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Supervised learning by extreme learning machines resp. neural networks withrandom weights is studied under a non-stationary spatial-temporal samplingdesign which especially addresses settings where an autonomous object moving ina non-stationary spatial environment collects and analyzes data. The stochasticmodel especially allows for spatial heterogeneity and weak dependence. Asefficient and computationally cheap learning methods (unconstrained) leastsquares, ridge regression and $\ell_s$-penalized least squares (including theLASSO) are studied. Consistency and asymptotic normality of the least squaresand ridge regression estimates as well as corresponding consistency results forthe $\ell_s$-penalty are shown under weak conditions. The results also coverbounds for the sample squared predicition error.

Consistency of Extreme Learning Machines and Regression under Non-Stationarity and Dependence for ML-Enhanced Moving Objects