Observational studies developing causal machine learning (ML) models for the prediction of individualized treatment effects (ITEs) seldom conduct empirical evaluations to assess the conditional exchangeability assumption. We aimed to evaluate the performance of these models under conditional exchangeability violations and the utility of negative control outcomes (NCOs) as a diagnostic. We conducted a simulation study to examine confounding bias in ITE estimates generated by causal forest and X-learner models under varying conditions, including the presence or absence of true heterogeneity. We simulated data to reflect real-world scenarios with differing levels of confounding, sample size, and NCO confounding structures. We then estimated and compared subgroup-level treatment effects on the primary outcome and NCOs across settings with and without unmeasured confounding. When conditional exchangeability was violated, causal forest and X-learner models failed to recover true treatment effect heterogeneity and, in some cases, falsely indicated heterogeneity when there was none. NCOs successfully identified subgroups affected by unmeasured confounding. Even when NCOs did not perfectly satisfy its ideal assumptions, it remained informative, flagging potential bias in subgroup level estimates, though not always pinpointing the subgroup with the largest confounding. Violations of conditional exchangeability substantially limit the validity of ITE estimates from causal ML models in routinely collected observational data. NCOs serve a useful empirical diagnostic tool for detecting subgroup-specific unmeasured confounding and should be incorporated into causal ML workflows to support the credibility of individualized inference.

Learning to defer uncertain predictions to costly experts offers a powerful strategy for improving the accuracy and efficiency of machine learning systems. However, standard training procedures for deferral algorithms typically require querying all experts for every training instance, an approach that becomes prohibitively expensive when expert queries incur significant computational or resource costs. This undermines the core goal of deferral: to limit unnecessary expert usage. To overcome this challenge, we introduce the budgeted deferral framework, which aims to train effective deferral algorithms while minimizing expert query costs during training. We propose new algorithms for both two-stage and single-stage multiple-expert deferral settings that selectively query only a subset of experts per training example. While inspired by active learning, our setting is fundamentally different: labels are already known, and the core challenge is to decide which experts to query in order to balance cost and predictive performance. We establish theoretical guarantees for both of our algorithms, including generalization bounds and label complexity analyses. Empirical results across several domains show that our algorithms substantially reduce training costs without sacrificing prediction accuracy, demonstrating the practical value of our budget-aware deferral algorithms.

Kernel methods represent a fundamental class of machine learning techniques and have gained widespread adoption across diverse domains [32], including computer vision [22, 13], natural language processing (NLP) [36, 4], and bioinformatics [29], among others. The core idea underlying kernel methods is to employ a kernel function that implicitly maps the input data into a high-dimensional feature space, thereby enabling the use of linear models to solve nonlinear learning tasks in the original space. Consequently, the selection of an appropriate kernel function is critical to the performance of the method. Traditional kernel methods predominantly rely on positive definite (PD) kernels, such as the polynomial kernel and the Gaussian kernel. According to Mercer's Theorem, a PD kernel ensures that the resulting kernel matrix is positive semidefinite (PSD), thereby facilitating the analysis of the learning problem within the framework of reproducing kernel Hilbert spaces (RKHS) [9]. The PSD property guarantees that the corresponding optimization problem is convex and thus tractable. These authors contributed equally to this work.

Single-cell technologies generate high-dimensional point clouds of cells, enabling detailed characterization of complex patient states and treatment responses. Yet each patient is represented by an irregular point cloud rather than a simple vector, making it difficult to directly quantify and compare biological differences between individuals. Nonlinear methods such as kernels and neural networks achieve predictive accuracy but act as black boxes, offering little biological interpretability. To address these limitations, we adapt the Linear Optimal Transport (LOT) framework to this setting, embedding irregular point clouds into a fixed-dimensional Euclidean space while preserving distributional structure. This embedding provides a principled linear representation that preserves optimal transport geometry while enabling downstream analysis. It also forms a registration between any two patients, enabling direct comparison of their cellular distributions. Within this space, LOT enables: (i) \textbf{accurate and interpretable classification} of COVID-19 patient states, where classifier weights map back to specific markers and spatial regions driving predictions; and (ii) \textbf{synthetic data generation} for patient-derived organoids, exploiting the linearity of the LOT embedding. LOT barycenters yield averaged cellular profiles representing combined conditions or samples, supporting drug interaction testing. Together, these results establish LOT as a unified framework that bridges predictive performance, interpretability, and generative modeling. By transforming heterogeneous point clouds into structured embeddings directly traceable to the original data, LOT opens new opportunities for understanding immune variation and treatment effects in high-dimensional biological systems.

This note introduces a unified theory for causal inference that integrates Riesz regression, covariate balancing, density-ratio estimation (DRE), targeted maximum likelihood estimation (TMLE), and the matching estimator in average treatment effect (ATE) estimation. In ATE estimation, the balancing weights and the regression functions of the outcome play important roles, where the balancing weights are referred to as the Riesz representer, bias-correction term, and clever covariates, depending on the context. Riesz regression, covariate balancing, DRE, and the matching estimator are methods for estimating the balancing weights, where Riesz regression is essentially equivalent to DRE in the ATE context, the matching estimator is a special case of DRE, and DRE is in a dual relationship with covariate balancing. TMLE is a method for constructing regression function estimators such that the leading bias term becomes zero. Nearest Neighbor Matching is equivalent to Least Squares Density Ratio Estimation and Riesz Regression.

