Quantifying structural uncertainty in chemical reaction network inference

Adriana Zanca; Ivo Siekmann; Jennifer A. Flegg; Yong See Foo

REVIEW 2 major objections 2 minor 1 cited by

Nonconvex penalties in sparse regularization cover more plausible chemical reaction networks than lasso when quantifying structural uncertainty.

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Nonconvex sparse penalties in CRN inference yield better coverage of plausible network structures than lasso regularization, supporting a hierarchical view of structural ambiguity from data.

T0 review reviewed 2026-05-22 challenge →

load-bearing objection Nonconvex penalties give wider coverage of plausible CRNs than lasso in the examples, but the work still needs to show that the local optima actually reach most high-likelihood networks. the 2 major comments →

arxiv 2505.15653 v3 submitted 2025-05-21 stat.ME q-bio.QM

Quantifying structural uncertainty in chemical reaction network inference

Yong See Foo , Adriana Zanca , Jennifer A. Flegg , Ivo Siekmann This is my paper

classification stat.ME q-bio.QM

keywords chemical reaction network inferencestructural uncertaintysparse regularizationnonconvex penaltieslasso regularizationdynamical systemssystems biologynetwork inference

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper examines how to measure uncertainty about the structure of chemical reaction networks inferred from observed changes in species concentrations over time. Standard lasso regularization typically points to one most likely network, but the authors test whether nonconvex penalties can generate a broader set of locally optimal solutions that together represent more of the networks consistent with the data. This matters because biologists often lack full knowledge of interactions in dynamical systems, and better uncertainty quantification supports more reliable predictions and targeted experiments. They map these solutions to candidate networks and show improved coverage, then apply the approach to real data where it recovers reactions noted across separate literature sources. The result is a hierarchical view of structural ambiguities that points to alternative reaction pathways suggested by the observations.

Core claim

Inducing sparsity with nonconvex penalty functions produces locally optimal solutions whose mapped CRN structures collectively cover a larger fraction of the plausible networks consistent with the observed concentration data than the lasso penalty achieves. This coverage difference allows construction of network-level probabilities that organize structural ambiguities hierarchically and identify alternative reaction pathways compatible with the data.

What carries the argument

Mapping locally optimal solutions from sparse-regularized optimization to candidate CRN structures, with nonconvex penalties used to promote sparsity.

Load-bearing premise

Locally optimal solutions obtained from sparse regularization can be mapped to CRN structures in a way that comprehensively represents the space of all plausible networks consistent with the data.

What would settle it

A complete enumeration or sampling of every CRN that fits the concentration time series data within measurement error would falsify the coverage claim if it revealed plausible networks reached only by lasso solutions and missed by nonconvex ones.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

Alternative reaction pathways consistent with the data become visible and can guide which experiments to run next.
Network-level probabilities produce a hierarchical representation that organizes structural ambiguities in the space of possible CRNs.
Real-world applications recover reactions proposed in multiple independent literature sources for the same system.
Quantified structural uncertainty improves confidence in both the inferred network and any downstream predictions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The coverage advantage may extend to other inverse problems where the goal is to recover sparse interaction graphs from noisy time series.
Combining the nonconvex regularization map with explicit model selection criteria could further narrow the set of high-probability networks.
The hierarchical ambiguity structure might be used to prioritize which reactions to verify first in laboratory settings.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Nonconvex penalties give wider coverage of plausible CRNs than lasso in the examples, but the work still needs to show that the local optima actually reach most high-likelihood networks.

read the letter

The key point is that nonconvex penalties recover more of the reactions mentioned across different literature sources than lasso does, and the authors turn the collection of local solutions into a hierarchical view of structural ambiguity. That shift from one network to a set of plausible ones is the practical step forward for systems biology work where data are sparse and multiple mechanisms can fit the same time series. They also show the approach on real examples and recover known reactions, which is a reasonable sanity check. The regularization machinery itself is not new, but mapping the stationary points to network-level probabilities and organizing the ambiguities hierarchically is a useful way to present the output. The main soft spot is that the coverage claim rests on the assumption that the local optima found by the solver are representative of the full set of data-consistent networks. The abstract gives no quantitative coverage numbers, no simulation study that checks completeness, and no argument that every high-likelihood network is reachable as a local optimum under the chosen penalty. Without that, the reported improvement could just reflect the fact that nonconvex penalties have more stationary points rather than genuinely better exploration. The real-data recovery is encouraging but still leaves open whether the method misses important alternatives. This is the kind of paper that would interest people doing inference on biological networks who already know sparse regularization and want a practical way to report uncertainty. A reader looking for new theory on sparse methods will not find much, but someone who needs to design follow-up experiments around ambiguous reaction sets could get ideas. It is worth sending to referees because the core idea is sound and the application is relevant; the revisions would mainly need clearer validation of the coverage claim and some controlled simulations.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a sparse regularization framework for inferring chemical reaction networks (CRNs) from time-series concentration data, with emphasis on quantifying structural uncertainty. Locally optimal solutions obtained under nonconvex penalties are mapped to candidate CRN structures; the central claim is that this yields better coverage of plausible networks than lasso regularization. The approach is illustrated on real data by recovering reactions proposed across multiple literature sources and includes a hierarchical representation of network-level ambiguities to suggest alternative pathways.

