{"id":"04c6670f-c102-4d65-b8df-217ad0a3863f","arxiv_id":"1909.00693","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A distance-scaling k-NN that multiplies distances to positive examples by a tuned factor γ improves F-measure on imbalanced classification.","lead":"This paper introduces γk-NN, a nearest-neighbor variant that shrinks distances to positive examples to improve F1 on imbalanced data. It reports strong results on public datasets and on French tax fraud data, especially when combined with oversampling methods.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported F1 gain of γk-NN may be a tuning artifact: the strongest distance-based baseline (dupkNN) uses a fixed duplication factor, while γ is tuned by cross-validation, so the comparison does not isolate the geometric mechanism.","rationale":"The theoretical propositions are the weakest part of the paper's writing, but they are not the most load-bearing weakness. For a fixed query, decreasing γ moves every positive neighbor earlier in the dγ ordering and never moves a negative earlier, so the number of positives among the k nearest neighbors is nondecreasing; hence the false-negative rate is monotone in γ for every k, not only k=1. The product-form proof in Section 4.2 is a sketch (ε is a random quantity and the equality should be conditional with an expectation), but the monotonicity conclusion survives, so the k=1/k=3 gap identified by the reader is unlikely to invalidate the method. The genuinely load-bearing issue is empirical: the headline comparisons do not control for hyperparameter tuning. dupkNN, the runner-up baseline in Table 2, uses a fixed IR-based duplication factor, while γk-NN tunes γ by cross-validation. Because γ is mathematically similar to a replication/class-weight parameter, the observed gain over dupkNN could be a tuning artifact. This concern can be settled directly by adding tuned duplication and threshold baselines. No code or private data are available to check the DGFiP results, which reinforces the need for such a baseline on the public datasets. The final verdict remains CONDITIONAL: the method is plausible and the experiments are suggestive, but the central claim should be conditioned on this control.","tokens_in":13260,"tokens_out":19365,"duration_ms":203649,"concrete_test":"Rerun the 19 public datasets with the same 80/20 splits, k=3, and 10-fold CV, adding: (i) tuned-dupkNN, where the positive replication factor r is selected from {1,...,ceil(IR)} by CV; and (ii) thresholded 3-NN, where a positive is predicted when the positive vote fraction exceeds θ, with θ selected on the same grid. If the test-set F1 of either tuned baseline is within one standard error of γk-NN's mean (Table 2), the central claim that γk-NN's distance scaling improves over existing methods is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 5.1 tunes γ for γk-NN on a 10-fold CV grid over [0,1], but the distance-based baselines in Table 2 are not given an equivalent tuned positive-influence parameter. In particular, dupkNN (Section 5.1) duplicates positives by the fixed IR and is the second-best baseline (mean F1 0.575 vs 0.607 for γk-NN). Since γ is essentially a continuous version of a positive-replication/class-weight parameter, the 3.2-point mean advantage may come from tuning that parameter rather than from the Voronoi geometry. The same confound appears in the sampling experiments: OS+γk-NN tunes two γ values (real vs synthetic positives) while the OS baselines are used with default parameters apart from the sampling ratio. A tuned decision threshold or a tuned vote-weight for the positive class on the same augmented data could plausibly match these F1 gains. This does not make the method wrong, but it makes the central empirical claim—that the distance-rescaling mechanism is responsible for the improvements—currently unsupported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes γk-NN, a k-nearest-neighbor variant for imbalanced classification in which the distance from a query to every positive training example is multiplied by a factor γ in (0,1). The authors argue that this expands the Voronoi regions of positive examples, reducing false negatives while controlling false positives, and provide two propositions (Section 4.2) intended to justify the choice γ<1 for the minority class. They evaluate the method on 19 public UCI/KEEL datasets and 11 private DGFiP tax-fraud datasets, comparing against distance-based baselines (k-NN, weighted k-NN, class-weighted k-NN, duplicated-positive k-NN, kRNN, LMNN) and oversampling methods (SMOTE, Borderline-SMOTE, ADASYN, SMOTE+ENN, SMOTE+Tomek), and they report improvements in