We study pointwise estimation and uncertainty quantification for a sparse varia-tional Gaussian process method with eigenvector inducing variables.

Explainable Artificial Intelligence (XAI) techniques, such as SHapley Additive exPlanations (SHAP), have become essential tools for interpreting complex ensemble tree-based models, especially in high-stakes domains such as healthcare analytics. However, SHAP values are usually treated as point estimates, which disregards the inherent and ubiquitous uncertainty in predictive models and data. This uncertainty has two primary sources: aleatoric and epistemic. The aleatoric uncertainty, which reflects the irreducible noise in the data. The epistemic uncertainty, which arises from a lack of data. In this work, we propose an approach for decomposing uncertainty in SHAP values into aleatoric, epistemic, and entanglement components. This approach integrates Dempster-Shafer evidence theory and hypothesis sampling via Dirichlet processes over tree ensembles. We validate the method across three real-world use cases with descriptive statistical analyses that provide insight into the nature of epistemic uncertainty embedded in SHAP explanations. The experimentations enable to provide more comprehensive understanding of the reliability and interpretability of SHAP-based attributions. This understanding can guide the development of robust decision-making processes and the refinement of models in high-stakes applications. Through our experiments with multiple datasets, we concluded that features with the highest SHAP values are not necessarily the most stable. This epistemic uncertainty can be reduced through better, more representative data and following appropriate or case-desired model development techniques. Tree-based models, especially bagging, facilitate the effective quantification of epistemic uncertainty.

An important challenge in scientific machine learning is to develop methods that can exploit and maximize the amount of learning possible from scarce data [1-4]. The need for such methods arises often in science and engineering, especially in the case of computational fluid dynamics (CFD), since expensive-to-evaluate high-fidelity (HF) models make many-query problems such as uncertainty quantification, risk analysis, optimization, and optimization under uncertainty computationally prohibitive [5]. Surrogate models that approximate the solutions to HF models can facilitate the design and analysis process; however, lack of sufficient HF data in tandem with high-dimensional quantities of interest adversely affect surrogate model accuracy. We propose multifidelity (MF) linear regression methods that leverage abundant low-cost, lower-fidelity (LF) data alongside limited HF data to construct linear regression models. These models operate within a reduced-dimensional subspace, obtained through the principal component analysis (PCA), to effectively handle both training data scarcity and the high dimensionality (on the order of tens of thousands of quantities of interest) inherent in our problem setting. Linear regression has been widely utilized as a surrogate modeling approach in aerospace applications due to its simplicity and interpretability. We note that linear regression encompasses a broad class of models that are linear in their parameters but can include features that are arbitrarily nonlinear functions of the input variables [6].

Recent advances in machine learning have greatly expanded the repertoire of predictive methods for medical imaging. However, the interpretability of complex models remains a challenge, which limits their utility in medical applications. Recently, model-agnostic methods have been proposed to measure conditional variable importance and accommodate complex non-linear models. However, they often lack power when dealing with highly correlated data, a common problem in medical imaging. We introduce Hierarchical-CPI, a model-agnostic variable importance measure that frames the inference problem as the discovery of groups of variables that are jointly predictive of the outcome. By exploring subgroups along a hierarchical tree, it remains computationally tractable, yet also enjoys explicit family-wise error rate control. Moreover, we address the issue of vanishing conditional importance under high correlation with a tree-based importance allocation mechanism. We benchmarked Hierarchical-CPI against state-of-the-art variable importance methods. Its effectiveness is demonstrated in two neuroimaging datasets: classifying dementia diagnoses from MRI data (ADNI dataset) and analyzing the Berger effect on EEG data (TDBRAIN dataset), identifying biologically plausible variables.

Tendon-driven robotic hands offer unparalleled dexterity for manipulation tasks, but learning control policies for such systems presents unique challenges. Unlike joint-actuated robotic hands, tendon-driven systems lack a direct one-to-one mapping between motion capture (mocap) data and tendon controls, making the learning process complex and expensive. Additionally, visual tracking methods for real-world applications are prone to occlusions and inaccuracies, further complicating joint tracking. Wrist-wearable surface electromyography (sEMG) sensors present an inexpensive, robust alternative to capture hand motion. However, mapping sEMG signals to tendon control remains a significant challenge despite the availability of EMG-to-pose data sets and regression-based models in the existing literature. We introduce the first large-scale EMG-to-Tendon Control dataset for robotic hands, extending the emg2pose dataset, which includes recordings from 193 subjects, spanning 370 hours and 29 stages with diverse gestures. This dataset incorporates tendon control signals derived using the MyoSuite MyoHand model, addressing limitations such as invalid poses in prior methods. We provide three baseline regression models to demonstrate emg2tendon utility and propose a novel diffusion-based regression model for predicting tendon control from sEMG recordings. This dataset and modeling framework marks a significant step forward for tendon-driven dexterous robotic manipulation, laying the groundwork for scalable and accurate tendon control in robotic hands. https://emg2tendon.github.io/

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this Wasserstein ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high confidence. We then formulate a distributionally robust logistic regression model that minimizes a worst-case expected logloss function, where the worst case is taken over all distributions in the Wasserstein ball. We prove that this optimization problem admits a tractable reformulation and encapsulates the classical as well as the popular regularized logistic regression problems as special cases. We further propose a distributionally robust approach based on Wasserstein balls to compute upper and lower confidence bounds on the misclassification probability of the resulting classifier. These bounds are given by the optimal values of two highly tractable linear programs.

We consider the problem of binary classification when the covariates conditioned on the each of the response values follow multivariate Gaussian distributions. We focus on the setting where the covariance matrices for the two conditional distributions are the same. The corresponding generative model classifier, derived via the Bayes rule, also called Linear Discriminant Analysis, has been shown to behave poorly in high-dimensional settings. We present a novel analysis of the classification error of any linear discriminant approach given conditional Gaussian models. This allows us to compare the generative model classifier, other recently proposed discriminative approaches that directly learn the discriminant function, and then finally logistic regression which is another classical discriminative model classifier. As we show, under a natural sparsity assumption, and letting $s$ denote the sparsity of the Bayes classifier, $p$ the number of covariates, and $n$ the number of samples, the simple ($\ell_1$-regularized) logistic regression classifier achieves the fast misclassification error rates of $O\left(\frac{s \log p}{n}\right)$, which is much better than the other approaches, which are either inconsistent under high-dimensional settings, or achieve a slower rate of $O\left(\sqrt{\frac{s \log p}{n}}\right)$.

Federated learning has emerged as an essential paradigm for distributed multi-source data analysis under privacy concerns. Most existing federated learning methods focus on the ``static" datasets. However, in many real-world applications, data arrive continuously over time, forming streaming datasets. This introduces additional challenges for data storage and algorithm design, particularly under high-dimensional settings. In this paper, we propose a federated online learning (FOL) method for distributed multi-source streaming data analysis. To account for heterogeneity, a personalized model is constructed for each data source, and a novel ``subgroup" assumption is employed to capture potential similarities, thereby enhancing model performance. We adopt the penalized renewable estimation method and the efficient proximal gradient descent for model training. The proposed method aligns with both federated and online learning frameworks: raw data are not exchanged among sources, ensuring data privacy, and only summary statistics of previous data batches are required for model updates, significantly reducing storage demands. Theoretically, we establish the consistency properties for model estimation, variable selection, and subgroup structure recovery, demonstrating optimal statistical efficiency. Simulations illustrate the effectiveness of the proposed method. Furthermore, when applied to the financial lending data and the web log data, the proposed method also exhibits advantageous prediction performance. Results of the analysis also provide some practical insights.