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I've been using BART (Bayesian Additive Regression Trees) for both regression and classification problems. BART, unlike many other tree based models, provides you with uncertainties on its predictions. So for a regression problem it will for example provide:

y_estimated = 100 +- 10

for a a classification problem:

y_prob = 0.6 +- 0.1

For the regression, it is reasonably intuitive to check the intervals provided. E.g., we can test that 90% of our test samples fall within their 90% confidence interval provided by the model.

For classification, I don't seem to find a similar approach. I found multiple papers [1][2] that assess calibration for both regression and classification models, but they seem to do this fundamentally different for regression and classification models. For regression problems, the provided uncertainty (+- 10 in our example, but in general a Gaussian distribution e.g.) is assessed, while for classification problems not the provided error but the estimated point estimate of probability is assessed (with a scoring rule).

I suspect I'm missing something here? Are there ways to assess the quality of provided uncertainties on the probability estimate in classification problems? And if not, why?

Thanks!

[1] http://www.gatsby.ucl.ac.uk/~balaji/ensembles_nipsbdl16.pdf

[2] http://mlg.eng.cam.ac.uk/pub/pdf/QuiRasSinetal06.pdf

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