mean F1, including further gains when γk-NN is combined with oversampling. The central claim is that the distance-rescaling mechanism itself, rather than incidental parameter tuning, is responsible for the reported gains.","tokens_in":13541,"tokens_out":5446,"duration_ms":50206,"significance":"If substantiated, this is a practically attractive contribution: the algorithm is simple, has the same complexity as k-NN, is easy to combine with sampling methods, and is evaluated on a real large-scale tax-fraud application that gives the study ecological validity. The theoretical propositions, although presented only as sketches, correctly capture the intuition that shrinking distances to positives enlarges their effective influence. However, the current evidence has three load-bearing gaps: the theory is proved only for k=1 while all experiments use k=3; the proof relies on an unjustified independence/fixed-ε factorization; and the empirical comparison does not control for the fact that γ is tuned by cross-validation while the main distance-based baselines use fixed influence parameters. The central idea is defensible and the gaps appear fixable, but the manuscript as written does not yet support the strong empirical and theoretical claims made in the abstract and Section 5.","major_comments":[{"comment":"The proof of Proposition 1 is not a derivation from first principles. Eq. (1) factorizes the false-negative probability as a product over positive training examples, treating each event x' ∈ S_{ε/γ}(z) as independent with the same probability and treating ε (the distance to the nearest neighbor) as fixed. For a random query, ε is itself a random variable that depends on the positions of both classes, and the events for different positives are not independent conditional on ε. The inequality FN_γ(z) ≤ FN(z) for γ≤1 actually follows immediately from monotonicity of the spherical probability in the radius, so the factorization is doing no work. The authors should either supply a rigorous derivation with explicit distributional assumptions or reframe the statement as a heuristic justification rather than a formal proposition.","section":"Section 4.2, Eq. (1) and Proposition 1"},{"comment":"The theoretical analysis is explicitly restricted to k=1, while every reported experiment uses k=3. The statement in Section 5.1 that \"the same Analysis can be conducted for other values of k\" is not a proof. For k>1 the false-negative event is not \"all positives are outside a sphere of radius ε/γ\": with k>1, a positive example can be among the k nearest neighbors yet still lose the majority vote, and negatives inside the sphere can also influence the outcome. Thus Propositions 1 and 2, as stated, do not cover the experimental results in Tables 2 and 3. The authors should either extend the analysis to k=3 (or general k) with a precise statement about the majority-vote rule, or report all experiments with k=1 and clearly separate the k=1 theoretical claim from the k=3 empirical claim.","section":"Section 4.2 and Section 5.1"},{"comment":"The main empirical comparison is confounded with hyperparameter tuning. The proposed method tunes γ on a 10-fold CV grid over [0,1], while dupk-NN uses a fixed duplication factor equal to the imbalance ratio and cwk-NN uses a fixed class-proportion weight. Since γ acts essentially as a continuous positive-instance replication/class-weight parameter, the reported mean advantage of γk-NN over dupk-NN (0.607 vs 0.575) may reflect the benefit of tuning a positive-influence parameter rather than the specific Voronoi geometry. The same issue appears in the sampling experiments, where OS+γk-NN tunes two γ values (one for real positives and one for synthetic positives) while the OS baselines use default parameters apart from the sampling ratio. The authors should include controlled baselines with an equivalently tuned positive-influence parameter (e.g., a tuned duplication factor or a tuned positive vote weight) and, if possible, report the performance of γk-NN with γ fixed to a value matched to the baseline's effective influence.","section":"Section 5.1, Table 2 and Fig. 4"},{"comment":"No statistical significance testing is reported. The headline result is a mean F1 gain of about 3.2 points over the second-best baseline, but with standard deviations in the 0.02–0.05 range and only 19 datasets, a paired test is needed to rule out chance. Moreover, Table 2 shows that γk-NN is the best method on only about 7 of 19 datasets, and the average gain is strongly influenced by the hayes dataset (0.593 vs 0.221 for the next best) and the german dataset. The authors should report per-dataset win/loss counts and a