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Universal schemes for learning the best nonlinear predictor given the infinite past and side information

机译:给定无限的过去和附带信息,用于学习最佳非线性预测变量的通用方案

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摘要

Let {X/sub t/} be a real-valued time series. The best nonlinear predictor of X/sub 0/ given the infinite past X/sub -/spl infin///sup -1/ in the least squares sense, is equal to the conditional mean E{X/sub 0/|X/sub -/spl infin///sup -1/}. Previously, it has been shown that certain predictors based on growing segments of past observations converge to the best predictor given the infinite past whenever {X/sub t/} is a stationary process with values in a bounded interval. The present paper deals with universal prediction schemes for stationary processes with finite mean. We also discuss universal schemes for learning the conditional mean E{X/sub 0/|X/sub -/spl infin///sup -1/Y/sub -/spl infin///sup -1/Y/sub 0/} from past observations of a stationary pair process {(X/sub t/, Y/sub t/)}, and schemes for learning the repression function m(y)=E{X|Y=y} from independent samples of (X, Y).
机译:令{X / sub t /}为实值时间序列。在最小二乘意义上,给定无限过去的X / sub-/ spl infin /// sup -1 /,则X / sub 0 /的最佳非线性预测值等于条件均值E {X / sub 0 / | X / sub-/ spl infin /// sup -1 /}。以前,已经证明,只要{X / sub t /}是一个固定值范围内的固定过程,基于过去观察的增长部分的某些预测变量就会收敛到最佳预测变量。本文讨论了具有有限均值的平稳过程的通用预测方案。我们还将讨论用于学习条件均值E {X / sub 0 / | X / sub-/ spl infin /// sup -1 / Y / sub-/ spl infin /// sup -1 / Y / sub 0的通用方案/}来自固定对过程{(X / sub t /,Y / sub t /)}的以往观察,以及用于从以下项的独立样本中学习抑制函数m(y)= E {X | Y = y}的方案(X,Y)。

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