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Hemant Ishwaran

Publications and source records attributed to Hemant Ishwaran.

16 recordsLinked to original sources
arXiv2026

Random Hazard Forests

Clinical data sources such as electronic health records and wearable sensors record patient status repeatedly over follow-up, often at irregular times and on different schedules for different measurements. These data create opportunities for continuously updated, individualized risk prediction. Existing approaches, however, often simplify the temporal structure for model fitting. We introduce Random Hazard Forests (RHF), a survival tree ensemble that estimates how a patient's hazard changes in continuous time as new measurements become available. The method formulates the estimation problem directly through a nonparametric hazard likelihood for predictable covariate processes. An efficient working model guides tree construction, after which flexible time-varying hazards are estimated for each terminal node. Given any predictable covariate path, each tree follows the path through its terminal nodes over time and assembles the corresponding node-level hazards into a trajectory. Averaging these trajectories across trees yields the pathwise hazard estimate. Because routing at each time uses only the covariate state available immediately beforehand, the construction accommodates internal longitudinal covariates without lookahead. Simulations and an intensive care application show that the forest accurately estimates changing risk under irregular and asynchronous covariate updates.

stat.ML↗
arXiv2026

General OOD Detection via Model-aware and Subspace-aware Variable Priority

Out-of-distribution (OOD) detection is essential for determining when a supervised model encounters inputs that differ meaningfully from its training distribution. While widely studied in classification, OOD detection for regression and survival analysis remains limited due to the absence of discrete labels and the challenge of quantifying predictive uncertainty. We introduce a framework for OOD detection that is simultaneously model aware and subspace aware, and that embeds variable prioritization directly into the detection step. The method uses the fitted predictor to construct localized neighborhoods around each test case that emphasize the features driving the model's learned relationship and downweight directions that are less relevant to prediction. It produces OOD scores without relying on global distance metrics or estimating the full feature density. The framework is applicable across outcome types, and in our implementation we use random forests, where the rule structure yields transparent neighborhoods and effective scoring. Experiments on synthetic and real data benchmarks designed to isolate functional shifts show consistent improvements over existing methods. We further demonstrate the approach in an esophageal cancer survival study, where distribution shifts related to lymphadenectomy identify patterns relevant to surgical guidelines.

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arXiv2024

Model-independent variable selection via the rule-based variable priority

While achieving high prediction accuracy is a fundamental goal in machine learning, an equally important task is finding a small number of features with high explanatory power. One popular selection technique is permutation importance, which assesses a variable's impact by measuring the change in prediction error after permuting the variable. However, this can be problematic due to the need to create artificial data, a problem shared by other methods as well. Another problem is that variable selection methods can be limited by being model-specific. We introduce a new model-independent approach, Variable Priority (VarPro), which works by utilizing rules without the need to generate artificial data or evaluate prediction error. The method is relatively easy to use, requiring only the calculation of sample averages of simple statistics, and can be applied to many data settings, including regression, classification, and survival. We investigate the asymptotic properties of VarPro and show, among other things, that VarPro has a consistent filtering property for noise variables. Empirical studies using synthetic and real-world data show the method achieves a balanced performance and compares favorably to many state-of-the-art procedures currently used for variable selection.

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arXiv2021

Boosted nonparametric hazards with time-dependent covariates

Given functional data from a survival process with time-dependent covariates, we derive a smooth convex representation for its nonparametric log-likelihood functional and obtain its functional gradient. From this, we devise a generic gradient boosting procedure for estimating the hazard function nonparametrically. An illustrative implementation of the procedure using regression trees is described to show how to recover the unknown hazard. The generic estimator is consistent if the model is correctly specified; alternatively, an oracle inequality can be demonstrated for tree-based models. To avoid overfitting, boosting employs several regularization devices. One of them is step-size restriction, but the rationale for this is somewhat mysterious from the viewpoint of consistency. Our work brings some clarity to this issue by revealing that step-size restriction is a mechanism for preventing the curvature of the risk from derailing convergence.

