arXiv subjects

Antonio R. Linero

Publications and source records attributed to Antonio R. Linero.

At least 19 recordsLinked to original sources

arXiv2026

Conditional Distribution Estimation for Functional Responses with Random Forests

Many functional data analyses reduce random functions to scalar summaries or conditional mean curves. This is limiting when we wish to understand how covariates affect the distribution of entire functional responses, including their shape, timing, or variability. We study the problem of estimating conditional laws of functional outcomes and show that these objects can be estimated and evaluated in a practical nonparametric framework. To do this, we introduce functional distributional random forests, which estimate each conditional law as a covariate-dependent distribution over sampled functions by training a random forest to minimize a kernel-based maximum mean discrepancy within the leaf nodes of the decision tree. This supports inference on arbitrary functionals of the conditional distribution while keeping predictive samples tied to realistic curves. We consider a variety of kernels defined on function spaces, including Sobolev and operator-induced kernels. We also provide conditions for consistency of our estimator and develop scoring rules for comparing it to baseline estimators. In simulations, our method recovers distributional changes that are missed by baseline methods. In an application to NHANES accelerometer data, it identifies interesting covariate-associated changes in both median activity profiles and predictive dispersion.

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arXiv2026

A Simple Example of Bayesian Nonparametric Inconsistency

I present a very simple example in which a full-support prior over distribution functions has an inconsistent posterior, which I believe has instructive value. The example is $Y_i \stackrel{\text{iid}}{\sim} P_0$ under the Bayesian hierarchical model $[Y_i \mid P] \stackrel{\text{iid}}{\sim} P$ and $P \sim \int \mbox{DP}(α, H) \, π_α(α) \ dα$ when $π_α(\cdot)$ has exponential (or heavier) tails, where $\mbox{DP}(α, H)$ denotes a Dirichlet process with concentration parameter $α$ and mean $H(\cdot)$; on the other hand, consistency is obtained under a light-tailed prior. This unifies and generalizes a consistency result of Freedman and Diaconis (1983) with an inconsistency result described by Ferguson et al. (1992).

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arXiv2026

Bayesian Causal Machine Learning for Cure Models

In survival studies, treatments can benefit patients through different mechanisms: a treatment may increase the probability of being cured or delay failure among patients who are not cured. Quantifying which mechanism is dominant, and whether it varies across subpopulations, is clinically important, yet there is limited work in the causal machine learning literature addressing this problem. Standard causal survival learners target finite-horizon survival or restricted mean survival time, while many cure models capture cure structures without estimating causal effects. In this work, we define meaningful causal effects in the presence of a cured subpopulation and introduce BartCure, a Bayesian causal machine learning approach for estimating them. The causal effects we recommend decompose the causal effect on restricted mean survival time into a stochastic cure and stochastic latency component, and we relate these new effects to both stochastic intervention effects and causal effects in principal strata. In simulations, BartCure is competitive for estimating average effects and is especially effective at conservatively detecting the direction of treatment-effect heterogeneity. We apply BartCure to estimate average and subgroup causal effects and to identify treatment effect heterogeneity in the CALGB 40101 breast cancer trial.

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arXiv2026

Defensive Model Expansion for Robust Bayesian Inference

Some applied researchers hesitate to use nonparametric methods, worrying that they will lose power in small samples or overfit the data when simpler models are sufficient. We argue that at least some of these concerns are unfounded when nonparametric models are strongly shrunk toward parametric submodels. We consider expanding a parametric model with a nonparametric component $r(x)$ that is heavily shrunk toward zero. This construction allows the model to adapt automatically: if the parametric model is correct, the nonparametric component disappears, recovering parametric efficiency, while if it is misspecified, the flexible component activates to capture the missing signal. We show that this adaptive behavior follows from simple and general conditions. Specifically, we prove that Bayesian nonparametric models anchored to linear regression, including variants of Gaussian process regression and Bayesian additive regression trees, consistently identify the correct parametric submodel when it holds and give asymptotically efficient inference for regression coefficients. In simulations, we find that the general BART model performs identically to correctly specified linear regression when the parametric model holds, and substantially outperforms it when nonlinear effects are present. This suggests a practical paradigm: defensive model expansion as a safeguard against model misspecification.

