Prediction in the presence of response-dependent missing labels

TL;DR

This paper introduces a novel method for handling response-dependent missing labels by jointly estimating event occurrence and detection likelihood, improving accuracy in datasets with biased missingness.

Contribution

The paper proposes a new non-convex algorithm that leverages prior knowledge to jointly estimate event occurrence and detection probability, addressing response-dependent missing labels.

Findings

Method outperforms existing approaches on synthetic data.

Algorithm achieves geometric convergence rates.

Effective in real wildfire detection dataset.

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.