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arxiv: 2606.01214 · v1 · pith:DAYRVGE3new · submitted 2026-05-31 · 📊 stat.AP

Markovianity-Based Conditioning Depth Diagnostics for Hidden Confounding in Observational Datasets

S. A. Adedayo This is my paper

Pith reviewed 2026-06-28 16:08 UTC · model grok-4.3

classification 📊 stat.AP
keywords causal discoverytime serieshidden confoundingMarkovianityconditioning depthgraph instabilityconstraint-based methodsobservational data
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The pith

Inferred causal graphs stabilize with added conditioning depth when the observed time series is approximately Markovian but keep changing if hidden confounding is present.

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

The paper tests constraint-based causal discovery methods on time series by tracking how much the output graph changes as the number of lagged observations available for conditioning grows. It claims that a finite-order Markov process produces stable graphs once the conditioning depth covers the relevant history. Hidden confounding or incomplete state representation leaves residual dependence, so the graph continues to shift with deeper conditioning. The resulting instability statistics serve as a practical check for when causal claims from observational data can be treated as stable.

Core claim

When the observed process is described approximately by a finite-order Markovian representation, inferred graphs should stabilize once sufficient past observations are observed. Hidden confounding and other hidden-memory mechanisms should remain sensitive to depth when the observed state is incomplete. The authors formalize this behavior with graph instability statistics computed over the conditioning-depth grid and evaluate the pattern on both synthetic systems with known ground truth and calcium imaging recordings.

What carries the argument

Graph instability statistics computed over the conditioning-depth grid, which quantify how much the inferred causal graph changes as more past observations are added to the conditioning set.

If this is right

  • In synthetic Markovian systems the inferred graphs stabilize after sufficient depth.
  • In synthetic systems with hidden memory the graphs remain sensitive to further depth increases.
  • c-GC variants produce the clearest separation between Markovian and hidden-memory cases.
  • In real calcium imaging data the number of inferred connections drops sharply then levels off with increasing depth.

Where Pith is reading between the lines

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

  • Practitioners could use the instability measure to select a minimal sufficient conditioning depth before reporting causal claims.
  • The diagnostic might be paired with separate tests for stationarity to reduce confusion between confounding and other sources of instability.
  • The same depth-sensitivity idea could be applied to score-based or other families of causal discovery algorithms beyond the constraint-based ones tested here.

Load-bearing premise

Observed changes in inferred graphs with conditioning depth are driven primarily by hidden confounding rather than lag-order misspecification, non-stationarity, or measurement error.

What would settle it

A controlled experiment in which a known finite-order Markovian system without hidden variables produces large continued graph changes with depth, or a system with documented hidden confounding produces no sensitivity to depth.

Figures

Figures reproduced from arXiv: 2606.01214 by S. A. Adedayo.

Figure 1
Figure 1. Figure 1: Schematic intuition for the Markovianity [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Conditioning depth sensitivity metrics for the single lag Markovian simulation, [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Conditioning depth sensitivity metrics for the single lag non-Markovian simulation with a smooth [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Conditioning depth sensitivity metrics for the Markovian simulation with multiple lags, [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Conditioning depth sensitivity metrics for the non-Markovian simulation with multiple lags and a [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: visualizes the decomposition into D− p and D+ p clarifies why this should be read as a depth sensitivity result rather than a simple plot of edge counts. For every recording and both methods, the largest graph change is the first transition from p = 1 to p = 2, and deletions dominate additions at that transition. Under c-GC, deletions account for 61.7% to 81.6% of [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

