arXiv subjects

Nikolaos Ignatiadis

Publications and source records attributed to Nikolaos Ignatiadis.

At least 19 recordsLinked to original sources

arXiv2026

Constrained Denoising, Empirical Bayes, and Optimal Transport

In latent variables models, two important goals are denoising and deconvolution: denoising aims to estimate the latent variables, whereas deconvolution aims to estimate the distribution of the latent variables. As has been recognized in the literature over the last century, these two goals are fundamentally in tension, since denoising yields a poor estimate of the distribution of the latent variables due to shrinkage, and deconvolution yields a distribution-valued estimate that carries no unit-specific information. In this paper, we provide a systematic study of denoisers, and empirical Bayes approximations thereof, which attain optimal denoising error subject to the constraint that the distribution of the denoised data matches, in some sense, the distribution of the latent variables. Our insight is that optimal transport allows practitioners to navigate the tension between denoising and deconvolution. More precisely, we propose a modular methodology that combines any suitable unconstrained empirical Bayes denoiser (arising, e.g., via $F$-modeling, $G$-modeling, conjugate-parametric models) with any suitable information about the distribution of the latent variables (e.g., its moments, support, or an approximation of the entire distribution via deconvolution) into a single denoised data set. We prove explicit rates of convergence for our proposed methodologies, and we apply the resulting methods in applications in astronomy, baseball analytics, and marketing.

stat.ME↗

arXiv2026

Compound decisions and empirical Bayes via Bayesian nonparametrics

We study compound decision theory from a nonparametric Bayesian perspective, with particular emphasis on their relationship to empirical Bayes (EB) procedures. Motivated by the sharp risk guarantees available for EB procedures based on the nonparametric maximum likelihood estimator (NPMLE), we investigate whether analogous guarantees can be established for fully Bayesian decision rules. In a class of Gaussian compound decision problems, we show that the fully Bayesian posterior mean achieves near-optimal risk. Moreover, it is admissible as a genuine Bayes rule, whereas the corresponding NPMLE plug-in rule is inadmissible. Simulations illustrate the performance of nonparametric Bayes procedures relative to common alternatives. As an application, we apply our methodology to Census tract-level estimates of economic mobility from the Opportunity Atlas.

math.ST↗

arXiv2026

Estimating the local false discovery rate under an unknown symmetric null

This paper is concerned with estimating the local false discovery rate (lfdr) in a two-groups model where the only assumption regarding the null distribution is symmetry about zero. Our motivation comes from the contemporary framework for multiple hypothesis testing, particularly relevant in variable selection problems, which transforms any user-specified scores into statistics whose null distributions are symmetric about zero, whereas enrichment to the right of zero is generally expected for the non-nulls. While modern methods such as the knockoff filter (Barber and Candes; 2015) are able to exploit the null property for controlling the false discovery rate (FDR), an arguably more appropriate goal is to target control of the local false discovery rate for the rejected hypotheses, as proposed in Soloff et al. (2024) where the standard two-groups model (known $f_0$ and independence) is analyzed. Here, we take a step in this direction and propose to estimate the lfdr by targeting the surrogate density ratio $f(-w)/f(w)$, for $w>0$, where $f$ is the marginal density in the aforementioned ``stripped-down'' two-groups model. We study several estimators and propose a logistic regression based method with natural cubic spline basis. We also show that any consistent estimator of this surrogate yields asymptotic lfdr control of the multiple testing procedure that thresholds the estimate at the nominal level.

stat.ME↗

arXiv2026

Normal approximations in nonparametric empirical Bayes

Empirical Bayes analyses routinely model noisy measurements of latent parameters as normal, justifying this by an informal appeal to the central limit theorem (CLT). This paper puts this heuristic appeal on firmer analytical grounds. We show that the denoising regret of the nonparametric maximum likelihood estimator (NPMLE) and related sieve methods is controlled by the rate attained under exact normality, plus a term reflecting the quality of the CLT approximation. The CLT need only hold marginally for each coordinate, and moreover only on average, without needing high-dimensional normal approximations. We identify two asymptotic regimes in which the normal approximation is adequate and the empirical Bayesian prior remains informative, and we show that our guarantees are robust to dependence and to variance estimation.

