Medical prediction applications often need to deal with small sample sizes compared to the number of covariates. Such data pose problems for prediction and variable selection, especially when the covariate-response relationship is complicated. To address these challenges, we propose to incorporate co-data, i.e. external information on the covariates, into Bayesian additive regression trees (BART), a sum-of-trees prediction model that utilizes priors on the tree parameters to prevent overfitting. To incorporate co-data, an empirical Bayes (EB) framework is developed that estimates, assisted by a co-data model, prior covariate weights in the BART model. The proposed method can handle multiple types of co-data simultaneously. Furthermore, the proposed EB framework enables the estimation of the other hyperparameters of BART as well, rendering an appealing alternative to cross-validation. We show that the method finds relevant covariates and that it improves prediction compared to default BART in simulations. If the covariate-response relationship is nonlinear, the method benefits from the flexibility of BART to outperform regression-based co-data learners. Finally, the use of co-data enhances prediction in an application to diffuse large B-cell lymphoma prognosis based on clinical covariates, gene mutations, DNA translocations, and DNA copy number data. Keywords: Bayesian additive regression trees; Empirical Bayes; Co-data; High-dimensional data; Omics; Prediction

A significant challenge for predictive maintenance in the pulp-and-paper industry is the infrequency of paper breaks during the production process. In this article, operational data is analyzed from a paper manufacturing machine in which paper breaks are relatively rare but have a high economic impact. Utilizing a dataset comprising 18,398 instances derived from a quality assurance protocol, we address the scarcity of break events (124 cases) that pose a challenge for machine learning predictive models. With the help of Conditional Generative Adversarial Networks (CTGAN) and Synthetic Minority Oversampling Technique (SMOTE), we implement a novel data augmentation framework. This method ensures that the synthetic data mirrors the distribution of the real operational data but also seeks to enhance the performance metrics of predictive modeling. Before and after the data augmentation, we evaluate three different machine learning algorithms-Decision Trees (DT), Random Forest (RF), and Logistic Regression (LR). Utilizing the CTGAN-enhanced dataset, our study achieved significant improvements in predictive maintenance performance metrics. The efficacy of CTGAN in addressing data scarcity was evident, with the models' detection of machine breaks (Class 1) improving by over 30% for Decision Trees, 20% for Random Forest, and nearly 90% for Logistic Regression. With this methodological advancement, this study contributes to industrial quality control and maintenance scheduling by addressing rare event prediction in manufacturing processes.

Driving is a complex daily activity indicating age and disease related cognitive declines. Therefore, deficits in driving performance compared with ones without mild cognitive impairment (MCI) can reflect changes in cognitive functioning. There is increasing evidence that unobtrusive monitoring of older adults driving performance in a daily-life setting may allow us to detect subtle early changes in cognition. The objectives of this paper include designing low-cost in-vehicle sensing hardware capable of obtaining high-precision positioning and telematics data, identifying important indicators for early changes in cognition, and detecting early-warning signs of cognitive impairment in a truly normal, day-to-day driving condition with machine learning approaches. Our statistical analysis comparing drivers with MCI to those without reveals that those with MCI exhibit smoother and safer driving patterns. This suggests that drivers with MCI are cognizant of their condition and tend to avoid erratic driving behaviors. Furthermore, our Random Forest models identified the number of night trips, number of trips, and education as the most influential factors in our data evaluation.

Recent research has highlighted the potential of linking predictive and prescriptive analytics. However, it remains widely unexplored how both paradigms could benefit from one another to address today's major challenges in healthcare. One of these is smarter planning of resource capacities for frail and elderly inpatient wards, addressing the societal challenge of an aging population. Frail and elderly patients typically suffer from multimorbidity and require more care while receiving medical treatment. The aim of this research is to assess how various predictive and prescriptive analytical methods, both individually and in tandem, contribute to addressing the operational challenges within an area of healthcare that is growing in demand. Clinical and demographic patient attributes are gathered from more than 165,000 patient records and used to explain and predict length of stay. To that extent, we employ Classification and Regression Trees (CART) analysis to establish this relationship. On the prescriptive side, deterministic and two-stage stochastic programs are developed to determine how to optimally plan for beds and ward staff with the objective to minimize cost. Furthermore, the two analytical methodologies are linked by generating demand for the prescriptive models using the CART groupings. The results show the linked methodologies provided different but similar results compared to using averages and in doing so, captured a more realistic real-world variation in the patient length of stay. Our research reveals that healthcare managers should consider using predictive and prescriptive models to make more informed decisions. By combining predictive and prescriptive analytics, healthcare managers can move away from relying on averages and incorporate the unique characteristics of their patients to create more robust planning decisions, mitigating risks caused by variations in demand.

