Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian mechanism for feature sparsity via marginal likelihood optimization. Yet, its reliance on a homoscedastic noise model renders it sensitive to data contaminations such as outliers or misspecified noise, harming model fit and predictions. Instead, we propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification via a single Bayesian objective. This symmetric pruning of model and data offers a natural extension that preserves conjugacy, admits closed-form updates for standard optimization procedures, and aligns with perspectives from robust regression and influence functions. Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.

Finding approximations to an intractable probability distribution π of interest (usually known only up to a normalizing constant) is a key problem in scientific computing. Variational Inference stands out as a particularly attractive tool for this task, owing to its statistical and computational efficiency, and it has been the framework underlying many advances in computational statistics over the past half century (Parisi, 1980; Hinton and Van Camp, 1993; Jordan et al., 1999; Bishop and Nasrabadi, 2006). The central idea is to seek a tractable approximation to π within a chosen family of tractable distributions Q by minimizing a divergence to π over that'variational' family. Often, it is convenient or well-motivated to work with the family of product (or tensor, or factorized) distributions Q = P m, and define optimality through minimisation of the Kullback-Leibler (KL) divergence (also'relative entropy') min KL(ϱ||π): ϱ P m . A key practical aspect of working with this particular loss function is that in solving the associated optimisation problem, one is only required to compute expectations under the tractable variational distribution ϱ, rather than under the intractable target distribution π. In Bayesian statistics, π typically represents the joint posterior distribution of latent variables z Z and some parameters β B given observed data y Y. In these cases, we often choose m = 2 and seek the best variational approximation µ(dz) ν(dβ) to π to solve min KL(µ ν||π): µ P(Z), ν P(B) . The coordinate ascent variational inference algorithm (CAVI, Bishop and Nasrabadi, 2006; Blei et al., 2017) solves this problem by iteratively minimizing the Kullback-Leibler divergence with respect to one element at a time: given a starting point ν0, it iterates µk:= argmin

We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures based on the resulting residuals can then inherit first-stage bias: regression error may induce spurious dependence between covariates and residuals, invalidating the assumptions needed for standard analysis. We construct a novel Hilbert-valued one-step estimator of the kernel covariance operator between covariates and residuals. Our estimator yields bootstrap-calibrated tests for residual independence and goodness of fit in additive noise models, while also providing asymptotically efficient confidence intervals for the kernel dependence measure under noise heterogeneity. The framework extends to settings with additional covariates, enabling inference on distributional heterogeneity of residual noise across treatment groups. Simulations show improved calibration and power relative to naive plug-in residual methods.

Fairness-accuracy trade-offs are a central concern in the deployment of fairness-aware machine learning methods. When sensitive attributes are unavailable at inference time-the so called unawareness setting, principled methods for obtaining accurate predictions under relaxed fairness constraints are largely missing. In this work, we address this gap by formulating regression under a demographic parity penalty as an optimal transport problem. Our framework unifies both the \emph{aware} and \emph{unaware} settings and characterizes optimal prediction functions via optimal transport maps, under both squared Wasserstein-2 and Total Variation penalties. These results reveal that the choice of penalty reflects fundamentally different fairness philosophies: the Wasserstein penalty induces a smooth, population-wide compromise, while Total Variation enforces exact parity for a subset of individuals. Building on these theoretical characterizations, we propose an algorithm that is simple to implement, computationally efficient, and consistently matches or outperforms state-of-the-art baselines on real-world benchmarks.

Traditional insurance pricing relies on risk-based principles that ensure actuarial fairness and solvency but do not explicitly account for policyholders' price sensitivity. We formulate insurance pricing as a decision-making problem and study it using tools from off-policy evaluation and stochastic control. We propose a kernelized inverse propensity score estimator that exploits local structure in the action space and yields variance reduction compared to the classical inverse propensity score estimator. Building on these value estimates, we investigate policy optimization and present two practical approaches for computing optimal pricing rules: an interpretable data-shared Lasso formulation and a flexible policy parameterization based on neural networks. Using a controlled synthetic travel insurance environment, we empirically confirm the theoretical results and show that neural networks outperform existing techniques for policy optimization.

Background Childhood Anemia affects an estimated 40% of children aged 6-59 months globally and arises from heterogeneous nutritional, infectious, and socioeconomic factors that vary substantially across settings. This variability challenges the generalizability of predictive machine learning models, which often degrade under cross-population or temporal shifts. We investigated the utility a modern transformer-based tabular foundation model (TabPFN) as a complementatry framework with respect to supervised classical machine learning methods across diverse country contexts, with particular attention to data-scarce settings where surveillance capacity is most limited. Methods We conducted a multi-country prediction study using Demographic and Health Surveys (DHS) children's recode data from 16 countries spanning Africa, Asia, Latin America, the Caucasus, and the Middle East. The harmonized analytic cohort comprised of (n = 68,856)children aged 6-59 months with valid hemoglobin measurements. Anemia was defined using WHO age and altitude-adjusted thresholds and treated as a binary outcome. We trained Logistic Regression, XGBoost, and LightGBM models using standard supervised learning, and evaluated TabPFN v2.6 in an in-context learning setting. Performance was assessed using Area Under the Receiver Operating Characteristic Curve (AUC-ROC) and other standard classification metrics, with calibration evaluated via Brier score and expected calibration error (ECE). Uncertainty in performance estimates was quantified using bootstrap resampling to derive 95% confidence intervals. Robustness was assessed in a few-shot learning setting. Cross-population generalization was examined using leave-one-country-out (LOCO) validation and reverse-LOCO experiments to assess directional transferability. Subgroup analyses were conducted across five demographic strata: child age group, sex, maternal education, residence type, and household wealth quintile. Feature importance was assessed using standard linear and tree-based explainer SHAP values for the three supervised models and an adapted version of SHAP for TabPFN, aggregated across countries and examined at the country level. TabPFN also yielded the best probabilistic calibration across all 16 countries, achieving the lowest mean Brier score (0.203) and Expected Calibration Error (ECE = 0.042) of all models evaluated; LightGBM and Logistic Regression exhibited the greatest miscalibration, particularly at higher predicted probabilities. Under full-data conditions, within-country discrimination was moderate across all models (AUC-ROC 0.59-0.76) Under LOCO validation, performance declined modestly (AUC-ROC 0.58-0.69) Reverse-LOCO analyses revealed asymmetric and directional transferability, with epidemiologically diverse populations serving as more informative training sources and certain target populations remaining persistently difficult to predict regardless of model or training data.