math.ST↗

arXiv2026

How does limma-trend work? An empirical partially Bayes perspective

In high-throughput biology, it is common to fit thousands of linear regressions -- one per gene, protein, or other unit -- with very few samples per unit. Limma-trend, one of the most widely used methods in this setting, improves power by shrinking variance estimates parametrically toward a fitted curve (the trend) relating variance to a unit-level summary (e.g., average intensity, peptide count), before computing p-values and applying the Benjamini-Hochberg procedure to control the false discovery rate (FDR). We study limma-trend through the lens of empirical partially Bayes inference, a paradigm in which a prior is posited and estimated for the nuisance parameters while parameters of interest remain fixed. From this perspective, limma-trend computes approximate partially Bayes p-values that condition on the residual sample variance and the unit-level summary. The same framework explains why MAnorm2, a popular variant for ChIP-seq, can sometimes fail to control FDR. We then derive a nonparametric generalization of limma-trend that estimates the residual variance prior using nonparametric maximum likelihood. Under dense signals, this procedure asymptotically controls the FDR -- even when the trend is misspecified or inconsistently estimated. To allow the full shape of the conditional variance distribution to depend on the unit-level summary, we develop a second procedure that learns it directly.

stat.ME↗

arXiv2026

Empirical Bayes Rebiasing

We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard debiasing approach, which subtracts the bias estimate from each biased estimate, inflates variance and yields long intervals. In this paper, we propose an empirical Bayes rebiasing strategy that starts from the fully debiased estimates and learns from data how much bias to reintroduce by estimating the unknown bias distribution. We provide convergence rates for the coverage of our intervals when the bias distribution is estimated using nonparametric maximum likelihood. Furthermore, we demonstrate substantial precision gains in prediction-powered inference, including pairwise LLM win-rate evaluations, as well as for inference of direct genetic effects in family-based GWAS.

stat.ME↗

arXiv2026

Tiny but uniform improvements of adaptive BH procedures via compound e-values

After the seminal Benjamini-Hochberg (BH) procedure for controlling the false discovery rate (FDR) was proposed, dozens of papers have attempted to improve its power by adapting to the unknown proportion of nulls. We observe that most null proportion estimates are simply compound e-values in disguise, and thus most adaptive FDR procedures can be interpreted as instances of the e-weighted BH (ep-BH) procedure of Ignatiadis, Wang, and Ramdas [2024], i.e., the BH procedure weighted by compound e-values. This lens helps us show that most existing procedures are inadmissible, and we provide uniform improvements to them. While the improvements are small in practice, they still come for free (without additional assumptions), and help unify the literature. We also use our "leave-one-out ep-BH method" to design a new method with finite-sample FDR control for the simultaneous t-test setting.

stat.ME↗

arXiv2026

Empirical Bayes learning from selectively reported confidence intervals

We develop a statistical framework for empirical Bayes learning from selectively reported confidence intervals, and apply it to provide context for interpreting results published in MEDLINE abstracts. We use a collection of 326,060 z-scores from MEDLINE abstracts (2000-2018) as the input for an empirical Bayes analysis, with publication bias as a key methodological challenge. We address publication bias through a selective tilting approach that extends empirical Bayes confidence intervals to truncated sampling. Our framework provides coverage guarantees for functionals including posterior estimands describing idealized replications and the symmetrized posterior mean, which we justify decision-theoretically as optimal among sign-equivariant (odd) estimators.

stat.ME↗

arXiv2025

Partially Bayes p-values for large scale inference

We seek to conduct statistical inference for a large collection of primary parameters, each with its own nuisance parameters. Our approach is partially Bayesian, in that we treat the primary parameters as fixed while we model the nuisance parameters as random and drawn from an unknown distribution which we endow with a nonparametric prior. We compute partially Bayes p-values by conditioning on nuisance parameter statistics, that is, statistics that are ancillary for the primary parameters and informative about the nuisance parameters. The proposed p-values have a Bayesian interpretation as tail areas computed with respect to the posterior distribution of the nuisance parameters. Similarly to the conditional predictive p-values of Bayarri and Berger, the partially Bayes p-values avoid double use of the data (unlike posterior predictive p-values). A key ingredient of our approach is that we model nuisance parameters hierarchically across problems; the sharing of information across problems leads to improved calibration. We illustrate the proposed partially Bayes p-values in two applications: the normal means problem with unknown variances and a location-scale model with unknown distribution shape. We model the scales via Dirichlet processes in both examples and the distribution shape via Pólya trees in the second. Our proposed partially Bayes p-values increase power and calibration compared to purely frequentist alternatives.

