Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a non-stationary spatial environment collects and analyzes data. The stochastic model especially allows for spatial heterogeneity and weak dependence. As efficient and computationally cheap learning methods (unconstrained) least squares, ridge regression and $\ell_s$-penalized least squares (including the LASSO) are studied. Consistency and asymptotic normality of the least squares and ridge regression estimates as well as corresponding consistency results for the $\ell_s$-penalty are shown under weak conditions. The resuts also cover bounds for the sample squared predicition error.

翻译：在非静止空间时空抽样设计下,对随机重量的神经网络进行了研究,特别针对在非静止空间环境中移动的自主物体收集和分析数据的设置。这种随机模型特别允许空间异质性和依赖性弱。作为高效和计算成本低廉的学习方法(不受限制的)最小方块、山脊回归和以美元计酬的最低方块(包括LASSO),还研究了最小方块和山脊回归估计的恒定性和失常性,以及美元/ell_s$-penal 的相应一致性结果,在薄弱的条件下展示。这些Resut也覆盖了样本方形前置误差的界限。