Conformal changepoint localization

Aaditya Ramdas; Rohan Hore

REVIEW 2 major objections 4 minor 1 cited by

Conformal changepoint localization

T0 review · 2 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read The paper proves that ranking each candidate changepoint by how often within-segment permutations beat its plausibility score yields a finite-sample confidence set that contains the true changepoint with probability at least 1−α, under no d

desk verdict CONCH gives a genuinely finite-sample, distribution-free confidence set for changepoint localization under exchangeability, and the paper deserves a serious referee despite a known gap between the learned-score theory and the experiments. read the letter →

arxiv 2602.06267 v2 pith:MH3R6333 submitted 2026-02-05 stat.ME stat.ML

Rohan Hore , Aaditya Ramdas This is my paper

classification stat.MEstat.ML MSC 62G0962G1562G20

keywords changepointlocalizationdistribution-freeconfidencesetconformalp-valuesexchangeabilityfinite-samplevaliditypermutationtestsNeyman-Pearsonlemmaasymptoticsharpness

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

This paper tries to establish that offline changepoint localization can be done with finite-sample confidence sets under no distributional assumptions beyond exchangeability. Its method gives, for every candidate change index, a p-value equal to the fraction of within-side permutations whose changepoint-plausibility score is at most the score of the observed sequence. The paper proves these p-values are super-uniform under the null hypothesis that the candidate is the true changepoint, so the set of candidates with p-value above α is guaranteed to contain the true changepoint with probability at least 1−α. It also shows that an oracle likelihood-ratio score minimizes the expected set length, that a learned score makes the set's normalized length shrink to zero, and that every distribution-free changepoint confidence set is a CONCH set for some score. The practical consequence is that a user can wrap CONCH around any classifier or heuristic score and obtain a valid, sharp confidence set.

What carries the argument

The central object is the split-permutation group Π_t, the set of permutations of the n indices that shuffle the left block among itself and the right block among itself without mixing across t. For any changepoint plausibility score S, the conformal p-value p_t is the rank of S_t(X) among the scores evaluated on all permuted data sets. This rank transform is what converts exchangeability of the two blocks into finite-sample coverage, and it is also what allows arbitrary black-box scores to be plugged in without altering validity.

What would settle it

Generate n observations with a changepoint where the pre-change block is an AR(1) process with nonzero autocorrelation and the post-change block is i.i.d.; run CONCH with a weighted-mean score over many replicates and check empirical coverage. If coverage falls materially below 1−α, the exchangeability assumption is load-bearing; if coverage remains at 1−α, the method tolerates more within-block dependence than Assumption 1 states.

Watch

Extended reading notes

Core claim

CONCH defines, for each candidate index t, a conformal p-value p_t as the fraction of all permutations that keep the left and right blocks intact for which the plausibility score at t is no larger than the score on the observed data. Theorem 3.1 shows that p_t is super-uniform under the null hypothesis that t is the true changepoint, so thresholding at α yields a distribution-free confidence set with coverage at least 1−α. Building on this, the paper proves a conformal Neyman–Pearson lemma: the score that maximizes power against a given alternative is the likelihood ratio between the two changepoint hypotheses, and any strictly increasing transform of this oracle score minimizes expected con

Load-bearing premise

The guarantee holds only if, under the null hypothesis that t is the true changepoint, the observations to the left of t are exchangeable among themselves, those to the right are exchangeable among themselves, and the two groups are independent.