stat.ME↗

arXiv2025

Prediction-Powered Adaptive Shrinkage Estimation

Prediction-Powered Inference (PPI) is a powerful framework for enhancing statistical estimates by combining limited gold-standard data with machine learning (ML) predictions. While prior work has demonstrated PPI's benefits for individual statistical problems, modern applications require answering numerous parallel statistical questions. We introduce Prediction-Powered Adaptive Shrinkage (PAS), a method that bridges PPI with empirical Bayes shrinkage to improve the estimation of multiple means. PAS debiases noisy ML predictions within each task and then borrows strength across tasks by using those same predictions as a reference point for shrinkage. The amount of shrinkage is determined by minimizing an unbiased estimate of risk, and we prove that this tuning strategy is asymptotically optimal. Experiments on both synthetic and real-world datasets show that PAS adapts to the reliability of the ML predictions and outperforms traditional and modern baselines in large-scale applications.

stat.ML↗

arXiv2025

Empirical partially Bayes two sample testing

A common task in high-throughput biology is to test for differences in means between two samples across thousands of features (e.g., genes or proteins), often with only a handful of replicates per sample. Moderated t-tests handle this problem by assuming normality and equal variances, and by applying the empirical partially Bayes principle: a prior is posited and estimated for the nuisance parameters (variances) but not for the primary parameters (means). This approach has been highly successful in genomics, yet the equal variance assumption is often violated in practice. Meanwhile, Welch's unequal variance t-test with few replicates suffers from inflated type-I error and low power. Taking inspiration from moderated t-tests, we extend the empirical partially Bayes paradigm to two-sample testing with unequal variances. We develop two procedures: one that models the ratio of the two sample-specific variances and another that models the two variances jointly, with prior distributions estimated by nonparametric maximum likelihood. Our empirical partially Bayes methods yield p-values that are asymptotically uniform as the number of features grows while the number of replicates remains fixed, ensuring asymptotic type-I error control. Simulations and applications to genomic data demonstrate substantial gains in power.

stat.ME↗

arXiv2025

Interpretation of local false discovery rates under the zero assumption

In large-scale studies with parallel signal-plus-noise observations, the local false discovery rate is a summary statistic that is often presumed to be equal to the posterior probability that the signal is null. We prefer to call the latter quantity the local null-signal rate to emphasize our view that a null signal and a false discovery are not identical events. The local null-signal rate is commonly estimated through empirical Bayes procedures that build on the `zero density assumption,' which attributes the density of observations near zero entirely to null signals. In this paper, we argue that this strategy does not furnish estimates of the local null-signal rate, but instead of a quantity we call the complementary local activity rate (clar). Although it is likely to be small, an inactive signal is not necessarily zero. The clar dominates both the local null-signal rate and the local false sign rate and is a weakly continuous functional of the signal distribution. As a consequence, it takes on sensible values when the signal is sparse but not exactly zero. Our findings clarify the interpretation of local false discovery rates estimated under the zero density assumption.

math.ST↗

arXiv2025

Stein's unbiased risk estimate and Hyvärinen's score matching

Given a collection of observed signals corrupted with Gaussian noise, how can we learn to optimally denoise them? This fundamental problem arises in both empirical Bayes and generative modeling. In empirical Bayes, the predominant approach is via nonparametric maximum likelihood estimation (NPMLE), while in generative modeling, score matching (SM) methods have proven very successful. In our setting, Hyvärinen's implicit SM is equivalent to another classical idea from statistics -- Stein's Unbiased Risk Estimate (SURE). Revisiting SURE minimization, we establish, for the first time, that SURE achieves nearly parametric rates of convergence of the regret in the classical empirical Bayes setting with homoscedastic noise. We also prove that SURE-training can achieve fast rates of convergence to the oracle denoiser in a commonly studied misspecified model. In contrast, the NPMLE may not even converge to the oracle denoiser under misspecification of the class of signal distributions. We show how to practically implement our method in settings involving heteroscedasticity and side-information, such as in an application to the estimation of economic mobility in the Opportunity Atlas. Our empirical results demonstrate the superior performance of SURE-training over NPMLE under misspecification. Collectively, our findings advance SURE/SM as a strong alternative to the NPMLE for empirical Bayes problems in both theory and practice.

