Abstract: Faced with distribution shift between and test set, we wish to detect and quantify the shift, and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets), cause symptoms (observations), we focus on shift, where the marginal $p(y)$ changes but the conditional $p(x|y)$ does not. We propose Shift Estimation (BBSE) to estimate the test distribution $p(y)$. BBSE exploits arbitrary box to reduce dimensionality prior to shift correction. While better give tighter estimates, BBSE works even when are biased, inaccurate, or uncalibrated, so long as their confusion matrices are invertible. We prove BBSE’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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