A link between cepstral shrinking and the weighted product rule in audio-visual speech recognition

The weighted product rule has been shown empirically to be of great benefit in audio-visual speech recognition (AVSR), for isolated word recognition tasks. A firm theoretical basis for the selection of effective weights is of considerable interest to the audio-visual speech processing community. In this paper a clear link is established between the selection of effective weightings and the approximately isotropic shrinkage that the distribution of acoustic cepstral features undergo in the presence of additive noise. An elucidation of the theoretical relationship between the cepstral shrinkage and the variance of the HMM audio log-likelihoods is then explored.