arXiv subjects

Eric V. Strobl

Publications and source records attributed to Eric V. Strobl.

At least 19 recordsLinked to original sources

arXiv2026

COMPACT: Spectral Adjustment Scores from a Complete and Irreducible Causal Criterion

Observational datasets frequently contain many baseline variables, yet investigators estimating causal effects may not know which variables to include in the adjustment set. Confounding information may also be distributed weakly across many variables. Propensity scores can simplify adjustment by reducing high-dimensional covariates to a scalar with binary treatment. Although the propensity score is the coarsest balancing score, this distributional optimality does not imply maximal specificity over causal graphs. We instead examine all causal graphs among a candidate score, treatment, and outcome while allowing latent variables. Under faithfulness, we identify the largest set of unconditional and conditional dependence relations whose truth is invariant to whether treatment causes the outcome, leaving treatment-effect estimation to the downstream analysis. This criterion defines the maximally specific graph class expressible through these relations. We then develop the proposed algorithm, which operationalizes the criterion through a generalized eigenvalue problem whose score space targets the span of a balancing coordinate and an outcome-guided coordinate. We show that sufficiently informative proxies can recover this span without direct observation of the adjustment variables, characterize the resulting estimation and causal errors, and establish bootstrap validity for the complete procedure. Simulations and a real-data application demonstrate superior performance over several alternatives.

stat.ME↗

arXiv2026

Fast Nonparametric Conditional Independence Testing via Two-Stage Regression

Constraint-based causal discovery relies on repeated conditional independence tests, but fast nonparametric tests often sacrifice calibration, especially when variables depend on the conditioning set through nonlinear relationships. We introduce BLITZ (Broad-to-Local Independence Testing via residualiZation), a nonparametric conditional independence test designed to run well under a second while maintaining the accuracy needed for the thousands of queries performed by constraint-based causal discovery algorithms. BLITZ first removes broad smooth dependence on the conditioning set using low-order polynomial regression, then applies a small nonlinear feature map and residualizes those features with shallow tree regressions. The resulting statistic tests residual cross-covariance, with a moment-matched chi-square approximation to the null distribution. We show theoretically that the two-stage design reduces the effective complexity faced by the tree residualizers, allowing shallow trees to control residual conditional-mean bias while avoiding excessive overfitting. In simulations, BLITZ provides better null calibration than fast kernel, random-feature, and regression-based competitors while remaining among the fastest methods tested. In causal discovery experiments on synthetic graphs and flow-cytometry data, BLITZ yields more reliable endpoint orientations among retained adjacencies and competitive structural recovery. These results suggest that broad-to-local residualization is a practical route to calibrated, scalable nonparametric conditional independence testing for causal discovery.

stat.ML↗

arXiv2026

Global Interpretability via Automated Preprocessing: A Framework Inspired by Psychiatric Questionnaires

Psychiatric questionnaires are highly context sensitive and often only weakly predict subsequent symptom severity, which makes the prognostic relationship difficult to learn. Although flexible nonlinear models can improve predictive accuracy, their limited interpretability can erode clinical trust. In fields such as imaging and omics, investigators commonly address visit- and instrument-specific artifacts by extracting stable signal through preprocessing and then fitting an interpretable linear model. We adopt the same strategy for questionnaire data by decoupling preprocessing from prediction: REFINE (Redundancy-Exploiting Follow-up-Informed Nonlinear Enhancement) uses follow-up information to learn a nonlinear, item-aligned preprocessing of baseline measurements, and then maps these stabilized baseline items to future severity through a linear coefficient matrix. This construction constrains where nonlinearity enters rather than restricting the end-to-end predictive function class, allowing the prognostic relationship to remain globally interpretable through a single coefficient matrix rather than through post hoc local attributions. In the population, the resulting predictor recovers the Bayes-optimal conditional mean, so global linear interpretability does not require sacrificing nonlinear predictive flexibility. In experiments, REFINE outperforms other interpretable approaches while preserving clear global attribution of prognostic factors across psychiatric and non-psychiatric longitudinal prediction tasks.

cs.LG↗

arXiv2026

Extracting Root-Causal Brain Activity Driving Psychopathology from Resting State fMRI

