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We investigate boosted online regression and propose a novel family ofregression algorithms with strong theoretical bounds. In addition, we implementseveral variants of the proposed generic algorithm. We specifically providetheoretical bounds for the performance of our proposed algorithms that hold ina strong mathematical sense. We achieve guaranteed performance improvement overthe conventional online regression methods without any statistical assumptionson the desired data or feature vectors. We demonstrate an intrinsicrelationship, in terms of boosting, between the adaptive mixture-of-experts anddata reuse algorithms. Furthermore, we introduce a boosting algorithm based onrandom updates that is significantly faster than the conventional boostingmethods and other variants of our proposed algorithms while achieving anenhanced performance gain. Hence, the random updates method is specificallyapplicable to the fast and high dimensional streaming data. Specifically, weinvestigate Newton Method-based and Stochastic Gradient Descent-based linearregression algorithms in a mixture-of-experts setting and provide severalvariants of these well-known adaptation methods. However, the proposedalgorithms can be extended to other base learners, e.g., nonlinear, tree-basedpiecewise linear. Furthermore, we provide theoretical bounds for thecomputational complexity of our proposed algorithms. We demonstrate substantialperformance gains in terms of mean square error over the base learners throughan extensive set of benchmark real data sets and simulated examples.

A Novel Family of Boosted Online Regression Algorithms with Strong Theoretical Bounds