Editorial extensions

If this is right

For any score S and any α, the set {t : p_t > α} contains the true changepoint with probability at least 1−α whenever the pre- and post-change blocks are exchangeable and independent.
The oracle likelihood-ratio score minimizes expected confidence-set length, so with a well-chosen score the confidence set can be a singleton or near-singleton.
If a learned log-likelihood ratio is L2-consistent on data independent of the test sequence, the normalized confidence-set length converges to zero as the sample size grows.
Any heuristic or model-based confidence set can be recalibrated into a distribution-free finite-sample-valid set by defining a score from membership in or distance to that set.
Any distribution-free changepoint localization procedure can be represented as CONCH with an appropriate score, making CONCH the canonical class for such methods.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Inference: Because validity is automatic for any score, the practical bottleneck is score design; investing in a distinguishing score (for example, classifier logits) is the main lever for set width, not further statistical machinery.
Inference: When within-segment exchangeability fails but dependence has a known block structure, replacing full permutations with block permutations is a natural repair; the paper's proof structure suggests this route, though the paper itself does not establish a formal guarantee for it.
Inference: The sharpness theory assumes the learned score is trained on separate data, while the experiments train on the same sequence; the authors flag this gap, and a useful test is whether in-sample training preserves both coverage and shrinking set length in practice.
Inference: The universality result positions CONCH as an audit layer: any black-box segmentation algorithm's reported changepoint can be turned into a finite-sample-valid confidence set without re-deriving distributional 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 central result holds up: the split-permutation conformal p-values in Theorem 3.1 are valid under exchangeability of the pre- and post-changepoint segments, and this gives a finite-sample, distribution-free confidence set for any score function. The proof is a standard exchangeability argument, cleanly written, and the Monte Carlo variant is handled properly. This is a real advance over the earlier MCP method, which tends to produce wider sets.

What is genuinely new is the algorithmic framework: calibrating a changepoint score by permuting within the two hypothesized segments, then thresholding the resulting p-values. The "second Conformal NP lemma" is a nice, if expected, extension of the first one, and it gives principled guidance for choosing scores. The universality theorem is a representation result in the spirit of full conformal prediction; it is simple once you see it, but it cleanly ties the whole class together. The paper also ships code and runs experiments on images and text, which is good evidence the method works in practice.

The weak spots are real but not load-bearing. Theorem 5.2 assumes the learned log-likelihood ratio was trained on data independent of the test sequence, yet the experiments, by the authors' own admission, train on the same data. They explicitly call this out and leave the formal analysis to future work. That is an honest and correctly scoped limitation; it does not affect the finite-sample coverage claim. The proof of Lemma 4.2 is a bit compressed—the step connecting the p-value threshold to the Neyman-Pearson threshold relies on the monotonicity of the permutation rank, which is true for a fixed vector but deserves a sentence or two more. The multiple-changepoint extension is heuristic and depends on a consistent segmentation algorithm; the cross-fitted variant restores asymptotic validity, but the conditions on the segmentation are relatively strong.

Overall, the paper is a solid contribution to distribution-free changepoint analysis. The main assumption—exchangeability within each segment and independence between them—is clearly stated and is genuinely weaker than the parametric or asymptotic assumptions used elsewhere. If you work on conformal inference or changepoint methods, this is worth reading. I would take it seriously in peer review and expect the independence gap in the sharpness theory to be addressed in a revision, but I would not block acceptance on it.

Referee Report

2 major / 4 minor

Summary. The paper proposes CONCH, a conformal prediction framework for offline changepoint localization. Given any changepoint plausibility score S, it defines a permutation p-value p_t by comparing S_t(X) against S_t(π(X)) over the split-permutation group Π_t, and outputs the confidence set {t : p_t > α}. The central theoretical claim (Theorem 3.1) is finite-sample distribution-free coverage under exchangeability of the pre-change segment, exchangeability of the post-change segment, and independence between the two. The paper further contributes an oracle optimal score via a "conformal Neyman-Pearson lemma," asymptotic sharpness results for oracle and learned log-likelihood-ratio scores (Theorems 5.1 and 5.2), a universality theorem (Theorem 6.1), a calibration procedure for heuristic confidence sets, an extension to multiple changepoints, and experiments on synthetic and real image/text data.

