{"id":"abda5fe4-11a7-42d5-9a06-b9abc537904f","arxiv_id":"2501.04300","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"HI-PMK is a data-dependent kernel for incomplete heterogeneous tabular data that treats missing values as a separate mass bucket and maximizes uncertainty, reporting improved classification and clustering over baselines.","lead":"HI-PMK is a new kernel for comparing data rows that contain missing values and mixed numerical/categorical features, without first filling in the missing entries. It extends an existing density-sensitive kernel and reports better classification and clustering than imputation-based baselines across 16 datasets.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Mercer/PSD validity of HI-PMK is asserted without proof; if the extended PMK matrix is indefinite, the SVM precomputed-kernel results are not supported as kernel-SVM results.","rationale":"The strongest claim is empirical, but the classification half of the evaluation is framed as kernel SVM. The only support for the required PSD property is the sentence after Eq. (2), which explicitly lists only symmetry and self-similarity; neither implies Mercer validity. The extension to categorical and missing features is a genuine modification of the m0 quantity, so the prior PMK literature cannot automatically supply the missing proof. Since no PSD check is reported and no formal verification exists, the SVM results are not grounded. The reader's weakest_assumption identifies exactly this gap. Independent support such as released code and extensive benchmarks is real credit, but it does not substitute for the missing analysis; a computational eigenvalue test would settle the point quickly. If the matrices turn out PSD, the concern would be resolved and the empirical claims could be reconsidered on their merits.","tokens_in":43540,"tokens_out":16388,"duration_ms":164287,"concrete_test":"Take one complete dataset from Table 3 (e.g., Adult at 20% MCAR), build the exact HI-PMK matrix used in the precomputed-kernel SVM, and compute its minimum eigenvalue and full eigenspectrum. If negative eigenvalues occur, the Section 4.1 Mercer claim is false; then rerun the same SVM with the nearest-PSD projection of that matrix and compare the F1. If the projected-kernel F1 drops materially, the reported classification gain depends on the indefinite kernel rather than a valid SVM.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.1 defines PMK by Eq. (2) and states that normalization ensures symmetry and self-similarity, aligning PMK with Mercer kernel requirements. Symmetry and self-similarity are necessary but not sufficient for positive semi-definiteness, which is exactly what a precomputed kernel in SVM (Section 5.1.3) requires. The H-component (Eq. 3) and I-component (Eqs. 4-7) replace the original m0 term with categorical and missingness-dependent quantities, so even if the original PMK were known to be PSD, this extension needs a new proof. No such proof, no eigenvalue check, and no formal verification are reported. If any HI-PMK matrix used in Table 3 has a negative eigenvalue, the SVM dual is nonconvex and the reported classification improvements are not the result of a valid Mercer-kernel SVM.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes HI-PMK, a data-dependent kernel for incomplete heterogeneous data that avoids imputation by combining a probability-mass-based dissimilarity (PMK) with two extensions: an H-component for mixed-type features (nominal, ordinal, numerical) and an I-component that handles missing values via a separate missing bucket Bk and a maximum-uncertainty (MaxU) strategy. The method is evaluated on classification (SVM with precomputed kernels) and clustering (k-means on the kernel matrix) over ten complete datasets with synthetic MCAR/MAR/MNAR missingness and six naturally incomplete datasets, reporting consistent improvements over imputation-based and kernel baselines. Ablation studies and scalability experiments are also included, and code is made available.","tokens_in":43717,"tokens_out":3918,"duration_ms":41648,"significance":"If the central claims hold, HI-PMK would be a useful imputation-free representation for mixed-type tabular data under multiple missingness mechanisms, with potential privacy benefits. The paper has concrete strengths: public code, a wide experimental sweep across 15+ datasets and three missingness mechanisms, ablation studies isolating the proposed components, and scalability experiments. However, the classification results are built on a precomputed-kernel SVM whose validity requires the HI-PMK matrix to be positive semidefinite; this property is asserted but never proved or checked. In addition, the cross-validation protocol for the