Discrete minimax classifier for personalized diagnosis in medicine

Overview & Synopsis

Machine Learning algorithms become more and more promising in precision medicine. From the clinical or biological profile of each patient, these methods can for example help the experts in the application field to diagnose a disease or to predict a response to a specific treatment. To this aim, supervised learning classifiers are fitted from a set of labeled learning samples by generally minimizing the global risk of classification errors on this training set. Intuitively, these methods map the feature space so that the founded regions in this space are assigned to a specific class, and such that the global risk of error is minimized. Then, the resulted decision rule, also called classifier, maps the new patients into this feature space and assigns them the class associated with the region to which they belong.Nowadays, supervised learning algorithms become more and more efficient for supervised classification tasks. However, most supervised classifiers do not deal well with imbalanced and uncertain class proportions which generally occur in medical datasets. For example, the number of individuals who have a disease is generally lower that the number of healthy individuals. Moreover, most methods assume that new individuals to be included in the dataset will follow the same distribution as the labeled training samples which may be not the case. Indeed, the proportion of individuals who have a disease may increase or decrease in time due to sampling issues resulting in the fitted classifier to be biased, therefore increasing the classification errors for the new individuals. Imbalanced datasets and uncertain class proportions are two major issues when applying machine learning methods in medicine. Designing robust classifiers that could deal with these two issues is highly warranted.During my Thesis, we developed a new mathematical method, a Discrete Minimax Classifier, for dealing with these class proportions issues. Our approach can take into account the knowledge or the interest of the experts of the application field, and is moreover suitable to other difficulties that usually appear in medicine field such that the presence of mixed attributes and the presence of dependencies between some features. In order to process mixed attributes, the numeric features are discretized which allows us to analytically calculate the empirical Bayes risk of errors over the simplex. Our Discrete Minimax Classifier is computed using a projected-subgradient-based algorithm which searches for the priors that maximize this empirical Bayes risk over the simplex. By construction, our resulted classifier minimizes the maximum of the risks per class and becomes robust face to prior probability shifts. We moreover tune our approach to compute au Gamma-minimax classifier that takes into account independent bounds on each class proportion in the case where the experts in the application field are able to estimate the uncertainty in each class proportion independently. Finally, we show that we can easily couple our approach with pre-trained decision trees or pre-trained convolutional neural networks in order to adjust these classifiers face to imbalanced datasets and prior probability shifts.Our research was performed in tight collaboration with the Institute of Molecular and Cellular Pharmacology (IPMC) in Valbonne, the Nice University Hospital in Nice (CHU) and the HalioDX private company in Marseille. The goal of our project with the IPMC was to improve diagnosis and treatments of psychiatric diseases using blood biomarkers. The goal of our project with the CHU was to conceive a machine learning classifier for diagnosing the presence of a non-alcoholic fatty liver disease from the clinical profile of patients. As for HalioDX, we did not actually work with the datasets from this company but the methods that we have developed will be used by HalioDX to identify cancer patients at risk of not responding to immune checkpoint therapy.