Significance. If the sharpness results were rigorously established, this would be a substantial contribution: it would provide the first finite-sample distribution-free confidence sets for changepoint localization that are also asymptotically sharp, complementing the broader conformal-prediction toolbox. The universality theorem is elegant and gives a useful design principle. The coverage theorem itself is clean and correct, and the paper is transparent about its assumptions and limitations. However, the proof of asymptotic sharpness contains a false deterministic inequality (Lemma B.8) that invalidates the proofs of Theorems 5.1 and 5.2 as written. Since asymptotic sharpness is one of the paper's headline contributions, the manuscript currently overclaims relative to what is proven.

major comments (2)

[Appendix B.3.4, Lemma B.8] Lemma B.8 claims p_{t,n} ≤ \tilde{p}_{t,n} deterministically for the CPP score (5.1). The inequality direction is reversed. For every π, S_t(π(X)) ≤ S^{(n)}_t(π(X)) because \hat{ξ}(π(X)) is the maximizer of the permuted prefix sum, while S_t(X) = S^{(n)}_t(X). Therefore {S^{(n)}_t(π(X)) ≤ S_t(X)} ⊆ {S_t(π(X)) ≤ S_t(X)}, giving \tilde{p}_{t,n} ≤ p_{t,n}. A concrete counterexample: take n=5, t=4, \hat{ξ}=2, and \hat{ℓ}-values (10,10,-100,100,-1). The permutation π=(1,3,4,2,5) gives S_4(π)=0 ≤ S_4(X)=0, so it contributes to p_4, but S^{(n)}_4(π)=110 > 0, so it does not contribute to \tilde{p}_4. Thus p_4 > \tilde{p}_4. The proofs of Theorem 5.1 (Step 1, Appendix B.3.2) and Theorem 5.2 (final inequality, Appendix B.3.3) rely on p_{t,n} ≤ \tilde{p}_{t,n}; with the inequality reversed, the stated arguments do not yield the claimed O_P(1) length or normalized-length convergence. The asymptotic
[Section 5.2] Theorem 5.2 assumes that \hat{ℓ}_n is estimated on an independent dataset D'_n, as stated in (5.3) and the surrounding text. The experiments in Section 8 train the score on the same sequence D_n, so the formal sharpness guarantee does not apply to the headline experimental results. The authors acknowledge this gap and suggest a sample-splitting scheme. This is a limitation rather than an internal inconsistency, but it is load-bearing for the practical interpretation of the sharpness claim: a sample-splitting experiment or a clear statement that the reported widths are only heuristic would be needed to connect Theorem 5.2 to the empirical results.

minor comments (4)

[Appendix B.3.3] Typo: 'Hnece' should be 'Hence'. Also in (5.2), the argument of \hat{ℓ}_n appears as x_s; it should be x_i.
[Appendix B.1.2] Typo: 'fucntion' should be 'function'.
[Appendix B.3.2] Typo: 'independet' should be 'independent'.
[Section 4.1] The phrase 'which we call the second1 Conformal NP Lemma' contains a stray footnote marker '1'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: central coverage theorem is a direct exchangeability argument; acknowledged Theorem 5.2 gap is an assumption mismatch, not a circular step.