paired significance test (e.g., Wilcoxon signed-rank test) with effect sizes, and they should discuss whether the conclusion is robust when the most influential datasets are removed.","section":"Section 5.2, Tables 2 and 3"}],"minor_comments":[{"comment":"The sentence \"The results for k = 1 are comparable as the presented results in this section\" is incomplete and no k=1 results are shown anywhere; please either provide the k=1 table or remove the sentence.","section":"Section 5.1, text after Table 2"},{"comment":"The text says the γ parameter is tuned \"in the range [0, 1]3 using a step of 0.1\"; the superscript 3 appears to be a typo, since γ is a scalar. It should read \"in the range [0,1] using a step of 0.1\", and the same correction applies to the quoted range for synthetic-positive γ in Section 5.2.","section":"Section 5.1, experimental setup"},{"comment":"The table uses comma decimal separators for some entries (e.g., 0,454) but the text and other tables use decimal points; please standardize the decimal notation.","section":"Table 3"},{"comment":"The figure legends/labels use \"3NN\" where the text refers to γk-NN (e.g., \"Comparison of -3NN with 3NN\" in Fig. 4 and \"-3NN and OS* + -3NN\" in Fig. 6). These labels should be clarified to read γk-NN and OS+γk-NN respectively.","section":"Figures 4 and 6"},{"comment":"The tie-breaking rule is implicit: for even k, the condition |NN_γ ∩ NN_+| ≥ k/2 means ties are resolved in favor of the positive class. This should be stated explicitly because it biases the algorithm toward recall and is relevant to the F1 comparison.","section":"Algorithm 1"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope and the empirical setting, including the DGFiP tax-fraud data, is appropriate. The main risk is that the current version overstates the support for its claims: the theory is not yet at the level of a formal result, and the experimental comparison does not isolate the proposed mechanism from tuning effects. These are fixable with additional experiments and a more careful statement of the theoretical scope, so I would encourage a major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a practical nearest-neighbor variant for imbalanced data — scale the distance to positive training examples by a tunable γ — and the paper backs it with a wide experimental sweep, including real tax-fraud data. The contribution over earlier class-weighted distances (Barandela et al. 2003) is the tuned γ and the second γ for synthetic positives. That is a modest extension, but a legitimate one.\n\nWhat it does well: the method is simple, easy to implement, and the experiments cover 19 public datasets plus 11 proprietary fraud datasets. The combination of γk-NN with SMOTE-style oversampling is a sensible idea and the results suggest the two are complementary. The paper is honest about the prior art, and the authors do not oversell the theory.\n\nThe soft spots, in order. First, the theoretical analysis in Section 4.2 is really a sketch. It is proved for k=1 only while every experiment uses k=3; the paper asserts without proof that the analysis extends. The proof itself assumes independence and a fixed ε, and the 'result' mostly restates the definition of dγ: shrinking distances to positives makes positives more likely to be neighbors. It does not say much about the F1 trade-off. Second, the main empirical comparison is not fully controlled. dupkNN, the second-best baseline, duplicates positives by the fixed IR; γk-NN tunes γ on validation F1. That means the reported margin could be a tuning artifact — essentially tuning a class-weight parameter — rather than evidence for the geometric mechanism. The sampling experiments have the same issue: γ is tuned for γk-NN while the oversamplers use default parameters. No significance tests are reported, so some of the 3-point gains may be within noise. Third, no code is released and the real data are private.\n\nNone of this kills the paper. The method is plausible and likely useful, and a tuned dupkNN or a tuned class-weight might match it — or might not. That is exactly what a revision should test. The theory should either be tightened or explicitly downgraded to a heuristic motivation.