The Choquet Kernel on the use of Regression Problem

Recently, we have presented a new family of kernels on the basis of the discrete Choquet integral. While a naive computation of this kernel has an exponential complexity in the number of features, we have proposed an efficient approach with computational complexity of O(m(2)log(m)).(1) This kernel family is able to recognize dependencies between features and moreover it can be regularized through a proper selection of q-additivity. In fact, to reduce the effect of over-fitting there is an opportunity to restrict the flexibility of kernel to a lower degree. A key feature of the Choquet integral in a data-driven way is its monotonicity, however, this representation does not consider any monotonicity constraint; hence it is versatile for other applications, too. This issue is highlighted in the experimental study. In this regard, we apply the Choquet kernel for regression task and compare the performance of the proposed kernel versus state-of-the-art support kernel-based regression methods as well as random forest. (C) 2020 Elsevier Inc. All rights reserved.