To form precipitation datasets that are accurate and, at the same time, have high spatial densities, data from satellites and gauges are often merged in the literature. However, uncertainty estimates for the data acquired in this manner are scarcely provided, although the importance of uncertainty quantification in predictive modelling is widely recognized. Furthermore, the benefits that machine learning can bring to the task of providing such estimates have not been broadly realized and properly explored through benchmark experiments. The present study aims at filling in this specific gap by conducting the first benchmark tests on the topic. On a large dataset that comprises 15-year-long monthly data spanning across the contiguous United States, we extensively compared six learners that are, by their construction, appropriate for predictive uncertainty quantification. These are the quantile regression (QR), quantile regression forests (QRF), generalized random forests (GRF), gradient boosting machines (GBM), light gradient boosting machines (LightGBM) and quantile regression neural networks (QRNN). The comparison referred to the competence of the learners in issuing predictive quantiles at nine levels that facilitate a good approximation of the entire predictive probability distribution, and was primarily based on the quantile and continuous ranked probability skill scores. Three types of predictor variables (i.e., satellite precipitation variables, distances between a point of interest and satellite grid points, and elevation at a point of interest) were used in the comparison and were additionally compared with each other. This additional comparison was based on the explainable machine learning concept of feature importance. The results suggest that the order from the best to the worst of the learners for the task investigated is the following: LightGBM, QRF, GRF, GBM, QRNN and QR...

Decision trees are essential yet NP-complete to train, prompting the widespread use of heuristic methods such as CART, which suffers from sub-optimal performance due to its greedy nature. Recently, breakthroughs in finding optimal decision trees have emerged; however, these methods still face significant computational costs and struggle with continuous features in large-scale datasets and deep trees. To address these limitations, we introduce a moving-horizon differential evolution algorithm for classification trees with continuous features (MH-DEOCT). Our approach consists of a discrete tree decoding method that eliminates duplicated searches between adjacent samples, a GPU-accelerated implementation that significantly reduces running time, and a moving-horizon strategy that iteratively trains shallow subtrees at each node to balance the vision and optimizer capability. Comprehensive studies on 68 UCI datasets demonstrate that our approach outperforms the heuristic method CART on training and testing accuracy by an average of 3.44% and 1.71%, respectively. Moreover, these numerical studies empirically demonstrate that MH-DEOCT achieves near-optimal performance (only 0.38% and 0.06% worse than the global optimal method on training and testing, respectively), while it offers remarkable scalability for deep trees (e.g., depth=8) and large-scale datasets (e.g., ten million samples).

ODTLearn is an open-source Python package that provides methods for learning optimal decision trees for high-stakes predictive and prescriptive tasks based on the mixed-integer optimization (MIO) framework proposed in (Aghaei et al., 2019) and several of its extensions. The current version of the package provides implementations for learning optimal classification trees, optimal fair classification trees, optimal classification trees robust to distribution shifts, and optimal prescriptive trees from observational data. We have designed the package to be easy to maintain and extend as new optimal decision tree problem classes, reformulation strategies, and solution algorithms are introduced. To this end, the package follows object-oriented design principles and supports both commercial (Gurobi) and open source (COIN-OR branch and cut) solvers.

Quantifying the usefulness of individual features in random forests learning can greatly enhance its interpretability. Existing studies have shown that some popularly used feature importance measures for random forests suffer from the bias issue. In addition, there lack comprehensive size and power analyses for most of these existing methods. In this paper, we approach the problem via hypothesis testing, and suggest a framework of the self-normalized feature-residual correlation test (FACT) for evaluating the significance of a given feature in the random forests model with bias-resistance property, where our null hypothesis concerns whether the feature is conditionally independent of the response given all other features. Such an endeavor on random forests inference is empowered by some recent developments on high-dimensional random forests consistency. Under a fairly general high-dimensional nonparametric model setting with dependent features, we formally establish that FACT can provide theoretically justified feature importance test with controlled type I error and enjoy appealing power property. The theoretical results and finite-sample advantages of the newly suggested method are illustrated with several simulation examples and an economic forecasting application.

Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be intractable for specific inputs. In this paper, we identify a restricted class of decision tree ensembles, called large-spread ensembles, which admit a security verification algorithm running in polynomial time. We then propose a new approach called verifiable learning, which advocates the training of such restricted model classes which are amenable for efficient verification. We show the benefits of this idea by designing a new training algorithm that automatically learns a large-spread decision tree ensemble from labelled data, thus enabling its security verification in polynomial time. Experimental results on public datasets confirm that large-spread ensembles trained using our algorithm can be verified in a matter of seconds, using standard commercial hardware. Moreover, large-spread ensembles are more robust than traditional ensembles against evasion attacks, at the cost of an acceptable loss of accuracy in the non-adversarial setting.

With the insight of variance-bias decomposition, we design a new hybrid bagging-boosting algorithm named SBPMT for classification problems. For the boosting part of SBPMT, we propose a new tree model called Probit Model Tree (PMT) as base classifiers in AdaBoost procedure. For the bagging part, instead of subsampling from the dataset at each step of boosting, we perform boosted PMTs on each subagged dataset and combine them into a powerful "committee", which can be viewed an incomplete U-statistic. Our theoretical analysis shows that (1) SBPMT is consistent under certain assumptions, (2) Increase the subagging times can reduce the generalization error of SBPMT to some extent and (3) Large number of ProbitBoost iterations in PMT can benefit the performance of SBPMT with fewer steps in the AdaBoost part. Those three properties are verified by a famous simulation designed by Mease and Wyner (2008). The last two points also provide a useful guidance in model tuning. A comparison of performance with other state-of-the-art classification methods illustrates that the proposed SBPMT algorithm has competitive prediction power in general and performs significantly better in some cases.