full rationale

The paper's central finite-sample guarantee (Theorem 3.1) is derived directly from Assumption 1: under H_{0,t}, X and any π(X) with π∈Π_t are equally distributed, so the conformal p-value p_t in (3.2) is super-uniform by Harrison's lemma. This argument does not fit any parameter, does not invoke the authors' prior results, and holds for any user-specified CPP score. The 'optimal score' results (Lemma 4.2, Theorem 4.3) are oracle benchmarks: they assume f0, f1, and ξ are known and use the classical Neyman-Pearson lemma; they are not predictions from fitted inputs. The universality result (Theorem 6.1) is a representation theorem - it constructs a CPP score from a given valid set and shows CONCH can reproduce it - but it is not used to establish coverage and is not a self-citation chain. The only notable caveat is an explicit limitation, quoted in Section 5.2: 'While Theorem 5.2 assumes that ℓ̂n is learned on data independent of Dn, CONCH would typically use ℓ̂n that is learned on Dn itself. Nevertheless, we expect that asymptotic sharpness should continue to hold provided the learned estimator is suitably stable... we leave it to future work.' This is an honest gap between the theorem's independence assumption and the same-data experiments, not a circular reduction. Self-citations to Dandapanthula and Ramdas (2025) are contextual or comparative, not load-bearing. Overall, the derivation is self-contained against the exchangeability assumption, and no step reduces by construction to its own input.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The main finite-sample validity theorem is self-contained and uses only the exchangeability assumption and a standard conformal p-value lemma. The asymptotic sharpness results add regularity conditions on the estimated log-likelihood ratio. No free parameters are fit to data in the mathematical claims; the listed parameters are practical hyperparameters.

free parameters (3)

Weight function w_{t,i} in score (4.3)
User-chosen weights (e.g., 1-|i-t|/n or exp(-|i-t|/n)) introduced to break t-symmetry; affect power, not validity.
Monte Carlo permutation count M (Algorithm 4)
User-specified; controls approximation quality of the p-value; larger M gives more precise p-values at higher cost.
Classifier architecture and training schedule (Section 8)
User-chosen for practical learned scores; affects statistical power only, not the finite-sample coverage guarantee.

assumptions (5)

domain assumption Exchangeability and independence of pre/post segments (Assumption 1)
Defines the model class; used in Theorem 3.1's proof to guarantee that π(X) =d X for π∈Π_t.
standard math Harrison (2012) Lemma 3
Used in the proof of Theorem 3.1 to show the rank-based p-value is super-uniform.
standard math Neyman-Pearson lemma
Basis for Lemma 4.2's optimality claim.
domain assumption Finite second moment of log-likelihood ratio and interior changepoint (Theorem 5.1)
Needed for exponential concentration of the MLE and drift bounds; if variances are infinite or τ→0,1, the proof fails.
domain assumption L2 consistency of estimated log-likelihood ratio on independent data (5.3)
Assumed in Theorem 5.2; used to control the difference between empirical and true log-likelihood ratios.

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Cite this review

Pith. "Pith review of Conformal changepoint localization." pith.science (2026). https://pith.science/paper/MH3R6333

@misc{pith2026260206267,
  author       = {Pith},
  title        = {Pith review of: Conformal changepoint localization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MH3R6333}},
  note         = {Machine review of arXiv:2602.06267}
}

read the original abstract

We study the problem of offline changepoint localization in a distribution-free setting. One observes a vector of data with a single changepoint, assuming that the data before and after the changepoint are i.i.d. (or more generally exchangeable) from arbitrary and unknown distributions. The goal is to produce a finite-sample confidence set for the index at which the change occurs without making any other assumptions. Existing methods often rely on parametric assumptions, tail conditions, or asymptotic approximations, or only produce point estimates. In contrast, our distribution-free algorithm, CONformal CHangepoint localization (CONCH), only leverages exchangeability arguments to construct confidence sets with finite sample coverage. By proving a conformal Neyman--Pearson lemma, we derive principled score functions that yield informative (small) sets. Moreover, with such score functions, the normalized length of the confidence set shrinks to zero under weak assumptions. We also establish a universality result showing that any distribution-free changepoint localization method must be an instance of CONCH. Experiments suggest that CONCH delivers precise confidence sets even in challenging settings involving images or text.

Figures

Figures reproduced from arXiv: 2602.06267 by the authors.

