Density-preserving sampling: robust and efficient alternative to cross-validation for error estimation

Sequestration of imaging studies in MIDRC: stratified sampling to balance demographic characteristics of patients in a multi-institutional data commons

Purpose

The Medical Imaging and Data Resource Center (MIDRC) is a multi-institutional effort to accelerate medical imaging machine intelligence research and create a publicly available image repository/commons as well as a sequestered commons for performance evaluation and benchmarking of algorithms. After de-identification, approximately 80% of the medical images and associated metadata become part of the open commons and 20% are sequestered from the open commons. To ensure that both commons are representative of the population available, we introduced a stratified sampling method to balance the demographic characteristics across the two datasets.

Approach

Our method uses multi-dimensional stratified sampling where several demographic variables of interest are sequentially used to separate the data into individual strata, each representing a unique combination of variables. Within each resulting stratum, patients are assigned to the open or sequestered commons. This algorithm was used on an example dataset containing 5000 patients using the variables of race, age, sex at birth, ethnicity, COVID-19 status, and image modality and compared resulting demographic distributions to naïve random sampling of the dataset over 2000 independent trials.

Results

Resulting prevalence of each demographic variable matched the prevalence from the input dataset within one standard deviation. Mann-Whitney U test results supported the hypothesis that sequestration by stratified sampling provided more balanced subsets than naïve randomization, except for demographic subcategories with very low prevalence.

Conclusions

The developed multi-dimensional stratified sampling algorithm can partition a large dataset while maintaining balance across several variables, superior to the balance achieved from naïve randomization.

Random Hyperboxes

This article proposes a simple yet powerful ensemble classifier, called Random Hyperboxes, constructed from individual hyperbox-based classifiers trained on the random subsets of sample and feature spaces of the training set. We also show a generalization error bound of the proposed classifier based on the strength of the individual hyperbox-based classifiers as well as the correlation among them. The effectiveness of the proposed classifier is analyzed using a carefully selected illustrative example and compared empirically with other popular single and ensemble classifiers via 20 datasets using statistical testing methods. The experimental results confirmed that our proposed method outperformed other fuzzy min-max neural networks (FMNNs), popular learning algorithms, and is competitive with other ensemble methods. Finally, we identify the existing issues related to the generalization error bounds of the real datasets and inform the potential research directions.

Distribution-Preserving Stratified Sampling for Learning Problems

The need for extracting a small sample from a large amount of real data, possibly streaming, arises routinely in learning problems, e.g., for storage, to cope with computational limitations, obtain good training/test/validation sets, and select minibatches for stochastic gradient neural network training. Unless we have reasons to select the samples in an active way dictated by the specific task and/or model at hand, it is important that the distribution of the selected points is as similar as possible to the original data. This is obvious for unsupervised learning problems, where the goal is to gain insights on the distribution of the data, but it is also relevant for supervised problems, where the theory explains how the training set distribution influences the generalization error. In this paper, we analyze the technique of stratified sampling from the point of view of distances between probabilities. This allows us to introduce an algorithm, based on recursive binary partition of the input space, aimed at obtaining samples that are distributed as much as possible as the original data. A theoretical analysis is proposed, proving the (greedy) optimality of the procedure together with explicit error bounds. An adaptive version of the algorithm is also introduced to cope with streaming data. Simulation tests on various data sets and different learning tasks are also provided.