Leveraging permutation testing to assess confidence in positive-unlabeled learning applied to high-dimensional biological datasets

Compared to traditional supervised machine learning approaches employing fully labeled samples, positive-unlabeled (PU) learning techniques aim to classify “unlabeled” samples based on a smaller proportion of known positive examples. This more challenging modeling goal reflects many real-world scenarios in which negative examples are not available—posing direct challenges to defining prediction accuracy and robustness. While several studies have evaluated predictions learned from only definitive positive examples, few have investigated whether correct classification of a high proportion of known positives (KP) samples from among unlabeled samples can act as a surrogate to indicate model quality.

In this study, we report a novel methodology combining multiple established PU learning-based strategies with permutation testing to evaluate the potential of KP samples to accurately classify unlabeled samples without using “ground truth” positive and negative labels for validation. Multivariate synthetic and real-world high-dimensional benchmark datasets were employed to demonstrate the suitability of the proposed pipeline to provide evidence of model robustness across varied underlying ground truth class label compositions among the unlabeled set and with different proportions of KP examples. Comparisons between model performance with actual and permuted labels could be used to distinguish reliable from unreliable models.

As in fully supervised machine learning, permutation testing offers a means to set a baseline “no-information rate” benchmark in the context of semi-supervised PU learning inference tasks—providing a standard against which model performance can be compared.