**Figure 1.** Distribution of conformal p-values (Gaussian mean-shift) for different methods. 8.1.2 Refinement of resampling-based confidence sets using CONCH-CAL We recall that the CONCH-CAL procedure (Algorithm 2) can refine confidence sets that were not originally designed with distribution-free validity guarantees. In particular, the Gaussian mean-shift model has been extensively studied, and several bootstrap-based methods p… view at source ↗

**Figure 2.** Refinement of bootstrap-based confidence sets using [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

**Figure 3.** Illustration of the DomainNet changepoint setup: samples switch from the real to the [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: p-values for domain shift detection between real and sketch domains: classifier scores [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]

**Figure 5.** Figure 5: CONCH p-values for sentiment shift in SST-2: from positive to negative reviews at ξ = 400 (left), and from 60% positive to 40% positive (right). 18 [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p048_6.png]

**Figure 7.** Figure 7: Left: observed sequence with multiple changepoints. Right: conformal [PITH_FULL_IMAGE:figures/full_fig_p049_7.png]

**Figure 8.** Figure 8: Two-urn changepoint experiment: CONCH confidence sets across δ values. Left: confidence sets always contain ξ = 350; right: average confidence set length decreases as dissimilarity δ increases. C.4 MNIST: detect change in digits We conduct a simulation based on the MN…

**Figure 9.** Figure 9: Illustration of MNIST changepoint setup: digit class shifts from ‘1’ to ‘7’ at [PITH_FULL_IMAGE:figures/full_fig_p050_9.png]

**Figure 10.** Figure 10: p-values for digit shift detection in MNIST: from digit ‘1’ to digit ‘7’ at [PITH_FULL_IMAGE:figures/full_fig_p051_10.png]

**Figure 11.** Figure 11: Illustration of CIFAR-100 changepoint setup: sequence shifts from bear images to beaver [PITH_FULL_IMAGE:figures/full_fig_p052_11.png]

**Figure 12.** Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p052_12.png]

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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

Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations
cs.LG 2026-07 conditional novelty 6.0 of 10

Weighted conformal changepoint localization (W-CONCH) and root-cause analysis (W-CROC) downweight likely-corrupted observations via classifier uncertainty, preserving coverage and shrinking confidence sets.

Reference graph

Works this paper leans on

17 extracted references · 5 linked inside Pith · cited by 1 Pith paper

[1]

Lemma B.8.Let{p t,n}be theCONCHp-values computed based on CPP score(5.1)

) (1 +ε 2,n/η+ 2 √ ε2,n/η) η  ≥1−4η, 42 as required. Lemma B.8.Let{p t,n}be theCONCHp-values computed based on CPP score(5.1). Then, it holds that deterministically, pt,n ≤˜pt,n,fort∈[n−1]. Proof.We start with observing that the original scoreS t(X)and frozen scoreS (n) t (X)can be equivalently written as St(x) = t∑ i=1 ˆℓn(xi)− ˆξn(x)∑ i=1 ˆℓn(xi), S (...

2005
[2]

Given samplesX∈R n, observe that d ( P[r] X|XL,t,XR,t ) d ( P[t] X|XL,t,XR,t )(X)∝ d(P[r] X ) d(P[r] X ) = ∏ i≤rf0(Xi)∏ i>rf1(Xi) ∏ i≤tf0(Xi)∏ i>tf1(Xi) =s ⋆(X)−1

B.2.2 Proof of Lemma 4.2: second conformal NP lemma In the setup of Section 4.1, we consider the following hypothesis testing problem: H′ 0 :X|X L,t,XR,t∼P [t] X|XL,t,XR,t v.s.H ′ 1 :X|X L,t,XR,t∼P [r] X|XL,t,XR,t . Given samplesX∈R n, observe that d ( P[r] X|XL,t,XR,t ) d ( P[t] X|XL,t,XR,t )(X)∝ d(P[r] X ) d(P[r] X ) = ∏ i≤rf0(Xi)∏ i>rf1(Xi) ∏ i≤tf0(Xi)...

