A sieve stochastic gradient descent estimator for online nonparametric regression in Sobolev ellipsoids
提出一种筛子随机梯度下降估计量，用于在线非参数回归，在Sobolev椭球假设空间下达到最优均方误差，且计算和内存成本极低。
The goal of regression is to recover an unknown underlying function that best links a set of predictors to an outcome from noisy observations. in nonparametric regression, one assumes that the regression function belongs to a pre-specified infinite-dimensional function space (the hypothesis space). in the online setting, when the observations come in a stream, it is computationally-preferable to iteratively update an estimate rather than refitting an entire model repeatedly. inspired by nonparametric sieve estimation and stochastic approximation methods, we propose a sieve stochastic gradient descent estimator (Sieve-SGD) when the hypothesis space is a Sobolev ellipsoid. We show that Sieve-SGD has rate-optimal mean squared error (MSE) under a set of simple and direct conditions. The proposed estimator can be constructed with a low computational (time and space) expense: We also formally show that Sieve-SGD requires almost minimal memory usage among all statistically rate-optimal estimators.