stat.ML↗
arXiv2020

Dynamic Competing Risk Modeling COVID-19 in a Pandemic Scenario

The emergence of coronavirus disease 2019 (COVID-19) in the United States has forced federal and local governments to implement containment measures. Moreover, the severity of the situation has sparked engagement by both the research and clinical community with the goal of developing effective treatments for the disease. This article proposes a time dynamic prediction model with competing risks for the infected individual and develops a simple tool for policy makers to compare different strategies in terms of when to implement the strictest containment measures and how different treatments can increase or suppress infected cases. Two types of containment strategies are compared: (1) a constant containment strategy that could satisfy the needs of citizens for a long period; and (2) an adaptive containment strategy whose strict level changes across time. We consider how an effective treatment of the disease can affect the dynamics in a pandemic scenario. For illustration we consider a region with population 2.8 million and 200 initial infectious cases assuming a 4% mortality rate compared with a 2% mortality rate if a new drug is available. Our results show compared with a constant containment strategy, adaptive containment strategies shorten the outbreak length and reduce maximum daily number of cases. This, along with an effective treatment plan for the disease can minimize death rate.

q-bio.PE↗
arXiv2017

A Machine Learning Alternative to P-values

This paper presents an alternative approach to p-values in regression settings. This approach, whose origins can be traced to machine learning, is based on the leave-one-out bootstrap for prediction error. In machine learning this is called the out-of-bag (OOB) error. To obtain the OOB error for a model, one draws a bootstrap sample and fits the model to the in-sample data. The out-of-sample prediction error for the model is obtained by calculating the prediction error for the model using the out-of-sample data. Repeating and averaging yields the OOB error, which represents a robust cross-validated estimate of the accuracy of the underlying model. By a simple modification to the bootstrap data involving "noising up" a variable, the OOB method yields a variable importance (VIMP) index, which directly measures how much a specific variable contributes to the prediction precision of a model. VIMP provides a scientifically interpretable measure of the effect size of a variable, we call the "predictive effect size", that holds whether the researcher's model is correct or not, unlike the p-value whose calculation is based on the assumed correctness of the model. We also discuss a marginal VIMP index, also easily calculated, which measures the marginal effect of a variable, or what we call "the discovery effect". The OOB procedure can be applied to both parametric and nonparametric regression models and requires only that the researcher can repeatedly fit their model to bootstrap and modified bootstrap data. We illustrate this approach on a survival data set involving patients with systolic heart failure and to a simulated survival data set where the model is incorrectly specified to illustrate its robustness to model misspecification.

stat.ML↗
arXiv2017

Random Forest Missing Data Algorithms

Random forest (RF) missing data algorithms are an attractive approach for dealing with missing data. They have the desirable properties of being able to handle mixed types of missing data, they are adaptive to interactions and nonlinearity, and they have the potential to scale to big data settings. Currently there are many different RF imputation algorithms but relatively little guidance about their efficacy, which motivated us to study their performance. Using a large, diverse collection of data sets, performance of various RF algorithms was assessed under different missing data mechanisms. Algorithms included proximity imputation, on the fly imputation, and imputation utilizing multivariate unsupervised and supervised splitting---the latter class representing a generalization of a new promising imputation algorithm called missForest. Performance of algorithms was assessed by ability to impute data accurately. Our findings reveal RF imputation to be generally robust with performance improving with increasing correlation. Performance was good under moderate to high missingness, and even (in certain cases) when data was missing not at random.

stat.ML↗
arXiv2017

Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods

Estimation of individual treatment effect in observational data is complicated due to the challenges of confounding and selection bias. A useful inferential framework to address this is the counterfactual (potential outcomes) model which takes the hypothetical stance of asking what if an individual had received both treatments. Making use of random forests (RF) within the counterfactual framework we estimate individual treatment effects by directly modeling the response. We find accurate estimation of individual treatment effects is possible even in complex heterogeneous settings but that the type of RF approach plays an important role in accuracy. Methods designed to be adaptive to confounding, when used in parallel with out-of-sample estimation, do best. One method found to be especially promising is counterfactual synthetic forests. We illustrate this new methodology by applying it to a large comparative effectiveness trial, Project Aware, in order to explore the role drug use plays in sexual risk. The analysis reveals important connections between risky behavior, drug usage, and sexual risk.