math.ST↗

arXiv2025

Reasonable uncertainty: Confidence intervals in empirical Bayes discrimination detection

We revisit empirical Bayes discrimination detection, focusing on uncertainty arising from both partial identification and sampling variability. While prior work has mostly focused on partial identification, we find that some empirical findings are not robust to sampling uncertainty. To better connect statistical evidence to the magnitude of real-world discriminatory behavior, we propose a counterfactual odds-ratio estimand with a attractive properties and interpretation. Our analysis reveals the importance of careful attention to uncertainty quantification and downstream goals in empirical Bayes analyses.

econ.EM↗

arXiv2025

Asymptotic and compound e-values: multiple testing and empirical Bayes

We explicitly define the notions of (bona fide, approximate or asymptotic) compound p-values and e-values, which have been implicitly presented and used in the recent multiple testing literature. While it is known that the e-BH procedure with compound e-values controls the FDR, we show the converse: every FDR controlling procedure can be recovered by instantiating the e-BH procedure with certain compound e-values. Since compound e-values are closed under averaging, this allows for combination and derandomization of arbitrary FDR procedures. We then connect compound e-values to empirical Bayes. In particular, we use the fundamental theorem of compound decision theory to derive the log-optimal simple separable compound e-value for testing a set of point nulls against point alternatives: it is a ratio of mixture likelihoods. As one example, we construct asymptotic compound e-values for multiple t-tests, where the (nuisance) variances may be different across hypotheses. Our construction may be interpreted as a data-driven instantiation of the optimal discovery procedure, and our results provide the first type-I error guarantees for the same, along with significant power gains.

stat.ME↗

arXiv2025

Noise-Induced Randomization in Regression Discontinuity Designs

Regression discontinuity designs assess causal effects in settings where treatment is determined by whether an observed running variable crosses a pre-specified threshold. Here we propose a new approach to identification, estimation, and inference in regression discontinuity designs that uses knowledge about exogenous noise (e.g., measurement error) in the running variable. In our strategy, we weight treated and control units to balance a latent variable of which the running variable is a noisy measure. Our approach is driven by effective randomization provided by the noise in the running variable, and complements standard formal analyses that appeal to continuity arguments while ignoring the stochastic nature of the assignment mechanism.

stat.ME↗

arXiv2024

Empirical Bayes estimation via data fission

We demonstrate how data fission, a method for creating synthetic replicates from single observations, can be applied to empirical Bayes estimation. This extends recent work on empirical Bayes with multiple replicates to the classical single-replicate setting. The key insight is that after data fission, empirical Bayes estimation can be cast as a general regression problem.

stat.ME↗

arXiv2024

Empirical partially Bayes multiple testing and compound $χ^2$ decisions

A common task in high-throughput biology is to screen for associations across thousands of units of interest, e.g., genes or proteins. Often, the data for each unit are modeled as Gaussian measurements with unknown mean and variance and are summarized as per-unit sample averages and sample variances. The downstream goal is multiple testing for the means. In this domain, it is routine to "moderate" (that is, to shrink) the sample variances through parametric empirical Bayes methods before computing p-values for the means. Such an approach is asymmetric in that a prior is posited and estimated for the nuisance parameters (variances) but not the primary parameters (means). Our work initiates the formal study of this paradigm, which we term "empirical partially Bayes multiple testing." In this framework, if the prior for the variances were known, one could proceed by computing p-values conditional on the sample variances -- a strategy called partially Bayes inference by Sir David Cox. We show that these conditional p-values satisfy an Eddington/Tweedie-type formula and are approximated at nearly-parametric rates when the prior is estimated by nonparametric maximum likelihood. The estimated p-values can be used with the Benjamini-Hochberg procedure to guarantee asymptotic control of the false discovery rate. Even in the compound setting, wherein the variances are fixed, the approach retains asymptotic type-I error guarantees.

math.ST↗