data-dependent kernel is ambiguous and could leak test information. These issues are load-bearing for the paper's headline claim of consistent classification gains, and the clustering evidence, while more robust to the Mercer question, is not enough to support the full claim as written.","major_comments":[{"comment":"The paper states that normalizing m0 by Eq. (2) 'ensures symmetry and self-similarity, aligning PMK with Mercer kernel requirements,' but symmetry and self-similarity are necessary, not sufficient, for positive semidefiniteness. The H-component (Eq. 3) and I-component (Eqs. 4–7) replace the original m0 term with categorical and missingness-dependent quantities, so even if the original PMK were known to be PSD, this extension requires a new proof. No such proof, eigenvalue check, or formal verification is reported. Since Section 5.1.3 evaluates HI-PMK using SVMs with precomputed kernels, a non-PSD matrix makes the SVM dual nonconvex and the reported classification improvements in Table 3 and the supplementary tables unsupported. The authors should either provide a proof of PSD for HI-PMK or, at minimum, report the eigenvalue spectrum of the kernel matrices used and confirm that no negative eigenvalues occur; if negative eigenvalues exist, the claims about kernel-SVM classification must be revised.","section":"§4.1, Eq. (2); §5.1.3; Tables 3 and 6"},{"comment":"The cross-validation procedure is underspecified with respect to the data-dependent nature of HI-PMK. The kernel depends on global statistics such as bin masses, the missing bucket Bk, and the frequencies used in Eqs. (3)–(7). If the kernel matrix is computed on the full dataset before the 5-fold split, then the training kernel entries are affected by test-set statistics, which is information leakage and can inflate the reported F1 scores. The paper must state clearly that, for each fold, the kernel is computed using only training-fold statistics and that test samples are embedded via those training-fold quantities, and it should describe how this is done for the precomputed-kernel SVM. Without this clarification, the comparison against imputation baselines is not a valid evaluation.","section":"§5.1.3"},{"comment":"There is a direct inconsistency between Eq. (7) and Algorithm 3 in the supplementary material for the 'both missing' nominal case. Eq. (7) defines |Rk(?, ?)| as the sum of the two largest category frequencies plus |Bk|, while Algorithm 3 line 5 computes only max_a M(a) + |Bk|, omitting the second-largest term. This changes the dissimilarity for every pair of instances with both values missing in a nominal feature, which can affect the reported experimental results. The intended definition must be specified and the experiments re-run if the algorithm text is the actual implementation.","section":"§4.3, Eq. (7); Supplementary Algorithm 3"},{"comment":"Section 4.5 claims that HI-PMK 'avoids binning and instead uses precomputed probability masses,' but Algorithm 1 explicitly discretizes numeric features into b bins and precomputes bin masses, and Eqs. (1)–(2) rely on region sizes defined through these bins. The complexity statement also omits the binning and bin-mass precomputation cost, which the paper's own earlier discussion (Section 4.5, first sentence) attributes as O(mnb + nb^2) for the original M0 measure. The full complexity of HI-PMK, including binning and the per-dataset tuning of b described in Supplementary Section 4.2, should be stated. This matters for the scalability claims in Section 5.3.","section":"§4.5; Supplementary Algorithm 1"}],"minor_comments":[{"comment":"The caption says 'NMI scores for clustering tasks on incomplete datasets and Classification accuracy for incomplete datasets,' but the table reports both ACC and NMI columns for every method; the caption should clarify which columns correspond to which task, and the same applies to the supplementary tables.","section":"Table 2"},{"comment":"The HI-PMK rows contain standard deviations such as 0.8506±0.8127 and 0.9875±0.9868, which are larger than plausible for the reported means and appear to be formatting errors. These values should be corrected, as they currently undermine the reproducibility of the experimental results.","section":"Supplementary Table 2"},{"comment":"The notation P(x_i ∨ x_j) for nominal features is not defined precisely; it should be stated whether this is P(x_i) + P(x_j) for distinct categories, or the probability of the union including the possibility that both are equal, since this affects the computed value of Eq. (3).","section":"Eq. (3)"},{"comment":"The sentence 'RBF kernels were computed over similarity matrices' is unclear: standard RBF is a function of distances, and a precomputed kernel is a different