Significance. If the coverage claim is substantiated, the work would provide a practical tool for uncertainty quantification in systems biology beyond single-point network estimates. The real-data application that simultaneously recovers reactions from disparate literature sources is a concrete strength and offers empirical grounding. The hierarchical representation of ambiguities is a useful presentational device for guiding experimental design. However, the absence of quantitative coverage metrics and a completeness argument for the local-optima sampling limits the immediate impact.

major comments (2)

[§4] §4 (coverage comparison): the claim that nonconvex penalties produce better coverage of plausible CRNs than lasso is central yet unsupported by any quantitative metric (e.g., fraction of high-likelihood networks recovered, number of distinct structures, or statistical test of difference). Without these numbers it is impossible to judge whether the observed increase reflects genuine exploration or simply the larger number of stationary points.
[§3.2] §3.2 (mapping local optima to CRN structures): the manuscript assumes that the set of locally optimal solutions under the chosen nonconvex penalty and solver constitutes a representative sample of all networks whose likelihood is consistent with the data. No argument or auxiliary validation (e.g., comparison with exhaustive enumeration on small systems or MCMC sampling) is supplied to show that high-likelihood networks are reachable as local optima rather than being missed by the optimization landscape.

minor comments (2)

[Abstract] Abstract: quantitative details on coverage improvement and on how literature reactions were scored as 'recovered' would strengthen the summary and allow readers to assess the strength of the empirical claims.
[Methods] Notation: the precise form of the regularized negative log-likelihood and the definition of the penalty functions should be stated explicitly with equation numbers to facilitate reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report. The comments correctly identify that the coverage claim and the representativeness of local optima require stronger substantiation. We respond to each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: §4 (coverage comparison): the claim that nonconvex penalties produce better coverage of plausible CRNs than lasso is central yet unsupported by any quantitative metric (e.g., fraction of high-likelihood networks recovered, number of distinct structures, or statistical test of difference). Without these numbers it is impossible to judge whether the observed increase reflects genuine exploration or simply the larger number of stationary points.

Authors: We agree that the manuscript currently supports the coverage claim primarily through the real-data recovery of reactions proposed in multiple literature sources rather than through explicit quantitative metrics. In the revised version we will add direct comparisons, reporting the number of distinct CRN structures recovered under each penalty, the fraction of literature-proposed reactions captured by each method, and the total number of local optima obtained, thereby allowing readers to assess whether the observed coverage exceeds what would be expected from the larger number of stationary points alone. revision: yes
Referee: §3.2 (mapping local optima to CRN structures): the manuscript assumes that the set of locally optimal solutions under the chosen nonconvex penalty and solver constitutes a representative sample of all networks whose likelihood is consistent with the data. No argument or auxiliary validation (e.g., comparison with exhaustive enumeration on small systems or MCMC sampling) is supplied to show that high-likelihood networks are reachable as local optima rather than being missed by the optimization landscape.

Authors: The manuscript presents local optima as a practical sampling mechanism but does not supply an auxiliary validation that these optima reach the relevant high-likelihood networks. We will add a validation subsection that applies exhaustive enumeration on a small synthetic CRN (where the full set of plausible structures can be enumerated) and compares the local optima recovered by the nonconvex solver against this ground truth, thereby providing concrete evidence on reachability for the method. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical comparison of regularization methods stands independently

full rationale

The paper's core contribution is an empirical demonstration that nonconvex penalties yield higher coverage of plausible CRNs than lasso when mapping locally optimal solutions to network structures. No equations, fitted parameters renamed as predictions, or self-citation chains that reduce the central claim to its own inputs appear in the provided abstract or skeptic summary. The mapping from optima to structures and the coverage metric are presented as methodological choices whose validity is tested on real data rather than enforced by definition. This is the normal case of a self-contained applied-statistics paper whose results can be externally validated or falsified.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The central claim rests on the unstated premise that locally optimal sparse solutions adequately sample the space of data-consistent networks.

reviewed 2026-05-22 · how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantifying structural uncertainty in chemical reaction network inference." pith.science (2026). https://pith.science/paper/2505.15653

@misc{pith2026250515653,
  author       = {Pith},
  title        = {Pith review of: Quantifying structural uncertainty in chemical reaction network inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2505.15653}},
  note         = {Machine review of arXiv:2505.15653}
}

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read the original abstract

Dynamical systems in biology are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing species concentrations over time, the unknown reactions between the species. Existing approaches such as sparse regularisation largely focus on identifying a single, most likely CRN, without addressing uncertainty about the network structure. However, it is important to quantify structural uncertainty to have confidence in our inference and predictions. In this work, we explore how effective sparse regularisation methods are for quantifying structural uncertainty. Locally optimal solutions to sparse regularisation are mapped to CRN structures; however, it is unclear whether this approach encompasses all plausible CRNs. We find that inducing sparsity with nonconvex penalty functions results in better coverage of the plausible CRNs compared to the popular lasso regularisation. To validate our approach, we apply our methods to real-world data examples, and are able to simultaneously recover reactions proposed across multiple literature sources for a reaction system. Our emphasis on network-level probabilities enables a novel, hierarchical representation of structural ambiguities in the space of CRNs. This representation translates into alternative reaction pathways suggested by the available data, thus guiding the efforts of future experimental design.

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Locally optimal solutions to sparse regularisation are mapped to CRN structures... inducing sparsity with nonconvex penalty functions results in better coverage
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean LogicNat_equiv_Nat unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

BIC(R) = −2 L̂ + |R| log |D| ... approximate posterior p(R|D)

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Forward citations

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This paper was first reviewed by grok-4.3 on May 22, 2026.

Quantifying structural uncertainty in chemical reaction network inference

The reading

Core claim §

What carries the argument

Load-bearing premise §

What would settle it §

If this is right

Where Pith is reading between the lines

discussion (0)

Lean theorems connected to this paper

Core claim

Load-bearing premise

What would settle it