Sparse Density Estimation on the Multinomial Manifold

Xia Hong

doi:10.1109/TNNLS.2015.2389273

Sparse Density Estimation on the Multinomial Manifold

2015-11-01

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DOI：10.1109/TNNLS.2015.2389273

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Abstract

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A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first-and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

Keywords:

Minimum integrated square error (MISE)

multinomial manifold

probability density function (pdf)

sparse modeling

Sparse Density Estimation on the Multinomial Manifold

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