Reliable causal discovery in time series depends on whether the conditioning set adequately represents the system state. If relevant history or unobserved processes are omitted, residual dependence can appear as direct causal links. We study this failure mode on promnient constraint-based causal discovery methods through a simple premise: how much does the inferred graph change as conditioning depth increases? When the observed process is described approximately by a finite-order Markovian representation, inferred graphs should stabilize once sufficient past observations are observed. Hidden confounding and other hidden-memory mechanisms should remain sensitive to depth when the observed state is incomplete. We formalise this behavior with graph instability statistics computed over the conditioning-depth grid. The empirical study covers synthetic systems with known ground truth and calcium imaging recordings with unknown causal structure. In simulations, both Markovian and non-Markovian systems relatively upheld our premise. With known ground truth, we evaluate recovery using confusion matrix metrics; while in real data without ground truth, we use descriptive graph instability summaries. Across synthetic Markovian and hidden memory systems, c-GC variants give the clearest separation, while PCMCI variants show weaker compatible trends. In real data, inferred connectivity drops sharply with conditioning depths and then levels off. This method, however, does not recover latent graphs, nor does it clearly separate latent confounding from lag-order misspecification, non-stationarity, measurement error. Its contribution is more modest and practical: and explicit model-checking tool for deciding when causal claims are stable and when they should be treated caustiosly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript proposes a conditioning-depth diagnostic for time series causal discovery based on the premise that, under approximate finite-order Markovianity, inferred graphs from constraint-based methods stabilize as the depth of conditioning on past observations increases, while hidden confounding or other hidden-memory effects produce persistent sensitivity. Graph instability statistics are introduced to quantify changes over a grid of conditioning depths. The approach is evaluated on synthetic systems with known ground truth (using confusion-matrix recovery metrics) and on calcium imaging recordings (using descriptive instability summaries). c-GC variants are reported to yield clearer separation than PCMCI variants; the authors explicitly state that the method does not recover latent graphs and cannot isolate confounding from lag-order misspecification, non-stationarity or measurement error, positioning the contribution as a practical model-checking tool for deciding when causal claims are stable.

Significance. If the reported empirical patterns hold, the work supplies a modest but directly usable diagnostic that helps practitioners assess the stability of causal inferences drawn from observational time series—an important practical need given the prevalence of unobserved processes. The study includes both controlled synthetic experiments and real-data application, and the authors are transparent about the method’s scope and limitations. These features make the contribution useful for applied causal discovery even without stronger claims about mechanism identification.

major comments (1)
  1. [Abstract] Abstract: the statement that simulations 'relatively upheld our premise' with 'clearer separation' for c-GC variants is presented without any reported numerical values of the instability statistics, separation metrics, or statistical tests comparing Markovian versus non-Markovian regimes. Because the central claim rests on these simulations supporting the diagnostic’s utility, the absence of quantitative results weakens the ability to judge the strength of evidence.
minor comments (3)
  1. [Abstract] Abstract: 'promnient' is a typographical error for 'prominent'.
  2. [Abstract] Abstract: 'caustiosly' is a typographical error for 'cautiously'.
  3. [Abstract] Abstract: the phrase 'Its contribution is more modest and practical: and explicit model-checking tool' contains a grammatical error ('and' should be 'an').

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that simulations 'relatively upheld our premise' with 'clearer separation' for c-GC variants is presented without any reported numerical values of the instability statistics, separation metrics, or statistical tests comparing Markovian versus non-Markovian regimes. Because the central claim rests on these simulations supporting the diagnostic’s utility, the absence of quantitative results weakens the ability to judge the strength of evidence.

    Authors: We agree that the abstract would be strengthened by including concrete numerical values. The main text reports confusion-matrix metrics and instability statistics for the synthetic experiments (including separation between Markovian and hidden-memory regimes), but these were summarized qualitatively in the abstract to respect length limits. In the revised version we will insert the key quantitative results (e.g., mean instability values and separation gaps for c-GC versus PCMCI) directly into the abstract while keeping the statement within the journal’s word limit. revision: yes

Circularity Check

0 steps flagged

No significant circularity; diagnostic defined independently of fitted outputs and validated on external synthetic benchmarks

full rationale

The paper states a premise about Markovian stabilization versus depth sensitivity under hidden memory, then defines graph instability statistics over a conditioning-depth grid as a model-checking tool. This definition does not reduce to a fitted parameter or self-referential construction; the statistics are computed directly from inferred graphs at varying depths. Synthetic experiments use known ground truth to evaluate recovery via confusion matrices, providing an external benchmark independent of the diagnostic itself. The abstract explicitly disclaims separation of confounding from misspecification or non-stationarity, confirming the contribution is modest and non-circular. No self-citation load-bearing steps or ansatz smuggling appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central premise rests on the domain assumption of approximate finite-order Markovianity in the absence of hidden memory; no free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption The observed process can be approximated by a finite-order Markovian representation in the absence of hidden confounding.
    Stated as the baseline behavior for graph stabilization in the abstract.

pith-pipeline@v0.9.1-grok · 5800 in / 1347 out tokens · 28253 ms · 2026-06-28T16:08:26.746341+00:00 · methodology

discussion (0)

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