Prediction in the presence of response-dependent missing labels

• URL: http://arxiv.org/abs/2103.13555v1
• Date: Thu, 25 Mar 2021 01:43:33 GMT
• Title: Prediction in the presence of response-dependent missing labels
• Authors: Hyebin Song, Garvesh Raskutti, Rebecca Willett
• Abstract summary: limitations of sensing technologies result in missing labels in wildfire data. We develop a new methodology and non-labeled algorithm P(ositive) U(ccurrence) M(agnitude) M(ixture) which jointly estimates the occurrence and detection likelihood of positive samples.
• Score: 28.932172873182115
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In a variety of settings, limitations of sensing technologies or other sampling mechanisms result in missing labels, where the likelihood of a missing label in the training set is an unknown function of the data. For example, satellites used to detect forest fires cannot sense fires below a certain size threshold. In such cases, training datasets consist of positive and pseudo-negative observations where pseudo-negative observations can be either true negatives or undetected positives with small magnitudes. We develop a new methodology and non-convex algorithm P(ositive) U(nlabeled) - O(ccurrence) M(agnitude) M(ixture) which jointly estimates the occurrence and detection likelihood of positive samples, utilizing prior knowledge of the detection mechanism. Our approach uses ideas from positive-unlabeled (PU)-learning and zero-inflated models that jointly estimate the magnitude and occurrence of events. We provide conditions under which our model is identifiable and prove that even though our approach leads to a non-convex objective, any local minimizer has optimal statistical error (up to a log term) and projected gradient descent has geometric convergence rates. We demonstrate on both synthetic data and a California wildfire dataset that our method out-performs existing state-of-the-art approaches.

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