The best-perfoming methodology at the time of writing (2018) replies on ‘Deep’ neural nets. There are many variations in a rapidly-developing technology: see
·Andrew Senior of DeepMind London gave a talk at Oxford in 2017, covering ‘the history of ASR models, from Gaussian Mixtures to attention augmented RNNs, the basic linguistics of speech, and the various input and output representations frequently employed.’
·Alex Acero of Apple spoke on ‘Deep Learning in Speech Recognition’ at Stanford, November 2017 : ‘In this talk I will give an introduction to speech recognition, go over the fundamentals of deep learning, explained what it took for the speech recognition field to adopt deep learning, and how that has been contributed to popularize personal assistants like Siri.’