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arXiv2026

Bayesian Additive Distribution Regression

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on individual measurements. We introduce DistBART, a Bayesian nonparametric approach to distribution regression that models the regression function as a linear functional with the Riesz representer assigned a Bayesian additive regression trees (BART) prior. We argue that shallow decision tree ensembles encode reasonable inductive biases for tabular data, making them appropriate in settings where the functional depends primarily on low-dimensional marginals of the distributions. We show this both empirically on synthetic and real data and theoretically through an adaptive posterior concentration result. We also establish connections to kernel methods, and use this connection to motivate variants of DistBART that can learn nonlinear functionals. To enable scalability to large datasets, we develop a random-feature approximation that samples trees from the BART prior and reduces inference to sparse Bayesian linear regression, achieving computational efficiency while retaining uncertainty quantification.

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arXiv2025

Decision Theoretic Subgroup Detection With Bayesian Machine Learning

We consider the problem of identifying promising subpopulations in terms of treatment effectiveness or treatment effect heterogeneity, from a Bayesian decision theoretic perspective. We first show that a straight-forward application of Bayesian decision theory to subgroup detection leads to a counter-intuitive risk-seeking (RS) behavior. Motivated by this observation, we introduce the Bayesian Risk-Aware Inference and Detection of Subgroups (BRAIDS) utility and use it to perform subgroup selection and post selection inference. The BRAIDS utility interpolates between risk-seeking (RS) and risk-averse (RA) identifications of subgroups, with a variant of the virtual twins algorithm as its risk-neutral midpoint. We also argue that effective subgroup estimation and inference requires the use of regularization priors to safeguard inferences from the winner's curse. We provide empirical evidence that posterior credible intervals for subgroup effects can still obtain nominal coverage levels, provided that an appropriate prior distribution is chosen. The proposed framework is illustrated on data from clinical trial assessing the efficacy of canagliflozin as a treatment for type 2 diabetes.

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arXiv2025

A Unified Bayesian Nonparametric Framework for Ordinal, Survival, and Density Regression Using the Complementary Log-Log Link

In this work, we develop applications of the complementary log-log (cloglog) link to problems in Bayesian nonparametrics. Although less commonly used than the probit or logit links, we find that the cloglog link is computationally and theoretically well-suited to several commonly used Bayesian nonparametric methods. Our starting point is a Bayesian nonparametric model for ordinal regression. We first review how the cloglog link uniquely sits at the intersection of the cumulative link and continuation ratio approaches to ordinal regression. Then, we develop a convenient computational method for fitting these ordinal models using Bayesian additive regression trees. Next, we use our ordinal regression model to build a Bayesian nonparametric stick-breaking process and show that, under a proportional hazards assumption, our stick-breaking process can be used to construct a weight-dependent Dirichlet process mixture model. Again, Bayesian additive regression trees lead to convenient computations. We then extend these models to allow for Bayesian nonparametric survival analysis in both discrete and continuous time. Our models have desirable theoretical properties, and we illustrate this analyzing the posterior contraction rate of our ordinal models. Finally, we demonstrate the practical utility of our cloglog models through a series of illustrative examples.

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arXiv2024

Analysis of spatially clustered survival data with unobserved covariates using SBART

Usual parametric and semi-parametric regression methods are inappropriate and inadequate for large clustered survival studies when the appropriate functional forms of the covariates and their interactions in hazard functions are unknown, and random cluster effects and cluster-level covariates are spatially correlated. We present a general nonparametric method for such studies under the Bayesian ensemble learning paradigm called Soft Bayesian Additive Regression Trees. Our methodological and computational challenges include large number of clusters, variable cluster sizes, and proper statistical augmentation of the unobservable cluster-level covariate using a data registry different from the main survival study. We use an innovative 3-step approach based on latent variables to address our computational challenges. We illustrate our method and its advantages over existing methods by assessing the impacts of intervention in some county-level and patient-level covariates to mitigate existing racial disparity in breast cancer survival in 67 Florida counties (clusters) using two different data resources. Florida Cancer Registry (FCR) is used to obtain clustered survival data with patient-level covariates, and the Behavioral Risk Factor Surveillance Survey (BRFSS) is used to obtain further data information on an unobservable county-level covariate of Screening Mammography Utilization (SMU).

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arXiv2024

Relative Survival Analysis Using Bayesian Decision Tree Ensembles

In cancer epidemiology, the \emph{relative survival framework} is used to quantify the hazard associated with cancer by comparing the all-cause mortality hazard in cancer patients to that of the general population. This framework assumes that an individual's hazard function is the sum of a known population hazard and an excess hazard associated with the cancer. Several estimands are derived from the excess hazard, including the \emph{net survival}, which are used to inform decisions and to assess the effectiveness of interventions on cancer management. In this paper, we introduce a Bayesian machine learning approach to estimating the excess hazard and identifying vulnerable subgroups, with a higher excess risk, using Bayesian additive regression trees (BART). We first develop a proportional hazards extension of the BART model to the relative survival setting, and then extend this model to non-proportional hazards. We develop tools for model interpretation and posterior summarization and then present an application using colon cancer data from England, highlighting the insights our proposed methodology offers when paired with state-of-the-art data linkage methods. This application demonstrates how these methods can be used to identify drivers of inequalities in cancer survival through variable importance quantification.

