This paper proposes a model for learning non-parametric densities using finite-dimensional parametric densities by applying Yamanishi's stochastic analogue of Valiant's probably approximately correct learning model to density estimation. The goal of our learning model is to find, with high probability, a good parametric approximation of the non-parametric target density with sample size and computation time polynomial in parameters of interest. We use a learning algorithm based on the minimum description length (MDL) principle and derive a new general upper bound on the rate of convergence of the MDL estimator to a true non-parametric density. On the basis of this result, we demonstrate polynomial-sample-size learnability of classes of non-parametric densities (defined under some smoothness conditions) in terms of exponential families with polynomial bases, and we prove that under some appropriate conditions, the sample complexity of learning them is bounded as O((1/ε)(2r
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Kenji YAMANISHI, "Learning Non-parametric Densities in terms of Finite-Dimensional Parametric Hypotheses" in IEICE TRANSACTIONS on Information,
vol. E75-D, no. 4, pp. 459-469, July 1992, doi: .
Abstract: This paper proposes a model for learning non-parametric densities using finite-dimensional parametric densities by applying Yamanishi's stochastic analogue of Valiant's probably approximately correct learning model to density estimation. The goal of our learning model is to find, with high probability, a good parametric approximation of the non-parametric target density with sample size and computation time polynomial in parameters of interest. We use a learning algorithm based on the minimum description length (MDL) principle and derive a new general upper bound on the rate of convergence of the MDL estimator to a true non-parametric density. On the basis of this result, we demonstrate polynomial-sample-size learnability of classes of non-parametric densities (defined under some smoothness conditions) in terms of exponential families with polynomial bases, and we prove that under some appropriate conditions, the sample complexity of learning them is bounded as O((1/ε)(2r
URL: https://global.ieice.org/en_transactions/information/10.1587/e75-d_4_459/_p
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@ARTICLE{e75-d_4_459,
author={Kenji YAMANISHI, },
journal={IEICE TRANSACTIONS on Information},
title={Learning Non-parametric Densities in terms of Finite-Dimensional Parametric Hypotheses},
year={1992},
volume={E75-D},
number={4},
pages={459-469},
abstract={This paper proposes a model for learning non-parametric densities using finite-dimensional parametric densities by applying Yamanishi's stochastic analogue of Valiant's probably approximately correct learning model to density estimation. The goal of our learning model is to find, with high probability, a good parametric approximation of the non-parametric target density with sample size and computation time polynomial in parameters of interest. We use a learning algorithm based on the minimum description length (MDL) principle and derive a new general upper bound on the rate of convergence of the MDL estimator to a true non-parametric density. On the basis of this result, we demonstrate polynomial-sample-size learnability of classes of non-parametric densities (defined under some smoothness conditions) in terms of exponential families with polynomial bases, and we prove that under some appropriate conditions, the sample complexity of learning them is bounded as O((1/ε)(2r
keywords={},
doi={},
ISSN={},
month={July},}
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TY - JOUR
TI - Learning Non-parametric Densities in terms of Finite-Dimensional Parametric Hypotheses
T2 - IEICE TRANSACTIONS on Information
SP - 459
EP - 469
AU - Kenji YAMANISHI
PY - 1992
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E75-D
IS - 4
JA - IEICE TRANSACTIONS on Information
Y1 - July 1992
AB - This paper proposes a model for learning non-parametric densities using finite-dimensional parametric densities by applying Yamanishi's stochastic analogue of Valiant's probably approximately correct learning model to density estimation. The goal of our learning model is to find, with high probability, a good parametric approximation of the non-parametric target density with sample size and computation time polynomial in parameters of interest. We use a learning algorithm based on the minimum description length (MDL) principle and derive a new general upper bound on the rate of convergence of the MDL estimator to a true non-parametric density. On the basis of this result, we demonstrate polynomial-sample-size learnability of classes of non-parametric densities (defined under some smoothness conditions) in terms of exponential families with polynomial bases, and we prove that under some appropriate conditions, the sample complexity of learning them is bounded as O((1/ε)(2r
ER -