Pearlmutter, Barak A. and Olsson, Rasmus K.
Linear program differentiation for single-channel speech separation.
In: Proceedings of the 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing, 6th - 8th September, 2006, Arlington, VA .
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.
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||Differentiation; Gradient methods; Linear programming; Matrix algebra; Signal representation; Speaker recognition; Constraint matrix; Gradient optimisation; Linear program differentiation; Linear programming; Signal processing; Single-channel speech separation; Sparse representation; Speaker identification task.
||Science & Engineering > Computer Science
Dr. Barak Pearlmutter
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