Improving online FDR procedures via online analogs of e-closure and compound e-values

Aaditya Ramdas; Lasse Fischer; Ziyu Xu

REVIEW 3 major objections 2 minor 1 cited by

Improving online FDR procedures via online analogs of e-closure and compound e-values

T0 review · 3 major / 2 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read Online e-closure and donation-based compound e-values give strict power gains for sequential FDR control under arbitrary dependence.

desk verdict Abstract-only: promising online FDR tools via e-closure and donation compound e-values, but validity and power claims are uncheckable without the paper. read the letter →

arxiv 2603.24792 v3 pith:HAODADV2 submitted 2026-03-25 stat.ME math.STstat.TH

Ziyu Xu , Lasse Fischer , Aaditya Ramdas This is my paper · ORCID

classification stat.MEmath.STstat.TH MSC 62H1562L10

keywords onlineFDRe-valuese-closureprinciplecompoundsequentialmultipletestingarbitrarydependencedonationmechanism

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

When hypotheses arrive continuously in a stream and must be tested online with false discovery rate control, standard e-value and p-value procedures leave power on the table. This paper shows that two online analogs of classical ideas—the e-closure principle and compound e-values built by a donation mechanism—recover that power while still guaranteeing FDR control under arbitrary dependence among the tests. Decisions remain computable in logarithmic time in the number of hypotheses seen so far. A sympathetic reader cares because many modern scientific pipelines (genomics, A/B testing platforms, continuous monitoring) are inherently sequential; any method that raises power without sacrificing validity or speed directly increases the number of true discoveries that can be reported with the same error guarantee.

What carries the argument

Online e-closure (the sequential analog of the classical e-closure principle) and donation-based online compound e-values: the former closes the family of admissible rejection rules online, while the latter lets later tests inherit unused e-value mass from earlier ones, producing the power gain under the same supermartingale validity conditions.

What would settle it

Construct a sequential stream of dependent e-values (or p-values) on which an existing state-of-the-art online FDR procedure rejects a strict superset of the discoveries produced by the new methods, or on which the new methods exceed the target FDR level.

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Extended reading notes

Core claim

The online e-closure principle, together with a novel formulation of online compound e-values defined through donations, yields strict power improvements over state-of-the-art e-value and p-value online FDR procedures while retaining FDR control under arbitrary dependence, with decisions computable in O(log t) time at step t.

Load-bearing premise

That the online versions of e-closure and of donation-defined compound e-values still form valid e-processes (or supermartingales) under arbitrary dependence, so the FDR guarantee carries over from the offline theory.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The one thing to know is that this abstract claims a clean methodological advance for online FDR under arbitrary dependence: an online e-closure principle plus a donation-based definition of online compound e-values, with strict power gains over current e- and p-value procedures, O(log t) decisions, and some empirical wins. That package would matter if it holds.

What looks new is the packaging. Online e-closure and the donation construction for compound e-values are presented as the levers that let them improve on named SOTA methods without giving up FDR under arbitrary dependence. The O(log t) claim is also concrete and useful if the algorithms are real. The abstract is clear about the target setting (streaming hypotheses, continuous testing) and does not hide behind vague language.

The soft spot is simply that we only have the abstract. The load-bearing piece is whether the online analogs still give valid e-processes or supermartingales so that FDR control survives the sequential stream and the power improvement is not free. That is asserted, not shown. Same for the algorithms and the experiments. I am not inventing a flaw in the argument; I cannot inspect the argument. The reader and stress-test are right that confidence has to stay low until the definitions and theorems are visible. Nothing in the abstract smells circular or tautological; the residual risk is ordinary “does the construction actually work.”

This is for people who already care about online multiple testing, e-values, and sequential FDR. A methods reader in that corner gets value from the framing even before the proofs. It deserves a serious referee once the full text is in hand; the problem is real and the claimed tools are specific enough that desk rejection would be premature. I would not cite it yet and would not put an abstract-only piece in reading group, but I would accept it for peer review and read the paper when it appears.

Referee Report

3 major / 2 minor

Summary. The manuscript (available here only as an abstract) proposes a framework for online multiple testing with FDR control under arbitrary dependence. It introduces two constructions: an online analog of the e-closure principle, and online compound e-values defined via a donation mechanism. The authors claim these yield strict power improvements over state-of-the-art e-value and p-value online FDR procedures while retaining FDR control, that decisions at time t can be computed in O(log t) time, and that the methods show improved empirical performance on synthetic and real data.

