{"id":"4b538a2d-0d3b-447a-a7e8-c5439bae4a1c","arxiv_id":"2506.16416","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A betting-based wealth process monitors whether a deployed predictor's bounded risk has crossed a safety level, raising a controlled-false-alarm signal under unknown distribution shift and a set of thresholds still considered safe.","lead":"This paper uses 'testing by betting' to continuously watch a machine learning system's error rate during deployment and raise an alarm when the error rate climbs above a safety threshold, while keeping false alarms statistically controlled. It is aimed at engineers who need automatic monitoring when data shifts over time, for example in outlier detection or prediction sets.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"False-alarm control is proven only for the conditional null E[z_t|F_{t-1}]<=ε, while the paper's stated target is the unconditional risk R_t=E[z_t]; under dependence these differ and the advertised unconditional guarantee is not established.","rationale":"The reader's weakest-assumption analysis identifies exactly this conditional-versus-unconditional mismatch, and I agree it is the load-bearing concern. The main theorems are internally valid: Lemma 4.1 correctly shows that M_t is a nonnegative supermartingale under the conditional null, and Lemma 4.2 follows from Ville's inequality. The issue is scope: the paper's problem statement and abstract promise monitoring of the unconditional risk R_t(ψ), while the guarantees are for the conditional mean E[z_t|F_{t-1}]. Because arbitrary time dependence is allowed in the main text, these two quantities can diverge, and a false alarm relative to the stated target is possible. This is not an internal inconsistency in the proofs, but it is a mismatch between the central claim and the assumptions. The fix is straightforward: either explicitly state the independence or conditional-mean assumption in the main text and restrict the claims accordingly, or reframe the contribution as monitoring conditional risk and verify that practitioners can interpret that quantity. I therefore recommend CONDITIONAL rather than REJECT, since the mathematical machinery is sound and the gap is addressable. I also note the paper's practical strengths: the code is available, the experiments cover multiple shifts and tasks, and the empirical tables report false-alarm rates and detection delays in detail. The secondary issue of Proposition 4.5 being a heuristic bound is real but less central, because the paper's headline guarantee is false-alarm control, not a rigorous delay bound.","tokens_in":28097,"tokens_out":3603,"duration_ms":41603,"concrete_test":"Simulate a binary-loss stream with dependence: P(z_t=1|z_{t-1}=1)=0.5 and P(z_t=1|z_{t-1}=0)=0.05, initialized from the stationary distribution. The stationary unconditional mean is 0.05/0.55≈0.091<ε=0.1, so R_t≤ε for all t, yet the conditional mean is 0.5>ε whenever z_{t-1}=1. Run the multiplicative wealth process M_t with ε=0.1, δ=0.1, and the paper's approximately-GRO betting rate from Eq. (6), over many trajectories. If P(∃t: M_t≥1/δ) is substantially larger than δ, the method raises false alarms relative to the unconditional target, confirming the gap. If the crossing frequency is at most δ, then the unconditional guarantee may hold empirically in this dependence structure and the concern would be weakened.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper defines the monitoring target as the unconditional risk R_t(ψ)=E_{P_t}[z_t] (Eq. 2) and claims finite-sample false-alarm control for violations of this risk. However, every theoretical guarantee (Lemma 4.1, Lemma 4.2, Lemma 4.3 and the ψ-CS construction in Eq. 5) is stated under the conditional null H0(ψ): E_{P_t}[z_t|F_{t-1}]≤ε for all t (Eq. 3). The two notions coincide only when z_t is independent of F_{t-1}, or more specifically when the conditional and marginal means agree. The appendix remark in A.3 explicitly acknowledges this gap: it says an independence assumption on samples drawn from P_t and P_t' 'can simplify' the hypothesis pair so that E[z_t|F_{t-1}]=E[z_t]=R_t(ψ), but this assumption is not part of the main problem statement and is not imposed in the theoretical section. Consequently, for an arbitrary time-dependent stream, a threshold can have R_t(ψ)≤ε for all t while E[z_t|F_{t-1}]>ε on some subset of histories, and the wealth process can cross 1/δ and raise an alarm even though the paper's stated monitoring target, the