arxiv: 2512.16001 · v2 · submitted 2025-12-17 · 📡 eess.SP · cs.LG

Concurrence: A dependence criterion for time series, applied to biological data

Evangelos Sariyanidi , John D. Herrington , Lisa Yankowitz , Pratik Chaudhari , Theodore D. Satterthwaite , Casey J. Zampella , Jeffrey S. Morris , Edward Gunning

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Robert T. Schultz Russell T. Shinohara Birkan Tunc

This is my paper

Pith reviewed 2026-05-16 21:03 UTC · model grok-4.3

classification 📡 eess.SP cs.LG

keywords concurrencetime series dependenceclassifier criterionbiological signalsfMRI analysisstatistical dependencenonlinear interactions

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The pith

Two time series are dependent if a classifier can tell aligned segments from misaligned ones.

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

The paper introduces concurrence as a criterion for statistical dependence between time series. Two signals count as dependent when a classifier succeeds at separating segments taken from them at matching times versus segments shifted out of alignment. The authors argue this test links directly to dependence and can handle complex non-linear relationships in biological signals without prior assumptions, parameter tuning, or large datasets.

Core claim

Concurrence defines two time series as dependent if one can construct a classifier that distinguishes temporally aligned segments from misaligned segments extracted from them. The authors establish that this criterion is theoretically linked to statistical dependence and demonstrate its use on fMRI, physiological, and behavioral data.

What carries the argument

The concurrence criterion, which tests dependence by training a classifier on temporally aligned versus misaligned segments of the two series.

If this is right

The method applies directly to fMRI, physiological, and behavioral signals.
No ad-hoc parameter tuning or large datasets are required.
It can serve as a standard dependence measure across scientific disciplines.
It captures non-linear interactions that current tools often miss.

Where Pith is reading between the lines

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

The approach may detect weak or transient dependencies in short recordings typical of experiments.
It could be paired with directionality tests to move from dependence to potential causation.

Load-bearing premise

A classifier's success at separating aligned from misaligned segments reliably signals statistical dependence between the series, regardless of signal type.

What would settle it

A pair of independent time series for which the classifier still distinguishes aligned from misaligned segments at above-chance accuracy, or a pair of dependent series for which it cannot.

Figures

Figures reproduced from arXiv: 2512.16001 by Birkan Tunc, Casey J. Zampella, Edward Gunning, Evangelos Sariyanidi, Jeffrey S. Morris, John D. Herrington, Lisa Yankowitz, Pratik Chaudhari, Robert T. Schultz, Russell T. Shinohara, Theodore D. Satterthwaite.

**Figure 1.** Figure 1: (a) Dependent signals x and y, and independent signals w and z. (b) Concurrent segments from x and y have different characteristics from non-concurrent segments, thus one can find functions f and g such that f(xi)g(yj ) is, on average, larger for concurrent segments (i.e., i = j) compared to non-concurrent segments (e.g., f as the identity operator and g the integral operator). (c) Concurrent and non-concu… view at source ↗

**Figure 2.** Figure 2: (a) Synthesized signals with deterministic dependence ( [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Pairs of (dependent) signals from six of the 100 synthesized datasets used in experiments. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: (a) Correlated fMRI signals from two brain regions. (b) Signals from regions that are [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: (a) Scatter plot and correlation between the respiration rate (RR) and ECG signal. (b) A [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

read the original abstract

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge or large datasets. We introduce a criterion for dependence, whereby two time series are deemed dependent if one can construct a classifier that distinguishes between temporally aligned vs. misaligned segments extracted from them. We show that this criterion, concurrence, is theoretically linked with dependence, and can become a standard approach for scientific analyses across disciplines, as it can expose relationships across a wide spectrum of signals (fMRI, physiological and behavioral data) without ad-hoc parameter tuning or large amounts of data.

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.

Desk Editor's Note private letter to a colleague

Concurrence gives a classifier-based dependence test that could be useful for bio signals, but the stationarity assumption creates a real risk of false positives on the non-stationary data it targets.

read the letter

The core idea is that two time series are dependent if a classifier can tell aligned segments apart from misaligned ones. That framing is new enough to stand out, and the paper positions it as a practical tool for nonlinear dependencies in biological signals without needing large data or tuning parameters. If the full text shows clean empirical wins on fMRI or physiological recordings, that would be a genuine plus for exploratory work in neuroscience and related areas where standard measures often fall short on complex interactions.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces 'concurrence' as a new criterion for statistical dependence in time series. Two series are deemed dependent if a classifier can be constructed to distinguish temporally aligned segments from misaligned ones extracted from the pair. The authors claim this criterion is theoretically linked to dependence and demonstrate its utility on biological signals (fMRI, physiological, and behavioral data) without requiring ad-hoc parameter tuning or large datasets.

