A Generative Product-of-Filters Model of Audio
Authors: Dawen Liang, Mathew D. Hoffman, Gautham Mysore
ICLR 2014

Abstract: We propose the product-of-filters (PoF) model, a generative model that decomposes audio spectra as sparse linear combinations of 'filters' in the log-spectral domain. PoF makes similar assumptions to those used in the classic homomorphic filtering approach to signal processing, but replaces hand-designed decompositions built of basic signal processing operations with a learned decomposition based on statistical inference. This paper formulates the PoF model and derives a mean-field method for posterior inference and a variational EM algorithm to estimate the model's free parameters. We demonstrate PoF's potential for audio processing on a bandwidth expansion task, and show that PoF can serve as an effective unsupervised feature extractor for a speaker identification task.


Peer review:
[Review]:
Very interesting, well written paper describing a novel model for explaining speech using a set of filters trained in a generative fashion. The paper describes a “product of filters” model, proposes a mean-field method for posterior inference and a variational EM algorithm to estimate the model’s free parameters. The paper draws parallels with the proposed approach and homomorphic filtering methods, NMF and its variants for speech analysis.

The paper however does not have a comprehensive experimental framework to evaluate the usefulness of the proposed model. Bandwidth expansion is a natural candidate for generative models and is an example used with similar techniques in vision - for example the recently proposed sum-product networks [Poon and Domingos, 2011]. The gains using the proposed model are however not very significant. 

Although the authors do state that they are not attempting to build a state-of-art speaker identification system, the experiment is nevertheless performed in a limited setting. It is hence not possible to completely evaluate the usefulness of features derived using the proposed technique. Can the features derived using the proposed framework generalize to be useful for more realistic speaker identification experiments? Do they generalize well? A natural additional question to ask would be – are these features useful in recognizing speech sounds since this is a generative model of speech? Can phoneme recognition experiments be performed using TIMIT using the derived features? Do the learnt bases represent classes of sound?