Neuroimaging studies of psychiatric disorders often correlate imaging patterns with diagnostic labels or composite symptom scores, yielding diffuse associations that obscure underlying mechanisms. We instead seek to identify root-causal maps -- localized BOLD disturbances that initiate pathological cascades -- and to link them selectively to symptom dimensions. We introduce a bilevel structural causal model that connects between-subject symptom structure to within-subject resting-state fMRI via independent latent sources with localized direct effects. Based on this model, we develop SOURCE (Symptom-Oriented Uncovering of Root-Causal Elements), a procedure that links interpretable symptom axes to a parsimonious set of localized drivers. Experiments show that SOURCE recovers localized maps consistent with root-causal BOLD drivers and increases interpretability and anatomical specificity relative to existing comparators.

eess.IV↗

arXiv2025

A tutorial on discovering and quantifying the effect of latent causal sources of multimodal EHR data

We provide an accessible description of a peer-reviewed generalizable causal machine learning pipeline to (i) discover latent causal sources of large-scale electronic health records observations, and (ii) quantify the source causal effects on clinical outcomes. We illustrate how imperfect multimodal clinical data can be processed, decomposed into probabilistic independent latent sources, and used to train taskspecific causal models from which individual causal effects can be estimated. We summarize the findings of the two real-world applications of the approach to date as a demonstration of its versatility and utility for medical discovery at scale.

cs.LG↗

arXiv2025

Learning Causally Predictable Outcomes from Psychiatric Longitudinal Data

Causal inference in longitudinal biomedical data remains a central challenge, especially in psychiatry, where symptom heterogeneity and latent confounding frequently undermine classical estimators. Most existing methods for treatment effect estimation presuppose a fixed outcome variable and address confounding through observed covariate adjustment. However, the assumption of unconfoundedness may not hold for a fixed outcome in practice. To address this foundational limitation, we directly optimize the outcome definition to maximize causal identifiability. Our DEBIAS (Durable Effects with Backdoor-Invariant Aggregated Symptoms) algorithm learns non-negative, clinically interpretable weights for outcome aggregation, maximizing durable treatment effects and empirically minimizing both observed and latent confounding by leveraging the time-limited direct effects of prior treatments in psychiatric longitudinal data. The algorithm also furnishes an empirically verifiable test for outcome unconfoundedness. DEBIAS consistently outperforms state-of-the-art methods in recovering causal effects for clinically interpretable composite outcomes across comprehensive experiments in depression and schizophrenia.

cs.LG↗

arXiv2025

A data-driven approach to discover and quantify systemic lupus erythematosus etiological heterogeneity from electronic health records

Systemic lupus erythematosus (SLE) is a complex heterogeneous disease with many manifestational facets. We propose a data-driven approach to discover probabilistic independent sources from multimodal imperfect EHR data. These sources represent exogenous variables in the data generation process causal graph that estimate latent root causes of the presence of SLE in the health record. We objectively evaluated the sources against the original variables from which they were discovered by training supervised models to discriminate SLE from negative health records using a reduced set of labelled instances. We found 19 predictive sources with high clinical validity and whose EHR signatures define independent factors of SLE heterogeneity. Using the sources as input patient data representation enables models to provide with rich explanations that better capture the clinical reasons why a particular record is (not) an SLE case. Providers may be willing to trade patient-level interpretability for discrimination especially in challenging cases.

cs.LG↗

arXiv2024

Unsupervised Discovery of Clinical Disease Signatures Using Probabilistic Independence

Insufficiently precise diagnosis of clinical disease is likely responsible for many treatment failures, even for common conditions and treatments. With a large enough dataset, it may be possible to use unsupervised machine learning to define clinical disease patterns more precisely. We present an approach to learning these patterns by using probabilistic independence to disentangle the imprint on the medical record of causal latent sources of disease. We inferred a broad set of 2000 clinical signatures of latent sources from 9195 variables in 269,099 Electronic Health Records. The learned signatures produced better discrimination than the original variables in a lung cancer prediction task unknown to the inference algorithm, predicting 3-year malignancy in patients with no history of cancer before a solitary lung nodule was discovered. More importantly, the signatures' greater explanatory power identified pre-nodule signatures of apparently undiagnosed cancer in many of those patients.

cs.LG↗

arXiv2023

Why Do Probabilistic Clinical Models Fail To Transport Between Sites?

