Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability for deep learning-based blood pressure (BP) estimation from photoplethysmography (PPG) signals under both in-distribution (ID) and OOD settings. Using an XResNet1D-50 trained on PulseDB and tested on four external datasets, we compared deep ensembles (DE) and Monte Carlo dropout (MCD) with Gaussian negative log-likelihood (GNLL) and mean squared error (MSE) losses, optionally followed by post-hoc recalibration via conformal prediction (CP), temperature scaling (TS), and isotonic regression (IR). The key findings of our study are as follows: (1) DE provides stronger predictive robustness under domain shift than MCD, an advantage that becomes clear primarily under external shift. (2) Recalibrated GNLL-based methods yield the best uncertainty calibration (e.g., GNLL+DE+CP for systolic blood pressure (SBP), GNLL+DE+TS for diastolic blood pressure (DBP)), while MSE-based uncertainty requires recalibration to become practically useful. (3) Across settings, CP and TS offer the most consistent gains, with IR remaining competitive in several cases. Overall, our results identify DE-based methods as most robust for predictive performance under domain shift, GNLL as strongest for native UQ, and recalibration as essential for making MSE-based uncertainty practical. These findings highlight the need to jointly assess predictive accuracy and calibration on external data for trustworthy cuffless BP estimation

This paper presents enhancements to the projection pursuit tree classifier and visual diagnostic methods for assessing their impact in high dimensions. The original algorithm uses linear combinations of variables in a tree structure where depth is constrained to be less than the number of classes -- a limitation that proves too rigid for complex classification problems. Our extensions improve performance in multi-class settings with unequal variance-covariance structures and nonlinear class separations by allowing more splits and more flexible class groupings in the projection pursuit computation. Proposing algorithmic improvements is straightforward; demonstrating their actual utility is not. We therefore develop two visual diagnostic approaches to verify that the enhancements perform as intended. Using high-dimensional visualization techniques, we examine model fits on benchmark datasets to assess whether the algorithm behaves as theorized. An interactive web application enables users to explore the behavior of both the original and enhanced classifiers under controlled scenarios. The enhancements are implemented in the R package PPtreeExt.

The numbers of the lower and upper bounds in the binarization layer are both in{5,10,50}. We utilize the Adam (Kingma and Ba, 2014) method for the training process with a mini-batch size of 32. Onlargedata sets, RRL is trained for 100 epochs, and we decay the learning rate by a factor of 0.75 every 20 epochs. Theinverse of regularization strength is in {1, 4, 16, 32}. Figure 7 shows the scatter plots of F1 score against log(#edges) for rule-based models trained on the other ten data sets.

Concentration of distances in high dimension is an important factor for the development and design of stable and reliable data analysis algorithms. In this paper, we address the fundamental long-standing question about the concentration of distances in high dimension for fractional quasi $p$-norms, $p\in(0,1)$. The topic has been at the centre of various theoretical and empirical controversies. Here we, for the first time, identify conditions when fractional quasi $p$-norms concentrate and when they don't. We show that contrary to some earlier suggestions, for broad classes of distributions, fractional quasi $p$-norms admit exponential and uniform in $p$ concentration bounds. For these distributions, the results effectively rule out previously proposed approaches to alleviate concentration by "optimal" setting the values of $p$ in $(0,1)$. At the same time, we specify conditions and the corresponding families of distributions for which one can still control concentration rates by appropriate choices of $p$. We also show that in an arbitrarily small vicinity of a distribution from a large class of distributions for which uniform concentration occurs, there are uncountably many other distributions featuring anti-concentration properties. Importantly, this behavior enables devising relevant data encoding or representation schemes favouring or discouraging distance concentration. The results shed new light on this long-standing problem and resolve the tension around the topic in both theory and empirical evidence reported in the literature.

Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique trees, whose decision rules are based on linear combinations of features, can sometimes yield better predictions than axis-aligned trees and exhibit excellent theoretical properties. We develop an oblique version of BART that leverages a data-adaptive decision rule prior that recursively partitions the feature space along random hyperplanes. Using several synthetic and real-world benchmark datasets, we systematically compared our oblique BART implementation to axis-aligned BART and other tree ensemble methods, finding that oblique BART was competitive with -- and sometimes much better than -- those methods.

Random forest (RF) stands out as a highly favored machine learning approach for classification problems. The effectiveness of RF hinges on two key factors: the accuracy of individual trees and the diversity among them. In this study, we introduce a novel approach called heterogeneous RF (HRF), designed to enhance tree diversity in a meaningful way. This diversification is achieved by deliberately introducing heterogeneity during the tree construction. Specifically, features used for splitting near the root node of previous trees are assigned lower weights when constructing the feature sub-space of the subsequent trees. As a result, dominant features in the prior trees are less likely to be employed in the next iteration, leading to a more diverse set of splitting features at the nodes. Through simulation studies, it was confirmed that the HRF method effectively mitigates the selection bias of trees within the ensemble, increases the diversity of the ensemble, and demonstrates superior performance on datasets with fewer noise features. To assess the comparative performance of HRF against other widely adopted ensemble methods, we conducted tests on 52 datasets, comprising both real-world and synthetic data. HRF consistently outperformed other ensemble methods in terms of accuracy across the majority of datasets.

Random Forest is a machine learning method that offers many advantages, including the ability to easily measure variable importance. Class balancing technique is a well-known solution to deal with class imbalance problem. However, it has not been actively studied on RF variable importance. In this paper, we study the effect of class balancing on RF variable importance. Our simulation results show that over-sampling is effective in correctly measuring variable importance in class imbalanced situations with small sample size, while under-sampling fails to differentiate important and non-informative variables. We then propose a variable selection algorithm that utilizes RF variable importance and its confidence interval. Through an experimental study using many real and artificial datasets, we demonstrate that our proposed algorithm efficiently selects an optimal feature set, leading to improved prediction performance in class imbalance problem.

Learn Machine Learning in a way that is accessible to absolute beginners. You will learn the basics of Machine Learning and how to use TensorFlow to implement many different concepts. Google provided a grant to make this course possible.

Gil discussed the future role that artificial intelligence systems may have as authors of scientific papers to produce their own experiments and shape …