2005
[3]

Offline changepoint localization using a matrix of conformal p-values.arXiv preprint arXiv:2505.00292,

Sanjit Dandapanthula and Aaditya Ramdas. Offline changepoint localization using a matrix of conformal p-values.arXiv preprint arXiv:2505.00292,

arXiv
[4]

Theorem A.1.For anyt∈[n],p t defined in(A.1)is a validp-value underH 0,t

Similar toCONCH, any randomly sampled π∈Π t preserves pre-change and post-change exchangeability underH 0,t, thereby providing us with a validp-value˜pt, as we state in Theorem A.1 and prove in Appendix B.1. Theorem A.1.For anyt∈[n],p t defined in(A.1)is a validp-value underH 0,t. In particular, for anyα∈(0,1),P ξ(˜pξ≤α)≤α. Consequently,C CONCH-MC 1−α is ...

2012
[5]

In particular, we partition the index set into two disjoint folds I1 :={t∈[n] :todd},andI 2 :={t∈[n] :teven}. 44 Algorithm 5:CONCH-SEG-crossfit Input:(X t)n t=1 (data);S: ⋃ m∈NXm→R m (CPP score function); segmentation algorithmSEG Output:C CONCH-SEG-crossfit 1−α 1I 1←{t≤n:todd},I 2←{t≤n:teven}; 2C←∅; 3forr∈{1,2}do 4( ˆK(r), ˆξ(r) 1 ,..., ˆξ(r) ˆK(r))←SEG ...

2018
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Post-detection inference for sequential changepoint localiza- tion.arXiv preprint arXiv:2502.06096,

Aytijhya Saha and Aaditya Ramdas. Post-detection inference for sequential changepoint localiza- tion.arXiv preprint arXiv:2502.06096,

arXiv
[14]

Figure 6 displays thep-value distributions from both methods

In the Gaussian mean-shift setting described in Section 8.1.1, we compare our framework against the changepoint localization method of Dandapanthula and Ramdas [2025], which also constructs distribution-free confidence sets for changepoints using a matrix of conformalp-values. Figure 6 displays thep-value distributions from both methods. Their approach yi...

2025
[15]

C.2 Gaussian mean-shift: localization of multiple changepoints We consider a multiple-changepoint Gaussian mean-shift model to illustrate the performance of CONCH-SEG (Algorithm 3)

andCONCHunder the Gaussian mean-shift model. C.2 Gaussian mean-shift: localization of multiple changepoints We consider a multiple-changepoint Gaussian mean-shift model to illustrate the performance of CONCH-SEG (Algorithm 3). In particular, we generaten= 1500observations with true change- points atξ1 = 150,ξ 2 = 500,ξ 3 = 820, andξ4 = 1100, segment means...

2018

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1”, and the latter observations are i.i.d. samples of the digit “7

withM= 300 permutations to obtain confidence sets. Whenδis small, the pre-change and post-change distributions are nearly indistinguishable. 49 Consequently, no method can sharply localize the changepoint, includingCONCHconfidence sets. Asδincreases, the two distributions beco...

2012
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Specifically, we construct a sequence ofn= 1,000 observations with a changepoint atξ= 400: the pre-change distributionP0,ξ consists of i.i.d

Threshold ( = 0.05) Figure 10: p-values for digit shift detection in MNIST: from digit ‘1’ to digit ‘7’ atξ= 400 C.5 CIFAR100: classifier strength affects power of CONCH We simulate a class-shift scenario using the CIFAR-100 image dataset [Krizhevsky et al., 2009] to evaluateC...

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Lemma B.8.Let{p t,n}be theCONCHp-values computed based on CPP score(5.1)

) (1 +ε 2,n/η+ 2 √ ε2,n/η) η  ≥1−4η, 42 as required. Lemma B.8.Let{p t,n}be theCONCHp-values computed based on CPP score(5.1). Then, it holds that deterministically, pt,n ≤˜pt,n,fort∈[n−1]. Proof.We start with observing that the original scoreS t(X)and frozen scoreS (n) t (X)can be equivalently written as St(x) = t∑ i=1 ˆℓn(xi)− ˆξn(x)∑ i=1 ˆℓn(xi), S (...

