Density Estimation Through Convex Combinations of Densities: Approximation and Estimation Bounds Export

@article{citeulike:311335, abstract = {We consider the problem of estimating a density function from a sequence identically distributed observations xi taking value in X [subset of] d. The estimation procedure constructs a convex mixture of "basis" densities and estimates the parameters using the maximum likelihood method. Viewing the error as a combination of two terms, the approximation error measuring the adequacy of the model, and the estimation error resulting from the finiteness of the sample size, we derive upper bounds to the expected total error, thus obtaining bounds for the rate of convergence. These results then allow us to derive explicit expressions relating the sample complexity and model complexity. Copyright (c) 1996 Elsevier Science Ltd.}, author = {Zeevi, Assaf J. and Meir, Ronny}, citeulike-article-id = {311335}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/S0893-6080(96)00037-8}, citeulike-linkout-1 = {http://www.sciencedirect.com/science/article/B6T08-3TDPYNM-2R/2/62c5d9899f74161b1ed8a50b86bdbe55}, citeulike-linkout-2 = {http://www.cs.orst.edu/~bulatov/papers/zeevi-density.ps}, comment = {Gives expression for best number of parameters (mixture components) in terms of sample size (and a constant depending on true distribution/basis used)}, doi = {10.1016/S0893-6080(96)00037-8}, journal = {Neural Networks}, keywords = {density}, month = {January}, number = {1}, pages = {99--109}, posted-at = {2005-09-04 05:20:05}, priority = {2}, title = {Density Estimation Through Convex Combinations of Densities: Approximation and Estimation Bounds}, url = {http://dx.doi.org/10.1016/S0893-6080(96)00037-8}, volume = {10}, year = {1997} }

TY - JOUR ID - citeulike:311335 L3 - citeulike-article-id:311335 N2 - We consider the problem of estimating a density function from a sequence identically distributed observations xi taking value in X [subset of] d. The estimation procedure constructs a convex mixture of "basis" densities and estimates the parameters using the maximum likelihood method. Viewing the error as a combination of two terms, the approximation error measuring the adequacy of the model, and the estimation error resulting from the finiteness of the sample size, we derive upper bounds to the expected total error, thus obtaining bounds for the rate of convergence. These results then allow us to derive explicit expressions relating the sample complexity and model complexity. Copyright (c) 1996 Elsevier Science Ltd. IS - 1 JF - Neural Networks EP - 109 TI - Density Estimation Through Convex Combinations of Densities: Approximation and Estimation Bounds VL - 10 SP - 99 KW - density N1 - Gives expression for best number of parameters (mixture components) in terms of sample size (and a constant depending on true distribution/basis used) AU - Zeevi, Assaf AU - Meir, Ronny PY - 1997/01// UR - http://dx.doi.org/10.1016/S0893-6080(96)00037-8 ER -