Improving the Aggregating Algorithm for Regression

S. Busuttil, Y. Kalnishkan, and A. Gammerman (UK)


Machine Learning, Regression, Least Squares, Kernels


Kernel Ridge Regression (KRR) and the recently de veloped Kernel Aggregating Algorithm for Regression (KAAR) are regression methods based on Least Squares. KAAR has theoretical advantages over KRR since a bound on its square loss for the worst case is known that does not hold for KRR. This bound does not make any assumptions about the underlying probability distribution of the data. In practice, however, KAAR performs better only when the data is heavily corrupted by noise or has severe outliers. This is due to the fact that KAAR is similar to KRR but with some fairly strong extra regularisation. In this paper we develop KAAR in such a way as to make it practical for use on real world data. This is achieved by controlling the amount of extra regularisation. Empirical results (including results on the well known Boston Housing dataset) suggest that in general our new methods perform as well as or better than KRR, KAAR and Support Vector Machines (SVM) in terms of the square loss they suffer.

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