unconditional risk, never violates ε. Lemma 4.2 does not bound the probability of this event because its null is not satisfied by such a stream. Thus the advertised false-alarm guarantee for the target risk R_t is not proven; the guarantee holds only for the conditional risk, which is a different quantity. The detection-delay bound in Proposition 4.5 is also heuristic rather than a proven worst-case bound, but the conditional-versus-unconditional mismatch is the more load-bearing issue because it concerns the core false-alarm claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a sequential-testing-by-betting framework for continuously monitoring whether a bounded risk of a deployed decision rule remains below a user-specified level ε in an evolving data stream. For each threshold ψ, the loss process z_t is monitored through a multiplicative wealth process M_t(ψ)=∏_{i=1}^t (1+λ_i(z_i−ε)), with a predictable betting rate λ_i; a threshold is flagged as violating when M_t(ψ) crosses 1/δ. The set of non-violating thresholds is reported as C_ψ^t={ψ:M_t(ψ)<1/δ}. The theoretical section claims a false-alarm guarantee by applying Ville's inequality to a test supermartingale (Lemma 4.2), asymptotic consistency under persistent violation (Lemma 4.3), and an approximate detection-delay bound (Proposition 4.5). Experiments on outlier detection (CIFAR-10/SVHN mixtures) and set prediction (FMoW and Naval propulsion) compare the wealth process with running-risk, summation, and Empirical-Bernstein baselines, reporting controlled false-alarm rates and competitive detection delays.","tokens_in":28554,"tokens_out":5369,"duration_ms":56096,"significance":"If the main guarantee were established for the paper's stated target, the framework would be a useful and broadly applicable contribution: it offers finite-sample, anytime-valid control of false alarms when monitoring a time-varying risk under unknown distribution shift, with essentially no distributional assumptions beyond boundedness and predictable betting rates. The paper gives credit to the underlying machinery (Waudby-Smith and Ramdas, Ville's inequality, GRO betting rates), and it provides open-source code and experiments on real datasets with multiple baselines. The principal advertised strength—a finite-sample false-alarm guarantee—does hold for the conditional null E[z_t|F_{t-1}]≤ε, via a correct use of Ville's inequality. However, the manuscript does not establish this guarantee for the unconditional risk R_t(ψ)=E[z_t] that it defines as the monitoring target, and the consistency and detection-delay statements are supported by heuristic arguments rather than complete proofs. These gaps bear directly on the paper's central claims.","major_comments":[{"comment":"The monitoring target is defined as the unconditional risk R_t(ψ)=E_{P_t}[z_t] (Eq. 2), but all theoretical guarantees—Lemma 4.1, Lemma 4.2, Lemma 4.3, and the ψ-CS construction in Eq. (5)—are stated under the conditional null E_{P_t}[z_t|F_{t-1}]≤ε (Eq. 3). Under arbitrary temporal dependence the two quantities need not coincide: a threshold may satisfy R_t(ψ)≤ε for all t while E[z_t|F_{t-1}]>ε on some histories, causing M_t(ψ) to cross 1/δ and raise a false alarm relative to the stated target. Lemma 4.2 does not bound the probability of this event because its null hypothesis is not satisfied by such a stream. The appendix remark in §A.3 acknowledges this gap, stating that an independence assumption on samples drawn from P_t and P_t' 'can simplify' the hypothesis pair so that E[z_t|F_{t-1}]=R_t(ψ), but this assumption is not part of the main problem statement and is not imposed in the theoretical section. The advertised false-alarm guarantee for the defined risk R_t is therefore not proven; the guarantee holds only for a different, conditional quantity. The authors should either re-define the monitoring target as the conditional risk E[z_t|F_{t-1}], or add an explicit, verifiable condition under which the conditional and unconditional means agree and check that the experiments satisfy it.","section":"§2–§4, Eq. (2)–(3), Lemma 4.2"},{"comment":"The proof of asymptotic consistency is not rigorous as written. The step 'Assuming a small, non-zero betting rate λ_t we use the approximation log(1+x)≈x' replaces an inequality with an uncontrolled approximation, so the subsequent Cesàro-mean argument does not constitute a proof. The statement lim inf_t (1/t)∑_{i=1}^t A_i ≥ lim inf_t A_t = λ·μ additionally requires a positive uniform lower bound on the conditional