\n\nBottom line: worth a serious referee, especially for the empirical study, but the authors need to close the tuning gap in the baselines, add significance testing, and either fix the k=1-to-k=3 leap or soften the theoretical claims.","headline":"A simple, practical kNN variant for imbalanced data with broad experiments, but the theoretical justification is thin and the main baseline comparison may be unfair due to unequal tuning.","tokens_in":14022,"tokens_out":2229,"would_cite":true,"duration_ms":62651,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Scaling the distance to positive examples by gamma<1 expands their Voronoi cells, lowers the false-negative rate, and improves the F-measure in k-NN on imbalanced data.","keywords":["imbalanced learning","k-nearest neighbors","F-measure","class-weighted distance","Voronoi regions","oversampling","SMOTE","tax fraud detection"],"falsifier":"Run gamma_kNN at k=3 on a public imbalanced dataset and check whether the cross-validated F1 curve over gamma in {0.1, 0.2, ..., 1.0} is flat or decreasing at gamma<1; if gamma<1 never yields higher F1 than gamma=1 under the same search procedure, the central claim is contradicted. Also measure the false-negative rate on a large test set as gamma varies: if it does not fall monotonically for gamma<1 at k=3, the k=1 theory does not extend to the experimental setting.","tokens_in":13109,"feed_emoji":"🎯","tokens_out":6228,"duration_ms":331894,"temperature":0.7,"pith_summary":"This paper argues that a one-line change to k-nearest-neighbor classification—multiply the distance from a query to every positive training example by a factor gamma<1—reshapes the decision boundary around the minority class and improves the F-measure on imbalanced data. The intuition is geometric: positives are rare, so their Voronoi cells are tiny and test positives often fall on the negative side; shrinking distances to positives expands their cells, cutting false negatives without, when gamma is chosen by cross-validation, exploding false positives. The paper proves for k=1 that gamma<=1 lowers the false-negative probability, and argues that because the negative class is much larger, the induced rise in false positives converges away faster. Experiments on 19 public datasets and 11 private tax-fraud datasets from the French tax administration report higher mean F1 than standard k-NN, distance-weighted variants, LMNN, and SMOTE-family oversamplers, and the largest gains appear when gamma_kNN is combined with oversampling.","feed_headline":"Scaled distances to positives lift F-measure in imbalanced k-NN","feed_subtitle":"Tuning one distance-scaling factor per class raises F1 across 19 public and 11 tax-fraud datasets.","key_machinery":"The key object is the gamma-scaled distance $d_\\gamma(x, x_i)=\\gamma d(x,x_i)$ for positive $x_i$ and $d(x,x_i)$ for negatives, with $\\gamma\\in(0,1)$. Although $d_\\gamma$ is not a true metric, it modifies the ranking of neighbors and thereby the Voronoi tessellation and the decision boundary: lower $\\gamma$ expands the effective basin of each positive training point. The theoretical engine is a per-point false-negative/false-positive probability written as a product over same-class training points of the probability that the point falls outside a sphere of radius $\\epsilon/\\gamma$, from which the $\\gamma\\le 1$ and $\\gamma\\ge 1$ comparisons follow. In the experimental pipeline, $\\gamma$ is selected by cross-validation on the training set and, in the oversampling variant, a second $\\gamma$ value is assigned to synthetic positives so the algorithm can down-weight or up-weight them independently.","core_discovery":"On the paper's own terms, the central discovery is that the imbalance problem in nearest-neighbor classification can be addressed by a scalar reweighting of the distance to positives, $d_\\gamma(x,x_+) = \\gamma d(x,x_+)$, rather than by generating new examples. For each query the algorithm finds the $k$ nearest positives and $k$ nearest negatives under the original distance, scales positive distances by $\\gamma$, merges the lists, and takes a majority vote on the $k$ closest; $\\gamma<1$ enlarges the effective Voronoi region of each positive. Propositions 1 and 2 show, for $k=1$ and under an independence factorization, that $\\gamma\\le 1$ decreases the false-negative probability while $\\gamma\\ge 1$ decreases the false-positive probability; since the minority class is small, the false-positive growth from $\\gamma<1$ is comparatively negligible, so the method restricts $\\gamma$ to $(0,1)$. Empirically, $\\gamma$ tuned by 10-fold cross-validation reaches the best mean F1 among the compared distance-based methods on public data, and applying a second $\\gamma$ (typically $>1$) to synthetic positives generated by oversamplers improves the combined pipeline.","pith_inferences":["Because the neighbor search is still performed with the original metric and only the merged ranking is scaled, $\\gamma k$-NN can be dropped into an approximate-nearest-neighbor index with negligible overhead, and a natural extension is an adaptive $\\gamma(x)$ that varies across