The rising popularity of artificial intelligence in healthcare is highlighting the problem that a computational model achieving super-human clinical performance at its training sites may perform substantially worse at new sites. In this perspective, we present common sources for this failure to transport, which we divide into sources under the control of the experimenter and sources inherent to the clinical data-generating process. Of the inherent sources we look a little deeper into site-specific clinical practices that can affect the data distribution, and propose a potential solution intended to isolate the imprint of those practices on the data from the patterns of disease cause and effect that are the usual target of probabilistic clinical models.

cs.LG↗

arXiv2023

Root Causal Inference from Single Cell RNA Sequencing with the Negative Binomial

Accurately inferring the root causes of disease from sequencing data can improve the discovery of novel therapeutic targets. However, existing root causal inference algorithms require perfectly measured continuous random variables. Single cell RNA sequencing (scRNA-seq) datasets contain large numbers of cells but non-negative counts measured by an error prone process. We therefore introduce an algorithm called Root Causal Inference with Negative Binomials (RCI-NB) that accounts for count-based measurement error by separating negative binomial distributions into their gamma and Poisson components; the gamma distributions form a fully identifiable but latent post non-linear causal model representing the true RNA expression levels, which we only observe with Poisson corruption. RCI-NB identifies patient-specific root causal contributions from scRNA-seq datasets by integrating novel sparse regression and goodness of fit testing procedures that bypass Poisson measurement error. Experiments demonstrate significant improvements over existing alternatives.

q-bio.GN↗

arXiv2023

Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Model

Complex diseases are caused by a multitude of factors that may differ between patients even within the same diagnostic category. A few underlying root causes may nevertheless initiate the development of disease within each patient. We therefore focus on identifying patient-specific root causes of disease, which we equate to the sample-specific predictivity of the exogenous error terms in a structural equation model. We generalize from the linear setting to the heteroscedastic noise model where $Y = m(X) + \varepsilonσ(X)$ with non-linear functions $m(X)$ and $σ(X)$ representing the conditional mean and mean absolute deviation, respectively. This model preserves identifiability but introduces non-trivial challenges that require a customized algorithm called Generalized Root Causal Inference (GRCI) to extract the error terms correctly. GRCI recovers patient-specific root causes more accurately than existing alternatives.

stat.ML↗

arXiv2023

Counterfactual Formulation of Patient-Specific Root Causes of Disease

Root causes of disease intuitively correspond to root vertices that increase the likelihood of a diagnosis. This description of a root cause nevertheless lacks the rigorous mathematical formulation needed for the development of computer algorithms designed to automatically detect root causes from data. Prior work defined patient-specific root causes of disease using an interventionalist account that only climbs to the second rung of Pearl's Ladder of Causation. In this theoretical piece, we climb to the third rung by proposing a counterfactual definition matching clinical intuition based on fixed factual data alone. We then show how to assign a root causal contribution score to each variable using Shapley values from explainable artificial intelligence. The proposed counterfactual formulation of patient-specific root causes of disease accounts for noisy labels, adapts to disease prevalence and admits fast computation without the need for counterfactual simulation.

cs.AI↗

arXiv2022

Generalizing Clinical Trials with Convex Hulls

Randomized clinical trials eliminate confounding but impose strict exclusion criteria that limit recruitment to a subset of the population. Observational datasets are more inclusive but suffer from confounding -- often providing overly optimistic estimates of treatment response over time due to partially optimized physician prescribing patterns. We therefore assume that the unconfounded treatment response lies somewhere in-between the observational estimate before and the observational estimate after treatment assignment. This assumption allows us to extrapolate results from exclusive trials to the broader population by analyzing observational and trial data simultaneously using an algorithm called Optimum in Convex Hulls (OCH). OCH represents the treatment effect either in terms of convex hulls of conditional expectations or convex hulls (also known as mixtures) of conditional densities. The algorithm first learns the component expectations or densities using the observational data and then learns the linear mixing coefficients using trial data in order to approximate the true treatment effect; theory importantly explains why this linear combination should hold. OCH estimates the treatment effect in terms both expectations and densities with state of the art accuracy.