CART random forests are among the most widely used modern predictive methods, with well-documented empirical success. Yet, at the mechanistic level, the algorithm is often treated as a black box because of its complexity. In this paper, we develop a stochastic-control perspective on feature-subsampled CART random forests, named CART random opportunity-set allocation (CART-ROSA). At each node, the random subset of features is interpreted as a random feasible action set, and the CART split rule as a masked-action allocation policy. This policy induces a controlled stochastic process over informative split-count states, whose terminal law determines both single-tree error and cross-tree interaction terms in the forest mean squared error (MSE). Such representation opens the black box of CART-forests by separating two design levers: the informative-opportunity rate induced by feature subsampling, and the contraction strength from the within-mask split policy. We establish that the CART policy is locally stabilizing: it contracts imbalances in informative split allocations and concentrates terminal tree geometry. At the system level, however, it can be globally suboptimal for the forest objective. Specializing to the linear model, we derive the MSE risk expansion explicitly. Our results show how an operations-research perspective makes tractable a theoretical gap difficult to access from the standard algorithmic description of CART forests.

The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes that require either line search or knowledge of the Lipschitz constant of the gradient. We develop a novel step size strategy that does not depend on the Lipschitz constant of the gradient, which allows us to extend the boosted Frank-Wolfe algorithm to the stochastic setting. We prove that boosting with this step size strategy can be combined with many modern gradient estimators, including SAGA, L-SVRG, SAG, Heavy Ball momentum, and zeroth-order estimators, among others, while retaining the worst-case convergence rates of ordinary stochastic Frank-Wolfe. Our analysis also yields the first convergence rates for boosted Frank-Wolfe on nonconvex and quasar-convex objectives, results which are new even for deterministic problems. Experiments on sparse logistic regression and quantum process tomography show that stochastic boosted Frank-Wolfe achieves faster convergence per gradient oracle call (and on wall-clock) compared to the non-boosted baseline.

In the era of precision medicine, genome-wide epigenetic modifications offer rich data that could inform risk prediction. However, these data are high-dimensional and exhibit complex dependence structures, which makes it difficult to jointly model them with low-dimensional covariates when the goal is to obtain interpretable effect estimates for covariate adjustment. Standard Bayesian additive regression trees (BART) provide strong predictive performance but treat all predictors uniformly within the tree ensemble, obscuring the contributions of significant covariates and complicating variable selection in high-dimensional settings. We propose a semi-parametric BART model (spBART) that addresses this limitation by modeling low-dimensional covariates through a parametric component with interpretable coefficients, while capturing complex nonlinear associations among high-dimensional predictors through the tree ensemble. To perform stable variable selection, we develop a cross-validation-based procedure that aggregates posterior inclusion probabilities across folds and applies Bayesian false discovery rate control. We apply the proposed method to a pooled case--control analysis of high-dimensional genome-wide 5-hydroxymethylcytosine profiles derived from circulating cell-free DNA in two multiple myeloma studies ($N = 869$). The approach identifies a parsimonious set of candidate loci and achieves strong out-of-sample discrimination (AUC $= 0.96$) in a held-out validation set. Overall, spBART provides a unified framework for combining interpretable covariate inference with flexible modeling and variable selection in high-dimensional biomedical studies.

Effective medication management in Parkinson's Disease (PD) is challenging due to heterogeneous disease progression, variable patient response, and medication side effects. While AI models can forecast levodopa equivalent daily dose (LEDD) as a measure of medication needs, standard uncertainty quantification often fails to communicate the reliability of these predictions, treating high and low confidence clinical decisions identically. We introduce CASCADE (Calibrated Adaptive Scaling via Conformal And Distributional Estimation), a novel conformal prediction framework that propagates epistemic uncertainty from a screening classifier to adapt downstream predictions. Unlike standard conformal methods that rely on auxiliary residual regression, we leverage epistemic uncertainty from a primary classification task (identifying whether a medication change is needed) to dynamically scale the prediction intervals of a secondary regression task (predicting how much change). By mapping Venn-Abers multi-probabilistic uncertainty directly to non-conformity scores, our framework achieves continuous risk adaptation. We demonstrate that this ``cascade effect'' produces highly efficient intervals for confident patients (38.9% narrower than standard conformal baselines) while automatically expanding intervals to ensure robust coverage for uncertain cases, bridging the gap between discrete clinical decision-making and continuous dose forecasting in PD.