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Inverse prediction concerns predicting one set of measurements from another set when the direction of causation and possibly error operates in the opposite direction. An example is that of calibration in which it is desired to use a cheap and quick but error-prone measurement Y, to predict the true amount of a constituent x, which in itself can be measured accurately in laboratory conditions but at much greater effort or cost. After taking data on samples using both measurements (the training or learning data) it is desired to use the cheap measurement in future.