the feature space.","The two-gamma treatment of synthetic positives suggests a general principle: any generative or oversampling augmentation can be assigned its own distance scale, allowing the classifier to down-weight low-confidence synthetic points; this idea transfers to GAN-based augmentation without retraining.","The $k=1$ product formula implies an optimal $\\gamma$ roughly tied to local positive density, so a testable extension is to set $\\gamma$ per query from the local imbalance ratio and check whether the F1 gains persist.","The framing of $\\gamma$ as a diagonal Mahalanobis matrix restricted to positive comparisons hints that learning a full positive-semidefinite matrix under an F-measure objective could capture direction-dependent imbalance, which the paper itself lists as future work."],"forward_implications":["Tuning a single scalar $\\gamma$ via cross-validation raises mean F1 on 19 public datasets from 0.543 (plain k-NN) to 0.607, beating all compared distance-based methods.","$\\gamma k$-NN outperforms each of five oversamplers used alone, and the best results come from applying $\\gamma k$-NN after oversampling, because synthetic positives fill empty regions while $\\gamma$ rescales the real positives.","Optimal $\\gamma$ decreases as the imbalance ratio grows, so the method automatically compensates for harder imbalance, leveling off at very high imbalance ratios.","On the private tax-fraud datasets, mean F1 rises from 0.148 for k-NN to 0.278 for $\\gamma k$-NN and 0.295 when combined with SMOTE, showing the effect on a real fraud-selection task."],"supporting_citations":[{"why":"Supplies the k-NN decision rule that gamma_kNN modifies.","marker":"Cover and Hart (1967)"},{"why":"Inverse-distance weighted k-NN voting, one of the distance-based baselines compared in the experiments.","marker":"Dudani (1976)"},{"why":"Proposes a class-weighted distance d' = (m_i/m)^(1/p)d; the closest existing strategy in the same family and a main comparison.","marker":"Barandela et al. (2003)"},{"why":"Introduces SMOTE, the main oversampling baseline that gamma_kNN is combined with.","marker":"Chawla et al. (2002)"},{"why":"kRNN baseline that adjusts the posterior probability using local and global imbalance, used as a competitor.","marker":"Zhang et al. (2017)"},{"why":"LMNN metric-learning baseline, and the motivation for viewing gamma as a restricted diagonal Mahalanobis matrix.","marker":"Weinberger and Saul (2009)"},{"why":"Surveys SMOTE-based sampling methods and frames the oversampling family used in the experimental comparison.","marker":"Fernández et al. (2018)"}],"fun_headline_variants":["Reweight distances to positives to boost F1 in k-NN","One scalar per class sharpens F1 for imbalanced k-NN","Scale positive distances to fix k-NN on rare classes","Tuning gamma for positive distances improves F1 in k-NN","Modify Voronoi regions to maximize F-measure"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The theoretical guarantees are proved only for k=1, while all reported experiments use k=3, and the proof assumes that the false-negative probability factorizes as an independent product over positives with a fixed nearest-neighbor distance epsilon; if that analysis does not carry over to higher k, the theory does not cover the reported results.","fun_headline_variants_meta":{"raw":{"variants":["Reweight distances to positives to boost F1 in k-NN","One scalar per class sharpens F1 for imbalanced k-NN","Scale positive distances to fix k-NN on rare classes","Tuning gamma for positive distances improves F1 in k-NN","Modify Voronoi regions to maximize F-measure"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000721,"raw_usage":{"total_tokens":3247,"prompt_tokens":967,"completion_tokens":2280,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":2192}},"tokens_in":583,"tokens_out":2280,"duration_ms":17918,"temperature":1.0,"reasoning_tokens":2192,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:39:20.391857+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run gamma_kNN at k=3 on a public imbalanced dataset and check whether the cross-validated F1 curve over gamma in {0.1, 0.2, ..., 1.0} is flat or decreasing at gamma<1; if gamma<1 never yields higher F1 than gamma=1 under the same search procedure, the central claim is contradicted. Also measure the false-negative rate on a large test set as gamma varies: if it does not fall monotonically for gamma<1 at k=3, the k=1 theory does not extend to the experimental setting.","supporting_citations":[{"cited_title":"and Hart, P","cited_arxiv_id":null,"evidence_quote":"Supplies the k-NN decision rule that gamma_kNN modifies."}],"review_version":1}