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arXiv2024

Bayesian Nonparametric Quasi Likelihood

A recent trend in Bayesian research has been revisiting generalizations of the likelihood that enable Bayesian inference without requiring the specification of a model for the data generating mechanism. This paper focuses on a Bayesian nonparametric extension of Wedderburn's quasi-likelihood, using Bayesian additive regression trees to model the mean function. Here, the analyst posits only a structural relationship between the mean and variance of the outcome. We show that this approach provides a unified, computationally efficient, framework for extending Bayesian decision tree ensembles to many new settings, including simplex-valued and heavily heteroskedastic data. We also introduce Bayesian strategies for inferring the dispersion parameter of the quasi-likelihood, a task which is complicated by the fact that the quasi-likelihood itself does not contain information about this parameter; despite these challenges, we are able to inject updates for the dispersion parameter into a Markov chain Monte Carlo inference scheme in a way that, in the parametric setting, leads to a Bernstein-von Mises result for the stationary distribution of the resulting Markov chain. We illustrate the utility of our approach on a variety of both synthetic and non-synthetic datasets.

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arXiv2023

Estimating Heterogeneous Causal Mediation Effects with Bayesian Decision Tree Ensembles

The causal inference literature has increasingly recognized that explicitly targeting treatment effect heterogeneity can lead to improved scientific understanding and policy recommendations. Towards the same ends, studying the causal pathway connecting the treatment to the outcome can be also useful. This paper addresses these problems in the context of \emph{causal mediation analysis}. We introduce a varying coefficient model based on Bayesian additive regression trees to identify and regularize heterogeneous causal mediation effects; analogously with linear structural equation models, these effects correspond to covariate-dependent products of coefficients. We show that, even on large datasets with few covariates, LSEMs can produce highly unstable estimates of the conditional average direct and indirect effects, while our \emph{Bayesian causal mediation forests} model produces estimates that are stable. We find that our approach is conservative, with effect estimates ``shrunk towards homogeneity.'' We examine the salient properties of our method using both data from the Medical Expenditure Panel Survey and empirically-grounded simulated data. Finally, we show how our model can be combined with posterior summarization strategies to identify interesting subgroups and interpret the model fit.

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arXiv2022

SoftBart: Soft Bayesian Additive Regression Trees

Bayesian additive regression tree (BART) models have seen increased attention in recent years as a general-purpose nonparametric modeling technique. BART combines the flexibility of modern machine learning techniques with the principled uncertainty quantification of Bayesian inference, and it has been shown to be uniquely appropriate for addressing the high-noise problems that occur commonly in many areas of science, including medicine and the social sciences. This paper introduces the SoftBart package for fitting the Soft BART algorithm of Linero and Yang (2018). In addition to improving upon the predictive performance of other BART packages, a major goal of this package has been to facilitate the inclusion of BART in larger models, making it ideal for researchers in Bayesian statistics. I show both how to use this package for standard prediction tasks and how to embed BART models in larger models; I illustrate by using SoftBart to implement a nonparametric probit regression model, a semiparametric varying coefficient model, and a partial linear model.

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arXiv2022

Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy

Bayesian additive regression trees have seen increased interest in recent years due to their ability to combine machine learning techniques with principled uncertainty quantification. The Bayesian backfitting algorithm used to fit BART models, however, limits their application to a small class of models for which conditional conjugacy exists. In this article, we greatly expand the domain of applicability of BART to arbitrary \emph{generalized BART} models by introducing a very simple, tuning-parameter-free, reversible jump Markov chain Monte Carlo algorithm. Our algorithm requires only that the user be able to compute the likelihood and (optionally) its gradient and Fisher information. The potential applications are very broad; we consider examples in survival analysis, structured heteroskedastic regression, and gamma shape regression.