expected log-increments under the alternative and on λ_t; the definition of μ as an infimum over {E[z_t−ε|F_{t-1}]>0} does not guarantee that such a bound exists. The boundedness claim |v_t−A_t|≤λ_t is also asserted without derivation. Since Lemma 4.3 underlies the claim that persistently violating thresholds are eventually detected with probability one, this proof needs to be made fully rigorous under transparent conditions or replaced by a citation to a standard power-one result (e.g., Darling and Robbins, 1968) with the assumptions explicitly matched.","section":"§A.4, proof of Lemma 4.3"},{"comment":"The proposed detection-delay characterization (τ(ψ)−τ*(ψ)) ≈ O((log(1/δ)+T)/(λ·μ)) is heuristic rather than a proven worst-case bound. The proof in §A.4 explicitly assumes a sharp changepoint T, a constant violation intensity μ, a fixed betting rate λ, and uses the log(1+x)≈x approximation to pass from the multiplicative wealth process to the summation process; it also defines 'worst-case' through a loose Azuma-Hoeffding bound in the summation case without accounting for the martingale fluctuation term in the multiplicative case. The notation '≈O' is not a well-defined asymptotic statement. The proposition should be either restated as a heuristic (and labeled as such in the contributions) or converted into a theorem with precise assumptions, a rigorous proof, and a clear definition of the worst case.","section":"§4, Proposition 4.5 and §A.4 proof"}],"minor_comments":[{"comment":"In the sentence describing the forecaster's guess, 'minimize the mean squared prediction error ..., thei best guess' contains a typo; it should read 'the best guess'.","section":"§3"},{"comment":"The caption states 'detection delays τ(ψ)−τ*(ψ) across all ψ∈H', but the threshold set is denoted Ψ elsewhere; this is inconsistent notation.","section":"Figure 4 caption"},{"comment":"The text says the gap between running risk and wealth process 'remains fairy narrow' in the Naval propulsion experiment; this should be 'fairly narrow'.","section":"§6, Experimental text"},{"comment":"The phrase 'which are negligable for sufficiently large streams' contains a typo; it should be 'negligible'.","section":"Appendix C"},{"comment":"The paragraph describing limitations says 'we are inherently limited in our safety assurances by the unpredictability of any occuring shift'; 'occuring' should be 'occurring'.","section":"§7 Discussion"},{"comment":"The claim 'we do not impose sample independence' is in tension with the conditional-versus-unconditional gap noted above; the paper should explicitly discuss how the experiments handle this distinction when reporting false-alarm rates against the true unconditional risk.","section":"§3.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is built on well-established test-martingale machinery, and the framing as risk monitoring under shift is appealing. The main technical novelty is limited but reasonable for a UAI-style contribution. The central issue for the editor is that the headline finite-sample false-alarm guarantee is proven for the conditional null only, while the paper defines and evaluates the guarantee against the unconditional risk; this mismatch is acknowledged in an appendix remark but not resolved in the main theoretical or experimental sections. The consistency and detection-delay results also need to be either made rigorous or clearly labeled heuristic. These are fixable within the scope of a revision, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick verdict: this is a competent and honest application of testing-by-betting to a real monitoring problem, but the headline guarantee as written is for a different quantity than the one the paper says it is monitoring. That gap is fixable and should not sink the paper.\n\nWhat's genuinely new: the threshold-indexed confidence set Cψ_t (Eq. 5) that inverts a per-threshold wealth process to give a time-varying set of risk-controlling thresholds, and the framing as instantaneous-risk monitoring under arbitrary shift. The building blocks—test supermartingales, GRO betting rates—come from Waudby-Smith and Ramdas and Podkopaev-Ramdas, and the paper says so. Lemma 4.2 is a correct Ville-inequality argument for the conditional null E[z_t|F_{t-1}] ≤ ε. The experiments are thorough: three tasks, several shift types, baselines including the Empirical-Bernstein process, and code is public. The false-alarm rates in the tables stay at zero for the martingale methods, which matches the theory for the conditional null.