In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.

We propose a data-driven framework for efficiently solving quadratic programming (QP) problems by reducing the number of variables in high-dimensional QPs using instance-specific projection. A graph neural network-based model is designed to generate projections tailored to each QP instance, enabling us to produce high-quality solutions even for previously unseen problems. The model is trained on heterogeneous QPs to minimize the expected objective value evaluated on the projected solutions. This is formulated as a bilevel optimization problem; the inner optimization solves the QP under a given projection using a QP solver, while the outer optimization updates the model parameters. We develop an efficient algorithm to solve this bilevel optimization problem, which computes parameter gradients without backpropagating through the solver. We provide a theoretical analysis of the generalization ability of solving QPs with projection matrices generated by neural networks. Experimental results demonstrate that our method produces high-quality feasible solutions with reduced computation time, outperforming existing methods.

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate balancing, targeted maximum likelihood estimation (TMLE), and density-ratio estimation. In many problems involving causal effects or structural models, the parameters of interest depend on regression functions. Plugging regression functions estimated by machine learning methods into the identifying equations can yield poor performance because of first-stage bias. To reduce such bias, debiased machine learning employs Neyman orthogonal estimating equations. Debiased machine learning typically requires estimation of the Riesz representer and the regression function. For this problem, we develop a direct debiased machine learning framework with an end-to-end algorithm. We formulate estimation of the nuisance parameters, the regression function and the Riesz representer, as minimizing the discrepancy between Neyman orthogonal scores computed with known and unknown nuisance parameters, which we refer to as Neyman targeted estimation. Neyman targeted estimation includes Riesz representer estimation, and we measure discrepancies using the Bregman divergence. The Bregman divergence encompasses various loss functions as special cases, where the squared loss yields Riesz regression and the Kullback-Leibler divergence yields entropy balancing. We refer to this Riesz representer estimation as generalized Riesz regression. Neyman targeted estimation also yields TMLE as a special case for regression function estimation. Furthermore, for specific pairs of models and Riesz representer estimation methods, we can automatically obtain the covariate balancing property without explicitly solving the covariate balancing objective.

Heavy-tailed distributions, prevalent in a lot of real-world applications such as finance, telecommunications, queuing theory, and natural language processing, are challenging to model accurately owing to their slow tail decay. Bernstein phase-type (BPH) distributions, through their analytical tractability and good approximations in the non-tail region, can present a good solution, but they suffer from an inability to reproduce these heavy-tailed behaviors exactly, thus leading to inadequate performance in important tail areas. On the contrary, while highly adaptable to heavy-tailed distributions, hyperexponential (HE) models struggle in the body part of the distribution. Additionally, they are highly sensitive to initial parameter selection, significantly affecting their precision. To solve these issues, we propose a novel hybrid model of BPH and HE distributions, borrowing the most desirable features from each for enhanced approximation quality. Specifically, we leverage an optimization to set initial parameters for the HE component, significantly enhancing its robustness and reducing the possibility that the associated procedure results in an invalid HE model. Experimental validation demonstrates that the novel hybrid approach is more performant than individual application of BPH or HE models. More precisely, it can capture both the body and the tail of heavy-tailed distributions, with a considerable enhancement in matching parameters such as mean and coefficient of variation. Additional validation through experiments utilizing queuing theory proves the practical usefulness, accuracy, and precision of our hybrid approach.

Machine learning (ML) has the potential to support and improve expert performance in monitoring the brain function of at-risk newborns. Developing accurate and reliable ML models depends on access to high-quality, annotated data, a resource in short supply. ML competitions address this need by providing researchers access to expertly annotated datasets, fostering shared learning through direct model comparisons, and leveraging the benefits of crowdsourcing diverse expertise. We compiled a retrospective dataset containing 353 hours of EEG from 102 individual newborns from a multi-centre study. The data was fully anonymised and divided into training, testing, and held-out validation datasets. EEGs were graded for the severity of abnormal background patterns. Next, we created a web-based competition platform and hosted a machine learning competition to develop ML models for classifying the severity of EEG background patterns in newborns. After the competition closed, the top 4 performing models were evaluated offline on a separate held-out validation dataset. Although a feature-based model ranked first on the testing dataset, deep learning models generalised better on the validation sets. All methods had a significant decline in validation performance compared to the testing performance. This highlights the challenges for model generalisation on unseen data, emphasising the need for held-out validation datasets in ML studies with neonatal EEG. The study underscores the importance of training ML models on large and diverse datasets to ensure robust generalisation. The competition's outcome demonstrates the potential for open-access data and collaborative ML development to foster a collaborative research environment and expedite the development of clinical decision-support tools for neonatal neuromonitoring.