Learning from Asymmetrically-corrupted Data in Regression for Sensor Magnitude

This paper addresses a regression problem in which output label values represent the results of sensing the magnitude of a phenomenon. A low value of such labels can either mean that the actual magnitude of the phenomenon has been low or that the sensor has made an incomplete observation. This leads to a bias toward lower values in labels and its resultant learning because labels for incomplete observations are recorded as lower than those for typical observations, even if both have monitored similar phenomena. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models the incomplete observations to be corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased with a regression learned from the uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.