stat.ML↗
arXiv2012

Characterizing $L_2$Boosting

We consider $L_2$Boosting, a special case of Friedman's generic boosting algorithm applied to linear regression under $L_2$-loss. We study $L_2$Boosting for an arbitrary regularization parameter and derive an exact closed form expression for the number of steps taken along a fixed coordinate direction. This relationship is used to describe $L_2$Boosting's solution path, to describe new tools for studying its path, and to characterize some of the algorithm's unique properties, including active set cycling, a property where the algorithm spends lengthy periods of time cycling between the same coordinates when the regularization parameter is arbitrarily small. Our fixed descent analysis also reveals a repressible condition that limits the effectiveness of $L_2$Boosting in correlated problems by preventing desirable variables from entering the solution path. As a simple remedy, a data augmentation method similar to that used for the elastic net is used to introduce $L_2$-penalization and is shown, in combination with decorrelation, to reverse the repressible condition and circumvents $L_2$Boosting's deficiencies in correlated problems. In itself, this presents a new explanation for why the elastic net is successful in correlated problems and why methods like LAR and lasso can perform poorly in such settings.

math.ST↗
arXiv2008

Consistency of Random Survival Forests

We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables--that is, under true implementation of the methodology. A key assumption made is that all variables are factors. Although this assumes that the feature space has finite cardinality, in practice the space can be a extremely large--indeed, current computational procedures do not properly deal with this setting. An indirect consequence of this work is the introduction of new computational methodology for dealing with factors with unlimited number of labels.

math.ST↗
arXiv2008

Random survival forests

We introduce random survival forests, a random forests method for the analysis of right-censored survival data. New survival splitting rules for growing survival trees are introduced, as is a new missing data algorithm for imputing missing data. A conservation-of-events principle for survival forests is introduced and used to define ensemble mortality, a simple interpretable measure of mortality that can be used as a predicted outcome. Several illustrative examples are given, including a case study of the prognostic implications of body mass for individuals with coronary artery disease. Computations for all examples were implemented using the freely available R-software package, randomSurvivalForest.

stat.AP↗
arXiv2008

Orthogonalized smoothing for rescaled spike and slab models

Rescaled spike and slab models are a new Bayesian variable selection method for linear regression models. In high dimensional orthogonal settings such models have been shown to possess optimal model selection properties. We review background theory and discuss applications of rescaled spike and slab models to prediction problems involving orthogonal polynomials. We first consider global smoothing and discuss potential weaknesses. Some of these deficiencies are remedied by using local regression. The local regression approach relies on an intimate connection between local weighted regression and weighted generalized ridge regression. An important implication is that one can trace the effective degrees of freedom of a curve as a way to visualize and classify curvature. Several motivating examples are presented.

stat.AP↗
arXiv2007

Variable importance in binary regression trees and forests

We characterize and study variable importance (VIMP) and pairwise variable associations in binary regression trees. A key component involves the node mean squared error for a quantity we refer to as a maximal subtree. The theory naturally extends from single trees to ensembles of trees and applies to methods like random forests. This is useful because while importance values from random forests are used to screen variables, for example they are used to filter high throughput genomic data in Bioinformatics, very little theory exists about their properties.

stat.ML↗
arXiv2005

Spike and slab variable selection: Frequentist and Bayesian strategies

Variable selection in the linear regression model takes many apparent faces from both frequentist and Bayesian standpoints. In this paper we introduce a variable selection method referred to as a rescaled spike and slab model. We study the importance of prior hierarchical specifications and draw connections to frequentist generalized ridge regression estimation. Specifically, we study the usefulness of continuous bimodal priors to model hypervariance parameters, and the effect scaling has on the posterior mean through its relationship to penalization. Several model selection strategies, some frequentist and some Bayesian in nature, are developed and studied theoretically. We demonstrate the importance of selective shrinkage for effective variable selection in terms of risk misclassification, and show this is achieved using the posterior from a rescaled spike and slab model. We also show how to verify a procedure's ability to reduce model uncertainty in finite samples using a specialized forward selection strategy. Using this tool, we illustrate the effectiveness of rescaled spike and slab models in reducing model uncertainty.

math.ST↗
arXiv2004

Least Angle Regression

The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a large collection of possible covariates from which we hope to select a parsimonious set for the efficient prediction of a response variable. Least Angle Regression (LARS), a new model selection algorithm, is a useful and less greedy version of traditional forward selection methods. Three main properties are derived: (1) A simple modification of the LARS algorithm implements the Lasso, an attractive version of ordinary least squares that constrains the sum of the absolute regression coefficients; the LARS modification calculates all possible Lasso estimates for a given problem, using an order of magnitude less computer time than previous methods. (2) A different LARS modification efficiently implements Forward Stagewise linear regression, another promising new model selection method;

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