However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is a challenge, and the resulting p-value is not a divergence metric.

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Although this verification problem is NP-complete in general, we give a more precise complexity characterization. We show that there is a simple linear time algorithm for verifying a single tree, and for tree ensembles the verification problem can be cast as a max-clique problem on a multi-partite graph withbounded boxicity. Forlowdimensional problems when boxicity can be viewed as constant, this reformulation leads to a polynomial time algorithm.

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To achieve a stable alignment of feature distributions, we also introduce a SDA strategy to mitigate domain discrepancy on the sphere.

Conversely, adaptive first order methods are very popular in Machine Learning, with AdaGrad, [12],beingthemostprominent methodamongthisclass. AdaGrad isanonlinelearning algorithm which adapts its learning rate using the feedback (gradients) received through the optimization process, and is known to successfully handle noisy feedback.

In this section, we provide further elaboration on this fine-tuning method.