\n\nThe soft spot is the conditional-versus-unconditional mismatch. The paper defines the monitoring target as R_t(ψ) = E_{P_t}[z_t] (Eq. 2) and says it raises a signal when R_t(ψ) > ε, but all the guarantees—Lemma 4.1, 4.2, 4.3, and the ψ-CS—are stated under E_{P_t}[z_t | F_{t-1}] ≤ ε. Those coincide only under independence or a conditional-independence assumption, which the appendix (A.3) mentions in a remark but the main text does not assume. Without it, a stream can have unconditional risk below ε while the conditional mean spikes, causing the wealth process to cross 1/δ and alarm even though the stated target never violated ε. So the advertised false-alarm control for R_t is not proven. I think the fix is straightforward: either add the conditional-independence assumption to the main problem statement, or explicitly redefine the monitored quantity as the conditional risk. The second option is arguably more natural for sequential decision-making, but the paper needs to say which it is doing.\n\nMinor issues: Proposition 4.5 is honestly labeled a heuristic with an '≈O' bound and a fixed-intensity changepoint model, so it should not be read as a worst-case guarantee. Lemma 4.3's proof implicitly assumes an eventually positive, bounded betting rate; that should be stated. The multiple-threshold simultaneity issue is disclosed and left out, which is fair.\n\nBottom line: the paper is useful for anyone building deployment monitors and deserves a serious referee. I'd send it out, with a request to close the conditional/unconditional gap before publication.","headline":"Solid testing-by-betting risk monitor with a real gap between the stated unconditional target and the proven conditional guarantee.","tokens_in":29063,"tokens_out":2950,"would_cite":false,"duration_ms":29059,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62L10","60G42"],"pacs":[],"model":"deepseek-v4-flash","headline":"A betting-style monitor can flag a deployed model's risk violations in real time under unknown distribution shift, while keeping the false-alarm rate bounded by a user-set level.","keywords":["risk monitoring","distribution shift","sequential hypothesis testing","testing by betting","test supermartingale","false alarm control","anytime-valid inference","bounded risk functions"],"falsifier":"Simulate a stream of bounded losses whose marginal mean at every time is at most $\\epsilon$ but whose conditional mean given the recent past exceeds $\\epsilon$, for instance losses that alternate predictably (high after low) with the low runs making up the majority, and run the monitor against the stated target $R_t(\\psi)$; if the wealth process crosses $1/\\delta$ with empirical frequency above $\\delta$ for small nominal $\\delta$, the guarantee does not protect the quantity the paper names as its monitoring target.","tokens_in":27889,"feed_emoji":"🎲","tokens_out":11031,"duration_ms":97759,"temperature":0.7,"pith_summary":"The paper claims that a monitoring system can watch an evolving data stream and raise an alarm whenever a deployed model's bounded risk exceeds a tolerance level, even when the distribution shifts in unknown ways. The approach casts risk monitoring as a sequential hypothesis test built on 'testing by betting': each candidate threshold runs a wealth process that multiplies small bets against the null hypothesis that the risk is under control, and a threshold is flagged when its wealth crosses a preset boundary. The central guarantee is finite-sample false-alarm control: a threshold whose risk is genuinely under control is falsely flagged with probability at most a user-set $\\delta$. If correct, this gives deployers a way to keep statistical safety assurances valid under arbitrary drift, which static risk-control methods cannot do.","feed_headline":"Betting-based monitor flags risk violations under unknown shifts","feed_subtitle":"A wealth process turns each new loss into evidence, alerting on real violations while capping false alarms.","key_machinery":"The load-bearing object is the wealth process $M_t(\\psi) = \\prod_{i=1}^t (1 + \\lambda_i (z_i - \\epsilon))$, a non-negative test supermartingale that starts at 1 and is driven by the centred losses $z_i - \\epsilon$ scaled by a predictable betting rate $\\lambda_i \\in [0, 1/\\epsilon)$. Its role is to convert a stream of bounded losses into accumulating evidence against the 'risk controlled' null; when the losses' conditional mean exceeds $\\epsilon$, the process drifts upward, and crossing the boundary $1/\\delta$ triggers rejection. The guarantees rest on three standard facts used by the paper: the supermartingale property under the null, Ville's inequality converting it into the time-uniform false-alarm bound, and the growth-rate-optimal (GRO) choice of betting rate to make evidence accumulate as fast as possible. The companion object is the confidence set $C^\\psi_t$, the set of thresholds whose wealth has not yet crossed the boundary.","core_discovery":"On the paper's own terms, the contribution is a test-supermartingale-based monitor for time-dependent risks. For each threshold $\\psi$ governing a decision mechanism, the process $M_t(\\psi) = \\prod_{i=1}^t (1 + \\lambda_i (z_i - \\epsilon))$ accumulates evidence against the null hypothesis $H_0(\\psi): E_{P_t}[z_t \\mid \\mathcal{F}_{t-1}] \\le \\epsilon$ for all times, with the betting rate $\\lambda_t$ chosen predictably (depending only on past losses) and capped at $1/\\epsilon$ to keep the wealth non-negative. Lemma 4.2 gives that under the null the wealth crosses the rejection boundary $1/\\delta$ with probability at most $\\delta$, which the paper interprets as control of the false alarm rate, and Lemma 4.3 gives that a persistently violating threshold is eventually rejected with probability one. The set of thresholds not yet rejected, $C^\\psi_t = \\{\\psi : M_t(\\psi) < 1/\\delta\\}$, is the live set of 'still trustworthy' settings, and its shrinkage signals that the model's reliability is deteriorating. Empirical results on outlier detection and set prediction under stepwise, immediate, and natural temporal shifts show the method detecting violations with controlled false alarms, in contrast to a running-risk estimator that flags safe thresholds.","pith_inferences":["Because the false-alarm guarantee is per-threshold across the whole run, an operator who each day selects the least conservative threshold still inside the confidence set faces a multiple-testing problem; a separate correction step, which the paper sets aside, would be needed before adaptive selection inherits the $\\delta$ guarantee.","The conditional-versus-unconditional gap in the null hypothesis is the natural stress point: a stream of positively autocorrelated bounded losses whose marginal mean stays below $\\epsilon$ while the conditional mean given the past sits above $\\epsilon$ would show whether the advertised false-alarm control protects the risk quantity an operator actually observes.","The shrinkage rate of the confidence set could be turned into an operational 'retrain now' signal; calibrating what shrink rate warrants an alert, as a function of $\\epsilon$ and $\\delta$, is a testable design question the paper leaves open.","The same machinery could monitor other bounded, online-observed quantities of a deployed system, such as calibration error or subgroup-specific error rates, since the proof only uses boundedness, predictability of the betting rate, and the supermartingale structure."],"forward_implications":["A threshold whose conditional risk stays at or below the tolerance $\\epsilon$ is falsely flagged with probability at most $\\delta$ over the entire monitoring run, so the false-alarm budget is respected without any assumption on the shift mechanism.","A threshold whose risk persistently exceeds $\\epsilon$ is eventually rejected with probability one, giving the monitor asymptotic completeness (power one).","Detection delay grows roughly as $(\\log(1/\\delta) + T)/(\\lambda \\mu)$, so stronger violations, more aggressive betting, and smaller $\\delta$ all speed detection, while shifts that arrive late are inherently harder to catch because earlier evidence must be overcome.","The live set of still-trustworthy thresholds $C^\\psi_t$ shrinks as shift intensity grows, providing a real-time picture of how much of the threshold grid remains reliable and when a model update is warranted.","Across outlier-detection and set-prediction tasks under stepwise, immediate, and natural temporal shifts, the wealth process matches the fastest baselines while keeping false alarms at zero in the reported runs, unlike the running-risk estimator, which flags safe thresholds."],"supporting_citations":[{"why":"Supplies Ville's inequality, which converts the wealth process's supermartingale property into the time-uniform false-alarm bound of Lemma 4.2.","marker":"[Ville, 1939]"},{"why":"Provides the multiplicative wealth-process form, the closed-form approximate-GRO betting rate, and the Empirical-Bernstein baseline used in experiments.","marker":"[Waudby-Smith and Ramdas, 2024]"},{"why":"Frames the approach as 'testing by betting' and supplies the game-theoretic interpretation of wealth accumulation as evidence.","marker":"[Ramdas et al., 2023]"},{"why":"Source of the power-one sequential test property that Lemma 4.3 invokes for eventual detection of violations.","marker":"[Darling and Robbins, 1968]"},{"why":"Azuma-Hoeffding inequality used in the appendix to bound the martingale terms in the detection-delay proof.","marker":"[Hoeffding, 1994]"},{"why":"Rolling risk control, reinterpreted as an implicit summation-type sequential test and used as a comparison baseline.","marker":"[Feldman et al., 2023]"},{"why":"Prior work tracking a running risk under shift; the running-risk estimator is evaluated as a baseline that lacks finite-sample false-alarm control.","marker":"[Podkopaev and Ramdas, 2022]"}],"fun_headline_variants":["Betting strategy spots risk violations in shifting data","Continuous risk monitor via betting, no fixed assumptions","Wealth process catches violations, controls false alarms","Real-time risk violation detection under unknown shift","Betting on losses to flag risk violations promptly"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The false-alarm guarantee is proved for the conditional mean of the loss given the past, $E_{P_t}[z_t \\mid \\mathcal{F}_{t-1}] \\le \\epsilon$, but the quantity the paper says it is monitoring is the unconditional risk $R_t(\\psi) = E_{P_t}[z_t]$; the two coincide only under an independence condition that is mentioned in an appendix remark rather than assumed in the main theorem.","fun_headline_variants_meta":{"raw":{"variants":["Betting strategy spots risk violations in shifting data","Continuous risk monitor via betting, no fixed assumptions","Wealth process catches violations, controls false alarms","Real-time risk violation detection under unknown shift","Betting on losses to flag risk violations promptly"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000555,"raw_usage":{"total_tokens":2646,"prompt_tokens":948,"completion_tokens":1698,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":564,"completion_tokens_details":{"reasoning_tokens":1628}},"tokens_in":564,"tokens_out":1698,"duration_ms":12914,"temperature":1.0,"reasoning_tokens":1628,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:27:45.276144+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate a stream of bounded losses whose marginal mean at every time is at most $\\epsilon$ but whose conditional mean given the recent past exceeds $\\epsilon$, for instance losses that alternate predictably (high after low) with the low runs making up the majority, and run the monitor against the stated target $R_t(\\psi)$; if the wealth process crosses $1/\\delta$ with empirical frequency above $\\delta$ for small nominal $\\delta$, the guarantee does not protect the quantity the paper names as its monitoring target.","supporting_citations":[{"cited_title":"E tude critique de la notion de collectif","cited_arxiv_id":null,"evidence_quote":"Supplies Ville's inequality, which converts the wealth process's supermartingale property into the time-uniform false-alarm bound of Lemma 4.2."},{"cited_title":"E stimating means of bounded random variables by betting","cited_arxiv_id":null,"evidence_quote":"Provides the multiplicative wealth-process form, the closed-form approximate-GRO betting rate, and the Empirical-Bernstein baseline used in experiments."},{"cited_title":"S ome nonparametric sequential tests with power one","cited_arxiv_id":null,"evidence_quote":"Source of the power-one sequential test property that Lemma 4.3 invokes for eventual detection of violations."},{"cited_title":"Probability Inequalities for Sums of Bounded Random Variables","cited_arxiv_id":null,"evidence_quote":"Azuma-Hoeffding inequality used in the appendix to bound the martingale terms in the detection-delay proof."},{"cited_title":"Achieving R isk C ontrol in O nline L earning S ettings","cited_arxiv_id":null,"evidence_quote":"Rolling risk control, reinterpreted as an implicit summation-type sequential test and used as a comparison baseline."},{"cited_title":"Tracking the risk of a deployed model and detecting harmful distribution shifts","cited_arxiv_id":null,"evidence_quote":"Prior work tracking a running risk under shift; the running-risk estimator is evaluated as a baseline that lacks finite-sample false-alarm control."}],"review_version":1}