Two-component Mixture Model in the Presence of Covariates

Nabarun Deb; Sujayam Saha; Adityanand Guntuboyina; Bodhisattva Sen

Home/Archive/arXiv

arXiv · 1810.07897

Two-component Mixture Model in the Presence of Covariates

Nabarun Deb·Sujayam Saha·Adityanand Guntuboyina·Bodhisattva Sen

View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature due to its applicability in multiple hypotheses testing problems. The model we consider allows for infinite dimensional parameters and offers flexibility in modeling the dependence of the response on the covariates. We discuss the identifiability issues arising in this model and systematically study several estimation strategies. We propose a tuning parameter-free nonparametric maximum likelihood method, implementable via the EM algorithm, to estimate the unknown parameters. Further, we derive the rate of convergence of the proposed estimators --- in particular, we show that the finite sample Hellinger risk for every `approximate' nonparametric maximum likelihood estimator achieves a near-parametric rate (up to logarithmic multiplicative factors). In addition, we propose and theoretically study two `marginal' methods that are more scalable and easily implementable. We demonstrate the efficacy of our procedures through extensive simulation studies and relevant data analyses --- one arising from neuroscience and the other from astronomy. We also outline the application of our methods to multiple testing. The companion R package $\texttt{NPMLEmix}$ implements all the procedures proposed in this paper.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Nabarun Deb, Sujayam Saha, Adityanand Guntuboyina, Bodhisattva Sen. 2019-01-31. Two-component Mixture Model in the Presence of Covariates. https://arxiv.org/abs/1810.07897

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Surprise Reduction and Nullification in Bayesian and Inverse Bayesian Inference under Ambiguous Prediction-Error Attribution

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

stat.ME↗

arXiv2026

Generalized Ridge Refitting for the Lasso and Prediction Improvement Bounds

We study a class of Lasso based estimators obtained by applying a quadratic correction on the Lasso equicorrelation set. The penalty matrix determines both the magnitude and geometry of the correction and contains, among other cases, the isotropic Lasso--Ridge correction, least squares refitting, Gram proportional interpolation between the Lasso and least squares, and coordinate specific penalties. We first derive a closed form representation and isolate the positive gain component of the resulting prediction improvement. We then control the remaining stochastic linear term in expectation by localizing the random signed equicorrelation model around a deterministic reference support. This yields a finite sample expectation bound that explicitly accounts for the randomness induced by Lasso model selection. The resulting decomposition provides a unified framework for understanding when Lasso based quadratic corrections can improve prediction.

stat.ME↗

arXiv2026

Discretization in covariate-adaptive randomization: gains and losses

Covariate-adaptive randomization(CAR) is widely implemented in clinical trials to balance prognostic covariates across treatment arms. Continuous covariates are often discretized into strata in practice, yet their consequences are not clearly understood. This paper provides a comprehensive study of the impact of discretization on both the CAR design process and the inferential results thereafter. We establish the asymptotic properties of both imbalance measures and treatment effect estimators under discretized and non-discretized settings. Practical recommendations are given on when and how discretization should be employed. We show that discretization in design is generally recommended, as it enhances robustness against model misspecification. However, if the true model is known, the most efficient strategy is to balance covariates according to that model in the design. The theoretical results are corroborated by extensive simulation studies and an empirical application to a diabetes trial dataset. Together, the results clarify the gains and losses of discretization in CAR and pave the way for learning impact of discretization to other designs and beyond.

stat.ME↗