Disclosed herein are systems, methods, and non-transitory computer-readable storage media for generating an acoustic model for use in speech recognition. A system configured to practice the method first receives training data and identifies non-contextual lexical-level features in the training data. Then the system infers sentence-level features from the training data and generates a set of decision trees by node-splitting based on the non-contextual lexical-level features and the sentence-level features. The system decorrelates training vectors, based on the training data, for each decision tree in the set of decision trees to approximate full-covariance Gaussian models, and then can train an acoustic model for use in speech recognition based on the training data, the set of decision trees, and the training vectors.