies the shared output probability distribution and the non-shared output distribution by state transition probabilities to obtain the second likelihood, and the first normal distribution is calculated by use of the feature of the input speech, the shared mean vector and the shared variance-covariance matrix.