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arXiv2022

Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our model is flexible, has a default prior specification, and is computationally convenient. To address the distinguished role of the response in the BART model we propose, we further introduce an approach to targeted smoothing which is possibly of independent interest for BART models. We study the proposed model theoretically and provide sufficient conditions for the posterior distribution to concentrate at close to the minimax optimal rate adaptively over smoothness classes in the high-dimensional regime in which many predictors are irrelevant. To fit our model we propose a data augmentation algorithm which allows for existing BART samplers to be extended with minimal effort. We illustrate the performance of our methodology on simulated data and use it to study the relationship between education and body mass index using data from the medical expenditure panel survey (MEPS).

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arXiv2022

The How and Why of Bayesian Nonparametric Causal Inference

Spurred on by recent successes in causal inference competitions, Bayesian nonparametric (and high-dimensional) methods have recently seen increased attention in the causal inference literature. In this paper, we present a comprehensive overview of Bayesian nonparametric applications to causal inference. Our aims are to (i) introduce the fundamental Bayesian nonparametric toolkit; (ii) discuss how to determine which tool is most appropriate for a given problem; and (iii) show how to avoid common pitfalls in applying Bayesian nonparametric methods in high-dimensional settings. Unlike standard fixed-dimensional parametric problems, where outcome modeling alone can sometimes be effective, we argue that most of the time it is necessary to model both the selection and outcome processes.

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arXiv2021

Causal Mediation and Sensitivity Analysis for Mixed-Scale Data

The goal of causal mediation analysis, often described within the potential outcomes framework, is to decompose the effect of an exposure on an outcome of interest along different causal pathways. Using the assumption of sequential ignorability to attain non-parametric identification, Imai et al. (2010) proposed a flexible approach to measuring mediation effects, focusing on parametric and semiparametric normal/Bernoulli models for the outcome and mediator. Less attention has been paid to the case where the outcome and/or mediator model are mixed-scale, ordinal, or otherwise fall outside the normal/Bernoulli setting. We develop a simple, but flexible, parametric modeling framework to accommodate the common situation where the responses are mixed continuous and binary, and apply it to a zero-one inflated beta model for the outcome and mediator. Applying our proposed methods to a publicly-available JOBS II dataset, we (i) argue for the need for non-normal models, (ii) show how to estimate both average and quantile mediation effects for boundary-censored data, and (iii) show how to conduct a meaningful sensitivity analysis by introducing unidentified, scientifically meaningful, sensitivity parameters.

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arXiv2021

In Nonparametric and High-Dimensional Models, Bayesian Ignorability is an Informative Prior

In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process which generates the response and the missing data mechanism which determines the data we observe. Under the ignorability condition of Rubin (1976), however, likelihood-based inference for the outcome process does not depend on the missing data mechanism so that only the former needs to be estimated; partially because of this simplification, ignorability is often used as a baseline assumption. We study the implications of Bayesian ignorability in the presence of high-dimensional nuisance parameters and argue that ignorability is typically incompatible with sensible prior beliefs about the amount of selection bias. We show that, for many problems, ignorability directly implies that the prior on the selection bias is tightly concentrated around zero. This is demonstrated on several models of practical interest, and the effect of ignorability on the posterior distribution is characterized for high-dimensional linear models with a ridge regression prior. We then show both how to build high-dimensional models which encode sensible beliefs about the selection bias and also show that under certain narrow circumstances ignorability is less problematic.

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arXiv2021

Semiparametric analysis of clustered interval-censored survival data using Soft Bayesian Additive Regression Trees (SBART)

Popular parametric and semiparametric hazards regression models for clustered survival data are inappropriate and inadequate when the unknown effects of different covariates and clustering are complex. This calls for a flexible modeling framework to yield efficient survival prediction. Moreover, for some survival studies involving time to occurrence of some asymptomatic events, survival times are typically interval censored between consecutive clinical inspections. In this article, we propose a robust semiparametric model for clustered interval-censored survival data under a paradigm of Bayesian ensemble learning, called Soft Bayesian Additive Regression Trees or SBART (Linero and Yang, 2018), which combines multiple sparse (soft) decision trees to attain excellent predictive accuracy. We develop a novel semiparametric hazards regression model by modeling the hazard function as a product of a parametric baseline hazard function and a nonparametric component that uses SBART to incorporate clustering, unknown functional forms of the main effects, and interaction effects of various covariates. In addition to being applicable for left-censored, right-censored, and interval-censored survival data, our methodology is implemented using a data augmentation scheme which allows for existing Bayesian backfitting algorithms to be used. We illustrate the practical implementation and advantages of our method via simulation studies and an analysis of a prostate cancer surgery study where dependence on the experience and skill level of the physicians leads to clustering of survival times. We conclude by discussing our method's applicability in studies involving high dimensional data with complex underlying associations.

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