We present an algorithm for high dimensional density estimation which is efficient (both computationally and statistically) when the distribution is concentrated close to a low dimensional smooth manifold. The algorithm uses several random projections to generate a hierarchical mixture of Gaussians which rapidly converges to the underlying manifold. We use this algorithm to perform robust estimation of the time delays in an ad-hoc microphone network. We utilize the model to calculate accurate time-delay vectors for two speakers that are talking at the same time.
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