Linear program differentiation for single-channel speech separation

Barak A. Pearlmutter, Rasmus Kongsgaard Olsson

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver. For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single-channel speech separation task, leading to 5 dB and 8 dB target-to-interference ratio improvements for same-gender and opposite-gender mixtures, respectively. Furthermore, the dictionaries are successfully applied to a speaker identification task.
    Original languageEnglish
    Title of host publicationIEEE International Workshop on Machine Learning for Signal Processing
    PublisherIEEE
    Publication date2006
    ISBN (Print)1-4244-0656-0
    DOIs
    Publication statusPublished - 2006
    Event16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing -
    Duration: 1 Jan 2006 → …

    Conference

    Conference16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing
    Period01/01/2006 → …

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