Significance. If the claims hold as stated, the work would be a meaningful contribution to online FDR methodology. Strict power gains that preserve validity under arbitrary dependence in a fully sequential stream are practically relevant, and an O(log t) decision algorithm would address a genuine computational bottleneck. The dual constructions (online e-closure and donation-based compound e-values) are of independent methodological interest. These strengths cannot be confirmed from the abstract alone; formal definitions, theorems, algorithms, and empirical design are required for a full assessment.

major comments (3)

Abstract: The load-bearing claim is that the online e-closure principle and donation-defined online compound e-values preserve the supermartingale / e-process properties needed for FDR control under arbitrary dependence in a fully sequential streaming model, while still producing strictly more rejections than existing procedures. This validity is asserted rather than exhibited: no formal definitions, theorem statements, or proof sketches appear in the available text. Without those, neither the FDR guarantee nor the strict-power claim can be checked.
Abstract: The claim of 'strict power improvements over state-of-the-art e-value and p-value procedures' is not accompanied by a precise statement of which procedures are dominated, under what conditions the improvement is strict, or any dominance theorem. That comparison is central to the contribution and remains uninspectable from the abstract.
Abstract: The O(log t) decision algorithm and the reported empirical gains on synthetic and real data are likewise uninspectable. Algorithmic description, complexity analysis, simulation design, data sources, and quantitative results are all absent from the available text, so these supporting claims cannot be evaluated.

minor comments (2)

Abstract: The phrase 'online analogs of e-closure and compound e-values' is used without even a one-sentence informal definition of either object; a brief clarifying clause would help readers orient before the full paper.
Abstract: 'Donations' is introduced as the defining mechanism for online compound e-values without any indication of what is being donated or how the accounting works; a short parenthetical would reduce ambiguity.

Circularity Check

0 steps flagged · score 0.0 of 10

Abstract-only review finds no circularity: claimed power gains and FDR control are presented as consequences of new constructions, not as tautologies or fitted renamings.

full rationale

Only the abstract is available, so no equations, definitions, or theorem statements can be inspected for self-definitional loops, fitted-input-as-prediction, or uniqueness theorems imported from the authors. The abstract presents two methodological objects—the online e-closure principle and online compound e-values defined via donations—as independent constructions that yield strict power improvements over existing e-value and p-value online FDR procedures while retaining FDR control under arbitrary dependence, plus O(log t) decision algorithms and empirical gains. Nothing in the abstract equates a claimed prediction or first-principles result to its own inputs by construction, renames a known empirical pattern as a derivation, or makes a load-bearing uniqueness claim that reduces solely to self-citation. Residual risk that prior author work on e-values/online FDR is cited is ordinary and not, by itself, circularity under the stated rules. Honest non-finding: score 0, empty steps.

Assumptions & free parameters 0 free parameters · 3 assumptions · 2 invented entities

Abstract-only audit. No numerical free parameters are fitted in the abstract. Background axioms are the standard e-value / e-process validity and online FDR definitions used throughout the Ramdas et al. line. The only clearly new conceptual entity is the donation-based online compound e-value; independent evidence for it is not provided beyond the abstract's claim that it yields power gains while preserving FDR.

assumptions (3)

domain assumption E-values / e-processes remain valid evidence under arbitrary dependence and can be combined for FDR control in online settings.
Standard foundation of the e-value literature the paper builds on; invoked as the substrate for online e-closure and compound e-values.
domain assumption Online FDR is the appropriate risk measure for a continuous stream of hypotheses with decisions required at each time t.
Problem framing stated in the opening of the abstract; not proved, taken as the target guarantee.
ad hoc to paper The donation mechanism that defines online compound e-values preserves the supermartingale or e-process property needed for FDR.
This is the paper-specific construction; its validity is asserted by the abstract as part of the framework and is not independently established in the available text.

invented entities (2)

Online compound e-values defined through donations
purpose: Reallocate unused evidence across the stream so that later tests can gain power while the overall FDR guarantee is retained.
Abstract presents this as a novel formulation. No external falsifiable handle (e.g., a predicted constant or independent theorem) is given outside the claimed power/FDR results themselves.
Online e-closure principle
purpose: Provide an online analog of e-closure that yields valid rejection rules for streaming multiple testing.
Positioned as a core methodological ingredient. Independent evidence beyond the paper's own FDR claims is not supplied in the abstract.

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Cite this review

Pith. "Pith review of Improving online FDR procedures via online analogs of e-closure and compound e-values." pith.science (2026). https://pith.science/paper/HAODADV2

@misc{pith2026260324792,
  author       = {Pith},
  title        = {Pith review of: Improving online FDR procedures via online analogs of e-closure and compound e-values},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HAODADV2}},
  note         = {Machine review of arXiv:2603.24792}
}

abstract

In many scientific applications, hypotheses are generated and tested continuously in a stream. We develop a framework for improving online multiple testing procedures with false discovery rate (FDR) control under arbitrary dependence. Our approach is two-fold: we construct methods via the online e-closure principle, as well as a novel formulation of online compound e-values that is defined through donations. This yields strict power improvements over state-of-the-art e-value and p-value procedures while retaining FDR control. We further derive algorithms that compute the decision at time $t$ in $O(\log t)$ time, and we demonstrate improved empirical performance on synthetic and real data.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Dynamic $e$-closure for online hypotheses with any-time-valid evidence: closure principles and projective mergers
math.ST 2026-08 accept novelty 8.0 of 10

Dynamic e-closure controls stopped and supremum FDR for growing hypothesis families with continuing evidence, and shows coherent admissible pointwise mergers require one global weight sequence.

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.