2005

[2] [2]

Given samplesX∈R n, observe that d ( P[r] X|XL,t,XR,t ) d ( P[t] X|XL,t,XR,t )(X)∝ d(P[r] X ) d(P[r] X ) = ∏ i≤rf0(Xi)∏ i>rf1(Xi) ∏ i≤tf0(Xi)∏ i>tf1(Xi) =s ⋆(X)−1

B.2.2 Proof of Lemma 4.2: second conformal NP lemma In the setup of Section 4.1, we consider the following hypothesis testing problem: H′ 0 :X|X L,t,XR,t∼P [t] X|XL,t,XR,t v.s.H ′ 1 :X|X L,t,XR,t∼P [r] X|XL,t,XR,t . Given samplesX∈R n, observe that d ( P[r] X|XL,t,XR,t ) d ( P[t] X|XL,t,XR,t )(X)∝ d(P[r] X ) d(P[r] X ) = ∏ i≤rf0(Xi)∏ i>rf1(Xi) ∏ i≤tf0(Xi)...

2005

[3] [3]

Offline changepoint localization using a matrix of conformal p-values.arXiv preprint arXiv:2505.00292,

Sanjit Dandapanthula and Aaditya Ramdas. Offline changepoint localization using a matrix of conformal p-values.arXiv preprint arXiv:2505.00292,

arXiv

[4] [4]

Theorem A.1.For anyt∈[n],p t defined in(A.1)is a validp-value underH 0,t

Similar toCONCH, any randomly sampled π∈Π t preserves pre-change and post-change exchangeability underH 0,t, thereby providing us with a validp-value˜pt, as we state in Theorem A.1 and prove in Appendix B.1. Theorem A.1.For anyt∈[n],p t defined in(A.1)is a validp-value underH 0,t. In particular, for anyα∈(0,1),P ξ(˜pξ≤α)≤α. Consequently,C CONCH-MC 1−α is ...

2012

[5] [5]

In particular, we partition the index set into two disjoint folds I1 :={t∈[n] :todd},andI 2 :={t∈[n] :teven}. 44 Algorithm 5:CONCH-SEG-crossfit Input:(X t)n t=1 (data);S: ⋃ m∈NXm→R m (CPP score function); segmentation algorithmSEG Output:C CONCH-SEG-crossfit 1−α 1I 1←{t≤n:todd},I 2←{t≤n:teven}; 2C←∅; 3forr∈{1,2}do 4( ˆK(r), ˆξ(r) 1 ,..., ˆξ(r) ˆK(r))←SEG ...

2018

[6] [6]

Post-detection inference for sequential changepoint localiza- tion.arXiv preprint arXiv:2502.06096,

Aytijhya Saha and Aaditya Ramdas. Post-detection inference for sequential changepoint localiza- tion.arXiv preprint arXiv:2502.06096,

arXiv

[7] [14]

Figure 6 displays thep-value distributions from both methods

In the Gaussian mean-shift setting described in Section 8.1.1, we compare our framework against the changepoint localization method of Dandapanthula and Ramdas [2025], which also constructs distribution-free confidence sets for changepoints using a matrix of conformalp-values. Figure 6 displays thep-value distributions from both methods. Their approach yi...

2025

[8] [15]

C.2 Gaussian mean-shift: localization of multiple changepoints We consider a multiple-changepoint Gaussian mean-shift model to illustrate the performance of CONCH-SEG (Algorithm 3)

andCONCHunder the Gaussian mean-shift model. C.2 Gaussian mean-shift: localization of multiple changepoints We consider a multiple-changepoint Gaussian mean-shift model to illustrate the performance of CONCH-SEG (Algorithm 3). In particular, we generaten= 1500observations with true change- points atξ1 = 150,ξ 2 = 500,ξ 3 = 820, andξ4 = 1100, segment means...

2018