KNN Ensembles for Tweedie Regression: The Power of Multiscale Neighborhoods
This work addresses the problem of improving regression accuracy for researchers and practitioners in machine learning, though it is incremental as it builds on existing KNN and ensemble techniques.
The paper tackles the lack of KNN ensembles by exploring seven algorithms that combine bagged features, bagged observations, and varied k, tested on Tweedie regression problems. Results show that varying k improves prediction beyond bagging, with KNN ensembles performing favorably against state-of-the-art methods and dramatically outperforming standard KNN regression.
Very few K-nearest-neighbor (KNN) ensembles exist, despite the efficacy of this approach in regression, classification, and outlier detection. Those that do exist focus on bagging features, rather than varying k or bagging observations; it is unknown whether varying k or bagging observations can improve prediction. Given recent studies from topological data analysis, varying k may function like multiscale topological methods, providing stability and better prediction, as well as increased ensemble diversity. This paper explores 7 KNN ensemble algorithms combining bagged features, bagged observations, and varied k to understand how each of these contribute to model fit. Specifically, these algorithms are tested on Tweedie regression problems through simulations and 6 real datasets; results are compared to state-of-the-art machine learning models including extreme learning machines, random forest, boosted regression, and Morse-Smale regression. Results on simulations suggest gains from varying k above and beyond bagging features or samples, as well as the robustness of KNN ensembles to the curse of dimensionality. KNN regression ensembles perform favorably against state-of-the-art algorithms and dramatically improve performance over KNN regression. Further, real dataset results suggest varying k is a good strategy in general (particularly for difficult Tweedie regression problems) and that KNN regression ensembles often outperform state-of-the-art methods. These results for k-varying ensembles echo recent theoretical results in topological data analysis, where multidimensional filter functions and multiscale coverings provide stability and performance gains over single-dimensional filters and single-scale covering. This opens up the possibility of leveraging multiscale neighborhoods and multiple measures of local geometry in ensemble methods.