Abstract: Faced with distribution between training and test set, we wish to detect and quantify the , and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets), cause symptoms (observations), we focus on , where the label marginal $p(y)$ changes but the conditional $p(x|y)$ does not. We propose Black Estimation (BBSE) to estimate the test distribution $p(y)$. BBSE exploits arbitrary black box to reduce dimensionality prior to correction. While better predictors give tighter estimates, BBSE works even when predictors are biased, inaccurate, or uncalibrated, so long as their confusion matrices are invertible. We prove BBSE217;s consistency, bound its error, and introduce a statistical test that uses BBSE to detect shift. We also leverage BBSE to correct classifiers. Experiments demonstrate accurate estimates and improved prediction, even on high-dimensional datasets of natural images.

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