Classification predictive modeling involves the accurate assignment of observations in a dataset to target classes or categories. There is an increasing growth of real-world classification problems with severely imbalanced class distributions. In this case, minority classes have much fewer observations to learn from than those from majority classes. Despite this sparsity, a minority class is often considered the more interesting class yet developing a scientific learning algorithm suitable for the observations presents countless challenges. In this article, we suggest a novel multi-class classification algorithm specialized to handle severely imbalanced classes based on the method we refer to as SAMME.C2. It blends the flexible mechanics of the boosting techniques from SAMME algorithm, a multi-class classifier, and Ada.C2 algorithm, a cost-sensitive binary classifier designed to address highly class imbalances. Not only do we provide the resulting algorithm but we also establish scientific and statistical formulation of our proposed SAMME.C2 algorithm. Through numerical experiments examining various degrees of classifier difficulty, we demonstrate consistent superior performance of our proposed model.

The presence of mislabelled observations in data is a notoriously challenging problem in statistics and machine learning, associated with poor generalisation properties for both traditional classifiers and, perhaps even more so, flexible classifiers like neural networks. Here we propose a novel double regularisation of the neural network training loss that combines a penalty on the complexity of the classification model and an optimal reweighting of training observations. The combined penalties result in improved generalisation properties and strong robustness against overfitting in different settings of mislabelled training data and also against variation in initial parameter values when training. We provide a theoretical justification, by proving that for logistic regression with multivariate Gaussian covariates, our proposed method can find the correct parameters exactly, i.e. estimate the parameters to exactly the same value as if there were no mislabelling. We demonstrate the double regularisation model, here denoted by DRFit, for neural net classification of (i) MNIST and (ii) CIFAR-10, in both cases with simulated mislabelling. We also illustrate that DRFit identifies mislabelled data points with very good precision. This provides strong support for DRFit as a practical of-the-shelf classifier, since, without any sacrifice in performance, we get a classifier that simultaneously reduces overfitting against mislabelling and gives an accurate measure of the trustworthiness of the labels.

Observational cohort studies with oversampled exposed subjects are typically implemented to understand the causal effect of a rare exposure. Because the distribution of exposed subjects in the sample differs from the source population, estimation of a propensity score function (i.e., probability of exposure given baseline covariates) targets a nonparametrically nonidentifiable parameter. Consistent estimation of propensity score functions is an important component of various causal inference estimators, including double robust machine learning and inverse probability weighted estimators. We propose the use of the probability of exposure from the source population in observation-weighted stacking algorithms to produce consistent estimators of propensity score functions. Simulation studies and a hypothetical health policy intervention data analysis demonstrate low empirical bias and variance for these stacked propensity score functions with observation weights.