Significance. If the theoretical equivalence holds under realistic conditions and the empirical results are robust, concurrence could provide a simple, general-purpose tool for detecting nonlinear dependencies in biological time series where traditional measures require strong assumptions or extensive data. The approach's claimed lack of tuning makes it potentially attractive for cross-disciplinary scientific analyses.

major comments (2)

[Theoretical link section (derivation of concurrence)] The theoretical link (asserted in the abstract) that aligned vs. misaligned segment pairs have identical distributions under independence requires the processes to be stationary, so that the joint law of (X_t, Y_t) equals that of (X_t, Y_{t+k}) for any lag k. Biological signals routinely violate stationarity due to trends or time-varying marginals; this can make aligned and misaligned pairs distinguishable even under independence, producing false positives. The manuscript must either prove the link under weaker assumptions or explicitly test robustness on non-stationary data.
[Empirical validation and applications] The abstract claims the method works 'across a wide spectrum of signals' without ad-hoc tuning, yet no details are given on classifier architecture, segment length selection, or quantitative benchmarks against established dependence measures (e.g., mutual information estimators or kernel-based methods). Without these, it is impossible to verify that performance gains are not due to implicit choices or dataset-specific effects.

minor comments (2)

[Abstract] The abstract is overloaded with claims; separating the theoretical statement from the empirical scope would improve readability.
[Methods] Notation for segments and alignment should be defined explicitly at first use to avoid ambiguity when describing the classifier input.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which highlight important aspects of the theoretical foundation and empirical validation. We address each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: [Theoretical link section (derivation of concurrence)] The theoretical link (asserted in the abstract) that aligned vs. misaligned segment pairs have identical distributions under independence requires the processes to be stationary, so that the joint law of (X_t, Y_t) equals that of (X_t, Y_{t+k}) for any lag k. Biological signals routinely violate stationarity due to trends or time-varying marginals; this can make aligned and misaligned pairs distinguishable even under independence, producing false positives. The manuscript must either prove the link under weaker assumptions or explicitly test robustness on non-stationary data.

Authors: We agree that the derivation establishing equivalence between concurrence and statistical dependence relies on stationarity to guarantee identical distributions for aligned and misaligned pairs under the null. The manuscript will be revised to explicitly state this assumption in the theoretical section. Additionally, we will add a new subsection with controlled simulations on non-stationary processes (including linear trends, time-varying means, and heteroscedasticity) to quantify robustness and report false-positive rates. These tests will be presented alongside the existing biological applications to clarify the method's practical scope. revision: yes
Referee: [Empirical validation and applications] The abstract claims the method works 'across a wide spectrum of signals' without ad-hoc tuning, yet no details are given on classifier architecture, segment length selection, or quantitative benchmarks against established dependence measures (e.g., mutual information estimators or kernel-based methods). Without these, it is impossible to verify that performance gains are not due to implicit choices or dataset-specific effects.

Authors: We will expand the Methods and Results sections to include: (i) the precise classifier architecture and training procedure, (ii) the rationale and selection protocol for segment length (including sensitivity analysis), and (iii) quantitative benchmark comparisons against mutual-information estimators and kernel-based dependence measures on both synthetic benchmarks and the reported biological datasets. These additions will enable direct verification that observed performance is not driven by undisclosed choices. revision: yes

Circularity Check

0 steps flagged

No circularity: operational definition of concurrence stands independently of the claimed theoretical link

full rationale

The paper defines concurrence directly as the existence of a classifier able to separate temporally aligned versus misaligned segments. The abstract asserts that this criterion is 'theoretically linked with dependence' but supplies no equations, no derivation steps, and no self-referential construction that would make the link tautological. No fitted parameters are renamed as predictions, no uniqueness theorem is imported from prior self-work, and no ansatz is smuggled via citation. The stationarity concern is an external modeling assumption rather than a reduction of the claimed result to its own inputs. The derivation chain therefore remains self-contained against the supplied text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; the central claim rests on an unshown theoretical linkage between classifier performance and dependence plus the assumption that the method requires no tuning or large data.

axioms (1)

domain assumption Classifier performance on aligned vs. misaligned segments indicates statistical dependence
This is the load-bearing definition stated in the abstract.

pith-pipeline@v0.9.0 · 5453 in / 1059 out tokens · 39788 ms · 2026-05-16T21:03:48.460280+00:00 · methodology

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.

We introduce a criterion for dependence, whereby two time series are deemed dependent if one can construct a classifier that distinguishes between temporally aligned vs. misaligned segments extracted from them.
IndisputableMonolith/Foundation/ArithmeticFromLogic.lean embed_strictMono_of_one_lt unclear

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

Theorem 1 … E{z+}−E{z−}=p(1−p)pαpβ(1−pϵx)(1−pϵy)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 4 internal anchors

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Remark1.The processes ˜hx[t]and ˜hy[t]are Bernoulli processes. Proof. The process ˜hx[t] defined as in equation 8 is equivalent to merging two processes (Bertsekas & Tsitsiklis, 2008), as it can also be written as ˜hx = min{α[t]h[t] +ϵ x[t],1}= max{α[t]h[t],ϵ x[t]}.(14) Moreover, the processes that are being merged are both Bernoulli processes: The proces...

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