arXiv subjects

Carlos García Meixide

Publications and source records attributed to Carlos García Meixide.

9 recordsLinked to original sources

arXiv2026

Shrinkage through multiple identifiability

We propose an empirical Bayes framework for combining estimators obtained from multiple identification functionals associated with the same estimand. We adaptively pool a collection of asymptotically linear estimators, each of which may target a different parameter because of violations of their identification assumptions. Although all estimators are computed from the same sample and are therefore dependent, we show that a working independence construction preserves consistency of the posterior mean under centered heterogeneity. Inference is driven by a latent heterogeneity parameter governing the dispersion of the different identification images. When this parameter is zero, the functionals share a common estimand and we construct frequentist confidence intervals using either sandwich variance estimation or subsampling. When it is positive, the functionals are interpreted as exchangeable draws from a latent population of causal effects, and we construct asymptotically valid Bayesian prediction intervals for the latent target of a new identification functional. These inferential procedures answer different questions, rely on distinct assumptions, and are therefore complementary rather than competing. We illustrate the framework by augmenting evidence from randomized controlled trials with observational studies.

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arXiv2026

Causal inference via implied interventions

In the context of having an instrumental variable, the standard practice in causal inference begins by targeting an effect of interest and proceeds by formulating assumptions enabling its identification. We turn this around by adhering to the interventions the observational distribution allows to identify, rather than starting with a desired causal estimand and imposing untestable conditions. The randomization of an instrument and its exclusion restriction define a class of auxiliary stochastic interventions on the treatment that are implied by stochastic interventions on the instrument. This mapping characterizes the identifiable causal effects of the treatment on the outcome given the observable distribution. The identified effect is the impact of a stochastic encouragement by the instrument that propagates through the unaltered treatment selection mechanism, rather than the effect of a hypothetical intervention that overrides how treatment is naturally chosen. Alternatively, searching for an intervention on the instrument whose implied one best approximates a desired target naturally leads to a projection representing the closest identifiable treatment effect. The generality of this projection allows to select different norms and indexing functional sets that give rise to diverse estimation problems, some of which we address using Expectation-Maximization and the Highly Adaptive Lasso.

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arXiv2026

Highly Adaptive Principal Component Regression

The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions due to the large design matrix it requires. The Highly Adaptive Ridge (HAR) has been proposed as a related ridge-regularized analogue. Building on both procedures, we introduce the Principal Component Highly Adaptive Lasso (PCHAL) and Principal Component Highly Adaptive Ridge (PCHAR). These estimators use an outcome-blind principal-component reduction of the HAL basis, offering substantial computational gains over HAL while achieving empirical performance comparable to HAL and HAR. We also describe an early-stopped gradient descent variant, which provides a convenient form of smooth spectral regularization without explicitly selecting a hard principal-component cutoff. Finally, we uncover that under special circumstances, the HAL kernel is identical to the covariance function of Brownian motion.

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arXiv2026

Highly Adaptive Empirical Risk Minimization with Principal Components

The Highly Adaptive Lasso (HAL) delivers unprecedented guarantees in nonparametric minimum loss estimation under minimal smoothness assumptions, such as dimension-free minimax optimal rates. However, the practical use of HAL has been severely limited by its exponentially growing computationally prohibitive indicator basis expansion in moderate to high dimensions. Existing screening strategies drastically reduce this dimension but lack any theoretical justification. We introduce the Principal Component Highly Adaptive (PC-HA) family of estimators, which for the first time provide a principled and theoretically valid dimension reduction. We establish formal results on the score equations solved by these PC-HA estimators, allowing to transfer plug-in efficiency and pointwise asymptotic normality results from HAL to these PC-HA estimators, under comparable complexity control.

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arXiv2025

Predictive posteriors under hidden confounding

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the distribution shift across domains, or bias-inducing regularization schemes to enhance generalization. While recent developments in point prediction under hidden confounding attempt to mitigate these shortcomings, they generally do not provide principled uncertainty quantification. We introduce a Bayesian framework that yields well-calibrated predictive distributions across external domains, supports valid model inference, and achieves posterior contraction rates that improve as the number of observed datasets increases. Simulations and a medical application highlight the remarkable empirical coverage of our approach, nearly unchanged when transitioning from low- to moderate-dimensional settings.

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arXiv2025

Covariance as a commutator

The covariance between real finite variance random variables can be expressed as the commutator of taking expectations and multiplying, both viewed as operators extended to act jointly on pairs of functions. The efficient influence curve of the mean represents a centering operator which we demonstrate to interact with expectations and products through simple commutator identities. These expressions reveal an underlying Lie algebraic structure that endows the calculus of efficient influence curves with a natural differential geometric interpretation.

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arXiv2025

Unsupervised domain adaptation under hidden confounding

We introduce a new predictive mechanism that operates in the presence of hidden confounding across distributionally diverse data sources while ensuring consistent estimation of causal parameters-despite their recognized suboptimality for prediction in the literature. Our method is based on a novel estimand that captures the dependence structure between response noise and covariates, incorporating causal parameters into a generative model that adaptively replicates the conditional distribution of the test environment. Identifiability is achieved under a straightforward, empirically verifiable assumption. Our approach ensures probabilistic alignment with test distributions uniformly across arbitrary interventions, enabling valid predictions without requiring worst-case optimization or assumptions about the strength of perturbations at test time. Through extensive simulations, we demonstrate that our method outperforms state-of-the-art invariance-based and domain adaptation approaches. Additionally, we validate its practical applicability and superior target risk performance on a cardiovascular disease dataset.

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arXiv2025

Uncertainty quantification for intervals

Data following an interval structure are increasingly prevalent in many scientific applications. In medicine, clinical events are often monitored between two clinical visits, making the exact time of the event unknown and generating outcomes with a range format. As interest in automating healthcare decisions grows, uncertainty quantification via predictive regions becomes essential for developing reliable and trustworthy predictive algorithms. However, the statistical literature currently lacks a general methodology for interval targets, especially when these outcomes are incomplete due to censoring. We propose an uncertainty quantification algorithm for interval responses and establish its theoretical properties using empirical process arguments based on a newly developed class of functions specifically designed for these interval data structures. Although this paper primarily focuses on deriving predictive regions for interval-censored data, the approach can also be applied to other statistical modeling tasks, such as goodness-of-fit assessments. Finally, the applicability of the method is demonstrated through simulations, showing up to a 60\% improvement in conditional coverage. Our new algorithm is also applied to various biomedical contexts, including two clinical examples: i) sleep duration and its association with cardiovascular diseases, and ii) survival time in relation to physical activity levels.

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arXiv2024

Neural interval-censored survival regression with feature selection

Survival analysis is a fundamental area of focus in biomedical research, particularly in the context of personalized medicine. This prominence is due to the increasing prevalence of large and high-dimensional datasets, such as omics and medical image data. However, the literature on non-linear regression algorithms and variable selection techniques for interval-censoring is either limited or non-existent, particularly in the context of neural networks. Our objective is to introduce a novel predictive framework tailored for interval-censored regression tasks, rooted in Accelerated Failure Time (AFT) models. Our strategy comprises two key components: i) a variable selection phase leveraging recent advances on sparse neural network architectures, ii) a regression model targeting prediction of the interval-censored response. To assess the performance of our novel algorithm, we conducted a comprehensive evaluation through both numerical experiments and real-world applications that encompass scenarios related to diabetes and physical activity. Our results outperform traditional AFT algorithms, particularly in scenarios featuring non-linear relationships.

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