3 research outputs found
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Sparse density estimation on the multinomial manifold
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
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Sparse density estimator with tunable kernels
A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators