{"id":"3d36a88f-88de-4d9d-a1e9-ec67f4da3bea","arxiv_id":"2511.15155","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"ROAMS adds a penalty for flagged time points to the state-space likelihood, jointly estimating model parameters and detecting additive outliers.","lead":"This paper introduces ROAMS, a method that estimates state-space models from time series while automatically detecting and excluding unusual measurements (outliers). It could make tracking data from animals, ships, or sensors more reliable when raw observations are noisy.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 1 has no convergence guarantee and the parallel hard-thresholding sweep is not an exact coordinate-wise minimizer, so the oracle-like zero-influence claim rests on an unverified fixed-point assumption.","rationale":"The reader's weakest assumption—lack of convergence guarantees for the alternating algorithm—is the same load-bearing concern I identify. The central empirical claim depends on Algorithm 1 actually reaching a solution with the zero-influence property; otherwise the comparisons with the oracle method in Section 4 are not measuring what the paper claims. I sharpened the concern by noting that the parallel hard-thresholding update is not an exact block-coordinate minimizer because future S and residuals depend on earlier γ updates, so monotonicity and fixed-point convergence are not automatic. This does not break the empirical evidence, but it makes the theoretical status of the method conditional. The paper provides reproducible code and extensive simulations, which are real evidence, but no convergence proof or diagnostics; a targeted computational check would settle whether the concern lands in practice. I therefore keep the reader's CONDITIONAL verdict unchanged.","tokens_in":19540,"tokens_out":9188,"duration_ms":98067,"concrete_test":"Instrument the released roam package to record objective (8), θ^(k), Γ^(k), and the fixed-point residual max_t |γ_t^(k) − r_t^(k)·1{flag_t}| at every iteration on all Study 1 replicates. Verify (i) the objective is nonincreasing to numerical precision and (ii) the terminal Γ satisfies the hard-threshold fixed-point equations (12) evaluated with K_t=0 for flagged t. If either fails, run 20 random outlier initializations per replicate and compare the spread of final θ; if this spread exceeds the Monte Carlo RMSE in Table 1, the reported oracle closeness is initialization-dependent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that minimizing objective (8) detects additive outliers and yields estimates close to the oracle—requires Algorithm 1 to terminate at a point where flagged observations are exactly excluded via (10) and the robustified likelihood (9). This is not established. Step 7 fixes Γ^(k-1), but Step 9 updates all γ_t simultaneously using residuals and covariances S_{t|t-1}(θ^(k),Γ^(k-1)_{t-1}) computed from the previous sweep. Since γ_t enters S_{s|s-1} for s>t through the Kalman gain in (10), a parallel sweep is not a coordinate-wise minimization of (8) for fixed θ^(k): after updating γ_t^(k), the S and residuals used for later coordinates are stale. The paper's statement that the hard-thresholding rule minimizes (8) given θ^(k) and Γ^(k-1)_n is therefore only true coordinate-by-coordinate conditional on the old Γ, not for the simultaneous update. Consequently, the objective need not be monotone and cycling is not ruled out. The convergence criterion in Algorithm 1 (line 15) checks only that successive iterates are close, which can hold at a non-fixed point. Without a proof or diagnostic that the terminal iterate satisfies γ_t∈{0,r_t} and K_t=0 for exactly the flagged t, the zero-influence property underpinning the oracle comparison in Section 4 is an assumption, not a guaranteed consequence of the algorithm.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ROAMS, a method for robust estimation and outlier detection in linear Gaussian state-space models. The observation equation is augmented with time-indexed mean-shift parameters γ_t, and estimation is performed by minimizing a robustified negative log-likelihood plus an L0 penalty on the number of nonzero shifts. The algorithm alternates between estimating the SSM parameters θ with the current outlier flags and updating the flags by a hard-thresholding rule; flagged observations are excluded from the Kalman update by setting the gain to zero, analogous to missing data. The tuning parameter λ is selected by BIC. The method is evaluated in three simulation studies against an oracle, classical maximum likelihood, and Huber/trimmed robust benchmarks, and is applied to four animal-tracking datasets. The paper also introduces a fast-updating threshold filter for online forecasting when future observations may be contaminated.","tokens_in":19932,"tokens_out":5636,"duration_ms":59318,"significance":"If the claimed performance holds, ROAMS is a practically useful contribution: it provides joint parameter estimation and additive-outlier detection in SSMs, has an intuitive missing-data interpretation, and comes with an open-source R package and reproducible simulation code. The simulation results are encouraging, showing ROAMS tracking an oracle that knows the true outliers in several contamination scenarios and outperforming classical and standard robust benchmarks, especially for observation-error variances. However, the methodological guarantees are not established: the alternating algorithm lacks a convergence proof, the zero-influence property of flagged observations is an assumption about the terminal iterate rather than a proven consequence, and the BIC-based selection of λ is heuristic for the nonregular L0-penalized objective. These gaps need to be addressed before the central claims can be fully accepted.","major_comments":[{"comment":"The hard-thresholding update (12) is a coordinate-wise minimizer of (8) conditional on θ^(k) and the previous Γ^(k-1), but step 9 updates all γ_t simultaneously using residuals and S_{t|t-1} computed from Γ^(k-1). This is not a joint minimization over Γ_n, and the objective need not decrease monotonically. The convergence criterion in line 15 only checks closeness of successive iterates, which can hold away from a fixed point. Consequently, the paper's central 'zero influence' property—flagged observations exactly excluded via K_t=0—is not guaranteed at termination. Please provide a convergence proof, a sequential coordinate-descent version with a monotonicity argument, or at least a final fixed-point check (γ_t ∈ {0, r_t} and K_t=0 for flagged t) with diagnostics in the simulation studies.","section":"Section 3.1, Eqs. (11)-(12), Algorithm 1 steps 6-15"},{"comment":"The BIC penalty k_λ log n is applied to a nonregular L0-penalized objective where the likelihood itself changes discontinuously with the flags (through both the log|S| indicator and the Kalman-gain zeroing). No justification or reference is given for using BIC in this setting. Since data-driven selection of λ is an advertised feature of ROAMS, the paper should either provide a theoretical rationale, cite relevant results on BIC for nonregular/penalized problems, or supply a dedicated simulation calibration showing BIC selects λ with good operating characteristics. As written, the BIC step is an additional heuristic layer.","section":"Section 3.2, Eq. (13)"},{"comment":"The claim that ROAMS 'tracks the oracle' is conditional on high sensitivity/specificity: when ROAMS flags exactly the true outliers, it coincides with the oracle by construction (both treat those points as missing). This is not circular, but it means the oracle comparison mostly reflects outlier-detection accuracy. The paper would be strengthened by reporting absolute RMSEs in addition to ratios relative to the oracle, and by quantifying the effect of missed/false flags on parameter estimates. Without such decomposition, the reader cannot tell how much of the oracle-like performance is due to correct flagging versus robustness of the objective to misclassification.","section":"Section 4, Table 1 and Figures 2-6"}],"minor_comments":[{"comment":"The fast-updating threshold filter's inflation constant b=2 is chosen 'based on empirical validation', but no sensitivity analysis or supporting experiments are shown. Since b is a free parameter of the proposed online filter, please provide a brief study of its effect on MSFE or at least a reference to a systematic calibration.","section":"Section 3.3, Eq. (15)"},{"comment":"The 'MSFE clean' metric removes points flagged by ROAMS-FUT for all methods. This may favor ROAMS, because the removed points are selected using ROAMS's own outlier detections. Please discuss this potential bias or compute an alternative metric that does not depend on the method being evaluated.","section":"Section 5.1, Table 3"},{"comment":"Simulation results are reported as averages over 200 runs without standard errors or confidence bands. Given the variability visible in outlier-detection rates, adding intervals or a measure of dispersion would help assess the reliability of the reported differences.","section":"Section 4, Figure 2 and Table 1"},{"comment":"The notation log|S_{t|t-1}| is used for the log-determinant; please define |·| as determinant at first use in the algorithm or equation (12), since |·| can be confused with cardinality or absolute value.","section":"Section 3.1, Algorithm 1 line 9"},{"comment":"The introduction states that no existing study combines SSM parameter estimation and outlier detection in one objective function. The claim is strong; please soften it or cite the closest related work (e.g., robust filters with explicit outlier indicators) to avoid overstating novelty.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The main technical gap is the lack of convergence/guarantee analysis for Algorithm 1. This is fixable within the manuscript's scope by adding a convergence theorem or a fixed-point verification, and the empirical claims are strong enough to merit a revision. The BIC heuristic also needs at least a calibration study or a more careful justification. I would not reject, but the current version overstates the theoretical grounding of the 'zero influence' property."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: this is a solid method paper. ROAMS takes the She-Owen mean-shift/L0 penalization idea and embeds it in linear Gaussian state-space estimation, zeroing the Kalman gain for flagged points and selecting the tuning parameter by BIC. That combination is genuinely new for SSMs, and the simulation studies are careful: they benchmark against an oracle that knows the true outliers, and ROAMS tracks the oracle well on parameter RMSE and out-of-sample MSFE across several contamination patterns. The animal-tracking applications, especially the blue whale example, make the point convincingly that classical estimates inflate observation-error variance when outliers are present. Code and data appear to be available, which is welcome.\n\nSoft spots, in order of seriousness. First, the convergence theory for Algorithm 1 is absent, and the stress-test note is right: the parallel hard-thresholding sweep is not an exact coordinate-wise minimization of (8) for fixed θ, because S_{t|t-1} and residuals for later timepoints are computed with stale Γ. The objective is therefore not guaranteed monotone, and the stopping rule (successive iterates close) does not imply a fixed point. The paper never claims to provide convergence theory, so this is an empirical heuristic, and the simulations suggest it behaves. But the sentence in Section 3.1 saying the hard-thresholding rule \"minimises (8) given θ^(k) and Γ^(k-1)_n\" is stronger than what is true unless read coordinate-by-coordinate. A referee should ask for either a convergence proof or a diagnostic verifying that the terminal iterate satisfies the zero-influence condition for flagged points.\n\nSecond, the fast-updating threshold filter uses b=2, chosen by empirical validation. That is a minor issue, but a sensitivity analysis for b would help. Third, the simulation tables report averaged RMSEs and MSFEs without uncertainty intervals; given run-to-run variability, standard errors or boxplots would be more informative. These are not fatal.\n\nThe literature treatment is honest and appropriately positioned: robust SSM estimation has been done with Huber/trimming and heavy-tailed errors, but joint outlier detection and estimation via L0 mean shifts in SSMs is new. The citation pattern looks reasonable.\n\nBottom line: this is a useful paper for anyone working in robust filtering or animal tracking. The central method works empirically; the theory gap is real but does not invalidate the contribution. It deserves serious peer review, with requests for clarification on the algorithm's convergence and perhaps a small proof or simulation diagnostic. I would bring it to our reading group if we were thinking about robust time series. Recommend engaging.","headline":"Solid method paper: mean-shift L0 penalization for SSMs, with strong simulations and an honest but real gap in convergence theory for the algorithm.","tokens_in":20358,"tokens_out":2425,"would_cite":true,"duration_ms":28318,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62F35","62M20","62M10"],"pacs":[],"model":"deepseek-v4-flash","headline":"A penalised mean-shift objective detects additive outliers in state-space models and keeps parameter estimates close to an oracle that knows the true outliers.","keywords":["state-space models","robust estimation","outlier detection","mean-shift penalisation","L0 penalty","Kalman filtering","BIC tuning","animal tracking"],"falsifier":"Generate a linear-Gaussian SSM with a single isolated 5-unit outlier repeated at the same time index across many independent runs, fit ROAMS, and check whether sensitivity and parameter RMSE match the oracle; also run the algorithm from several starting values and see whether the final flagged set and parameter estimates are stable. If estimates vary with initialisation, or the flagged set misses a moderate-size outlier such as one at 3 units, the central claim is not supported.","tokens_in":19448,"feed_emoji":"📡","tokens_out":3739,"duration_ms":41729,"temperature":0.7,"pith_summary":"The paper proposes ROAMS, an estimation method for linear Gaussian state-space models contaminated by additive outliers. It introduces a per-timepoint mean-shift parameter and adds an L0 penalty on the number of nonzero shifts, so one objective simultaneously flags outliers and estimates model parameters. The robustified likelihood drops the variance term for flagged points and sets the Kalman gain to zero, making flagged observations behave exactly like missing values. Simulations show ROAMS tracks the performance of an oracle that knows the true outlier locations, and it separates observation noise from genuine contamination better than classical, Huber, and trimmed-likelihood benchmarks. For practitioners, this removes the need to pre-specify the contamination fraction and provides BIC-based diagnostics for choosing the detection threshold.","feed_headline":"A mean-shift penalty flags outliers and protects state-space fits","feed_subtitle":"ROAMS treats flagged observations as missing, matching an oracle that knows the true outliers in simulations.","key_machinery":"The time-indexed mean-shift parameter gamma_t added to the observation equation, together with the L0-penalised robustified likelihood in objective (8)-(9). The hard-thresholding rule (12) updates gamma_t to the current residual whenever a Mahalanobis-type score exceeds lambda, and equation (10) zeroes the Kalman gain for flagged points — the mechanism that converts detection into zero influence. The alternating algorithm (11)-(12) ties the two together.","core_discovery":"The central claim is that replacing the Gaussian likelihood with a mean-shift-augmented likelihood plus an L0 penalty on the shift vector delivers joint robust parameter estimation and automatic outlier detection in linear Gaussian state-space models. For a flagged timepoint the Kalman gain is set to zero, so that observation has no influence on state updates or parameter estimation, exactly as if it were missing. The paper argues this detect-and-reject mechanism is what lets ROAMS match an oracle estimator that knows the true outlier locations, and demonstrates it through simulations across fixed-distance, multi-level, and clustered outlier configurations, plus animal-tracking data where cl","pith_inferences":["The mean-shift-as-missing-value view suggests the same objective could be applied to genuinely irregular observation times or partially missing multivariate vectors; the paper does not explore this.","A formal consistency result for the L0-penalised estimator under a sparse additive-outlier model would be a natural next step; the paper supplies simulations but no asymptotic theory.","The fast-updating threshold filter's single scalar b could be tuned adaptively or per coordinate, which might improve handling of consecutive outliers.","Because ROAMS decomposes variance between state noise and observation noise, it could serve as a diagnostic to distinguish sensor-type error from true environmental variability in other tracking contexts."],"forward_implications":["State-space parameters can be estimated robustly without knowing the contamination proportion in advance; lambda is chosen by BIC or by a user-specified target proportion.","Flagged observations are treated exactly as missing values, so ROAMS inherits the machinery for missing data and can handle both outliers and regular missingness in the same framework.","The observation-vs-state variance split is corrected: inflated observation error estimates caused by outliers are avoided, as shown in the blue whale application.","A fast-updating threshold filter is proposed for online forecasting and reduces the cascade of false outlier detections that can follow a single detected outlier.","On clean data ROAMS remains competitive with classical estimation, so robustness does not come at a large cost in outlier-free settings."],"fun_headline_variants":["Mean-shift penalty flags outliers in state-space models","ROAMS: robust state-space fits by penalizing shifts","Penalized mean-shift identifies outliers in time series","Outlier-proof state-space estimation via L0 shift penalty","Detect outliers and estimate state-space models jointly"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The method's oracle-like behaviour rests on the alternating hard-thresholding algorithm converging to a fixed point where the flagged set is exactly the set whose influence is removed; the paper does not prove this convergence, so an early or poor stopping point would break the guarantee.","fun_headline_variants_meta":{"raw":{"variants":["Mean-shift penalty flags outliers in state-space models","ROAMS: robust state-space fits by penalizing shifts","Penalized mean-shift identifies outliers in time series","Outlier-proof state-space estimation via L0 shift penalty","Detect outliers and estimate state-space models jointly"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000168,"raw_usage":{"total_tokens":1067,"prompt_tokens":686,"completion_tokens":381,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":430,"completion_tokens_details":{"reasoning_tokens":317}},"tokens_in":430,"tokens_out":381,"duration_ms":3901,"temperature":1.0,"reasoning_tokens":317,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T21:26:24.038301+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate a linear-Gaussian SSM with a single isolated 5-unit outlier repeated at the same time index across many independent runs, fit ROAMS, and check whether sensitivity and parameter RMSE match the oracle; also run the algorithm from several starting values and see whether the final flagged set and parameter estimates are stable. If estimates vary with initialisation, or the flagged set misses a moderate-size outlier such as one at 3 units, the central claim is not supported.","supporting_citations":[],"review_version":1}