arXiv subjects

Omar Melikechi

Publications and source records attributed to Omar Melikechi.

9 recordsLinked to original sources

arXiv2026

Causal Stability Selection

Identifying covariates that modify treatment effects is a central problem in causal inference. Yet existing data-adaptive procedures do not provide finite-sample control over the expected number of false discoveries, risking spurious findings that fail to replicate. We introduce causal stability selection, an algorithm that combines cross-fitted estimation of conditional average treatment effects with integrated path stability selection. The method accommodates arbitrary treatment effect estimators and arbitrary base selectors, and produces a selection set with an explicit, non-asymptotic bound on the expected number of false positives. Under standard causal identifying assumptions and regularity conditions on the base selector, we prove that the estimated selection probabilities converge to their oracle counterparts at the rate of the underlying treatment effect estimator. This establishes a direct connection between treatment effect estimation and effect modifier discovery. We illustrate the method on simulated data and on real-world data from a randomized oncology trial and an observational study of maternal smoking and infant birthweight.

stat.ME↗

arXiv2025

Local graph estimation with pathwise false discovery control

Many datasets include a small set of variables, such as biomarkers or clinical outcomes, whose relationships to the broader system are of primary scientific interest. Estimating the full network of inter-variable relationships in such settings often obscures local structures around these targets, limiting interpretability. To address this fundamental problem, we introduce local graph estimation, a statistical framework for inferring substructures around target variables. We show that traditional graph estimation methods often fail to recover local structure, and present pathwise feature selection (PFS) as an effective alternative. PFS estimates local subgraphs by iteratively applying feature selection and propagating uncertainty along network paths, providing rigorous finite-sample false discovery control even in settings with mixed variable types and nonlinear dependencies. In four distinct applications spanning environmental and public health, multiomics, brain connectomics, and single-nucleus RNA sequencing, PFS recovers interpretable networks consistent with domain knowledge, highlighting its ability to uncover established mechanisms and generate novel hypotheses.

stat.ME↗

arXiv2024

Nonparametric IPSS: Fast, flexible feature selection with false discovery control

Feature selection is a critical task in machine learning and statistics. However, existing feature selection methods either (i) rely on parametric methods such as linear or generalized linear models, (ii) lack theoretical false discovery control, or (iii) identify few true positives. Here, we introduce a general feature selection method with finite-sample false discovery control based on applying integrated path stability selection (IPSS) to arbitrary feature importance scores. The method is nonparametric whenever the importance scores are nonparametric, and it estimates q-values, which are better suited to high-dimensional data than p-values. We focus on two special cases using importance scores from gradient boosting (IPSSGB) and random forests (IPSSRF). Extensive nonlinear simulations with RNA sequencing data show that both methods accurately control the false discovery rate and detect more true positives than existing methods. Both methods are also efficient, running in under 20 seconds when there are 500 samples and 5000 features. We apply IPSSGB and IPSSRF to detect microRNAs and genes related to cancer, finding that they yield better predictions with fewer features than existing approaches.

stat.ML↗

arXiv2024

Integrated path stability selection

Stability selection is a popular method for improving feature selection algorithms. One of its key attributes is that it provides theoretical upper bounds on the expected number of false positives, E(FP), enabling false positive control in practice. However, stability selection often selects few features because existing bounds on E(FP) are relatively loose. In this paper, we introduce a novel approach to stability selection based on integrating stability paths rather than maximizing over them. This yields upper bounds on E(FP) that are much stronger than previous bounds, leading to significantly more true positives in practice for the same target E(FP). Furthermore, our method requires no more computation than the original stability selection algorithm. We demonstrate the method on simulations and real data from two cancer studies.

stat.ME↗

arXiv2023

Random Splitting of Fluid Models: Positive Lyapunov Exponents

In this paper we give sufficient conditions for random splitting systems to have a positive top Lyapunov exponent. We verify these conditions for random splittings of two fluid models: the conservative Lorenz-96 equations and Galerkin approximations of the 2D Euler equations on the torus. In doing so, we highlight particular structures in these equations such as shearing. Since a positive top Lyapunov exponent is an indicator of chaos which in turn is a feature of turbulence, our results show these randomly split fluid models have important characteristics of turbulent flow.

math.DS↗

arXiv2023

Sequential Gibbs Posteriors with Applications to Principal Component Analysis

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.

stat.ME↗

arXiv2023

Ellipsoid fitting with the Cayley transform

We introduce Cayley transform ellipsoid fitting (CTEF), an algorithm that uses the Cayley transform to fit ellipsoids to noisy data in any dimension. Unlike many ellipsoid fitting methods, CTEF is ellipsoid specific, meaning it always returns elliptic solutions, and can fit arbitrary ellipsoids. It also significantly outperforms other fitting methods when data are not uniformly distributed over the surface of an ellipsoid. Inspired by growing calls for interpretable and reproducible methods in machine learning, we apply CTEF to dimension reduction, data visualization, and clustering in the context of cell cycle and circadian rhythm data and several classical toy examples. Since CTEF captures global curvature, it extracts nonlinear features in data that other machine learning methods fail to identify. For example, on the clustering examples CTEF outperforms 10 popular algorithms.

stat.ML↗

arXiv2022

Random Splitting of Fluid Models: Ergodicity and Convergence

We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector fields preserving some fundamental aspects of the original dynamics. Randomness is injected by sequentially following each vector field for a random amount of time. We show under general assumptions that these random dynamics possess a unique invariant measure and converge almost surely to the original, deterministic model in the small noise limit. We apply our construction to the Lorenz-96 equations, often used in studies of chaos and data assimilation, and Galerkin approximations of the 2D Euler and Navier-Stokes equations. An interesting feature of the models developed is that they apply directly to the conservative dynamics and not just those with excitation and dissipation.

math.PR↗

arXiv2021

Limits of epidemic prediction using SIR models

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the model parameters based on noisy observations early in the outbreak, well before the epidemic reaches its peak. This allows prediction of the subsequent course of the epidemic and design of appropriate interventions. However, accurately inferring SIR model parameters in such scenarios is problematic. This article provides novel, theoretical insight on this issue of practical identifiability of the SIR model. Our theory provides new understanding of the inferential limits of routinely used epidemic models and provides a valuable addition to current simulate-and-check methods. We illustrate some practical implications through application to a real-world epidemic data set.

stat.AP↗