stat.ML↗

arXiv2022

Sample-Specific Root Causal Inference with Latent Variables

Root causal analysis seeks to identify the set of initial perturbations that induce an unwanted outcome. In prior work, we defined sample-specific root causes of disease using exogenous error terms that predict a diagnosis in a structural equation model. We rigorously quantified predictivity using Shapley values. However, the associated algorithms for inferring root causes assume no latent confounding. We relax this assumption by permitting confounding among the predictors. We then introduce a corresponding procedure called Extract Errors with Latents (EEL) for recovering the error terms up to contamination by vertices on certain paths under the linear non-Gaussian acyclic model. EEL also identifies the smallest sets of dependent errors for fast computation of the Shapley values. The algorithm bypasses the hard problem of estimating the underlying causal graph in both cases. Experiments highlight the superior accuracy and robustness of EEL relative to its predecessors.

stat.ML↗

arXiv2022

Identifying Patient-Specific Root Causes of Disease

Complex diseases are caused by a multitude of factors that may differ between patients. As a result, hypothesis tests comparing all patients to all healthy controls can detect many significant variables with inconsequential effect sizes. A few highly predictive root causes may nevertheless generate disease within each patient. In this paper, we define patient-specific root causes as variables subject to exogenous "shocks" which go on to perturb an otherwise healthy system and induce disease. In other words, the variables are associated with the exogenous errors of a structural equation model (SEM), and these errors predict a downstream diagnostic label. We quantify predictivity using sample-specific Shapley values. This derivation allows us to develop a fast algorithm called Root Causal Inference for identifying patient-specific root causes by extracting the error terms of a linear SEM and then computing the Shapley value associated with each error. Experiments highlight considerable improvements in accuracy because the method uncovers root causes that may have large effect sizes at the individual level but clinically insignificant effect sizes at the group level. An R implementation is available at github.com/ericstrobl/RCI.

stat.ML↗

arXiv2021

Dirac Delta Regression: Conditional Density Estimation with Clinical Trials

Personalized medicine seeks to identify the causal effect of treatment for a particular patient as opposed to a clinical population at large. Most investigators estimate such personalized treatment effects by regressing the outcome of a randomized clinical trial (RCT) on patient covariates. The realized value of the outcome may however lie far from the conditional expectation. We therefore introduce a method called Dirac Delta Regression (DDR) that estimates the entire conditional density from RCT data in order to visualize the probabilities across all possible outcome values. DDR transforms the outcome into a set of asymptotically Dirac delta distributions and then estimates the density using non-linear regression. The algorithm can identify significant differences in patient-specific outcomes even when no population level effect exists. Moreover, DDR outperforms state-of-the-art algorithms in conditional density estimation by a large margin even in the small sample regime. An R package is available at https://github.com/ericstrobl/DDR.

stat.ML↗

arXiv2021

Synthesized Difference in Differences

We consider estimating the conditional average treatment effect for everyone by eliminating confounding and selection bias. Unfortunately, randomized clinical trials (RCTs) eliminate confounding but impose strict exclusion criteria that prevent sampling of the entire clinical population. Observational datasets are more inclusive but suffer from confounding. We therefore analyze RCT and observational data simultaneously in order to extract the strengths of each. Our solution builds upon Difference in Differences (DD), an algorithm that eliminates confounding from observational data by comparing outcomes before and after treatment administration. DD requires a parallel slopes assumption that may not apply in practice when confounding shifts across time. We instead propose Synthesized Difference in Differences (SDD) that infers the correct (possibly non-parallel) slopes by linearly adjusting a conditional version of DD using additional RCT data. The algorithm achieves state of the art performance across multiple synthetic and real datasets even when the RCT excludes the majority of patients.

stat.ML↗

arXiv2020

Automated Hyperparameter Selection for the PC Algorithm

The PC algorithm infers causal relations using conditional independence tests that require a pre-specified Type I $α$ level. PC is however unsupervised, so we cannot tune $α$ using traditional cross-validation. We therefore propose AutoPC, a fast procedure that optimizes $α$ directly for a user chosen metric. We in particular force PC to double check its output by executing a second run on the recovered graph. We choose the final output as the one which maximizes stability between the two runs. AutoPC consistently outperforms the state of the art across multiple metrics.

stat.ML↗