object. Please specify exactly how the RBF kernel is computed for incomplete binary-class datasets and how it relates to the precomputed-kernel SVM used for HI-PMK.","section":"§5.1.3"}],"recommendation":"reject","confidential_remarks":"The paper addresses a relevant problem and includes useful empirical resources, but the central classification claim rests on an unverified positive-semidefiniteness property and an ambiguous cross-validation protocol for a data-dependent kernel. If the authors can supply a proof or eigenvalue verification of PSD and a leakage-free CV description, and reconcile Eq. (7) with Algorithm 3, a resubmission could be reconsidered. As it stands, the main quantitative evidence is not reliable enough for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Core idea is a legitimate extension: replace the original PMK's numerical-only region mass with categorical treatment (H-component) and handle missing values by assigning maximal plausible dissimilarity (MaxU, plus the missingness bucket B_k). The paper is honest about building on Aryal's PMK, the experiments are broad (16 datasets, MCAR/MAR/MNAR, multiple missing rates), and the code is public. That is a solid base.\n\nWhat worries me: Section 4.1 asserts the normalized kernel is a Mercer kernel because it is symmetric and self-similar. That is not sufficient for positive semi-definiteness, which is exactly what precomputed-kernel SVM needs. The H- and I-components change the region mass term, so a new proof is required; none is given, and no eigenvalue check is reported. As written, the classification results in Table 3 are unsupported if any HI-PMK matrix is indefinite. The authors could fix this quickly by adding an eigenvalue check or a PSD proof (or by relabeling the SVM experiment as \"similarity-based SVM\" rather than kernel SVM).\n\nThe CV description is too terse. If the data-dependent kernel matrix is computed once on the full dataset and then split into folds, test information leaks into the kernel and the reported gains are inflated. The paper should state explicitly that the kernel is recomputed on each training (or inner) fold. Without that, I cannot take the classification improvements at face value.\n\nThe abstract's \"consistently outperforms\" is also stronger than the tables. For example, Banknote under MAR at 20% missingness, MisF scores 0.8550 vs HI-PMK's 0.8390. No method wins every cell, but the text should say \"often outperforms\" or qualify the claim.\n\nMinor: Section 4.5 says HI-PMK avoids binning, but the method description and Algorithm 1 discretize into b bins. A wording slip, not a substantive error.\n\nWho is this for: people working on imputation-free similarity for mixed-type, partially observed tabular data. The paper deserves a serious referee; it has a concrete method, code, and enough empirical work to justify a careful review. I would send it out, with reviewers directed to the PSD and CV issues as the key points.","headline":"A useful, well-documented extension of PMK to heterogeneous incomplete data, but the SVM results rest on an unproven PSD claim and a possibly leaky CV protocol.","tokens_in":44202,"tokens_out":2298,"would_cite":false,"duration_ms":23165,"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":"A data-dependent kernel computes similarity from observed entries of incomplete, mixed-type data and, without imputation, outperforms imputation-based pipelines and kernel baselines on more than fifteen benchmark datasets.","keywords":["incomplete data","heterogeneous data","kernel methods","data-dependent kernel","probability mass dissimilarity","missingness mechanisms","imputation-free representation learning","mixed-type features"],"falsifier":"Compute the eigenvalues of the HI-PMK Gram matrix on a published dataset configuration, such as Banknote at 20% MCAR missingness; if any eigenvalue is negative, the kernel is not positive semi-definite and the SVM-with-precomputed-kernel results are not supported.","tokens_in":43326,"feed_emoji":"🧩","tokens_out":9806,"duration_ms":82176,"temperature":0.7,"pith_summary":"The paper tries to establish that similarity between two incomplete, mixed-type data points can be computed directly from the observed entries, without imputing missing values, and that this similarity works better than imputation-based pipelines and existing kernel methods. The proposed HI-PMK kernel combines a probability-mass dissimilarity that adapts to local data density with a conservative uncertainty treatment that assigns maximum plausible dissimilarity to missing entries. If the claim holds, practitioners working with messy tabular data gain an imputation-free, privacy-preserving representation that handles numerical, ordinal, and nominal features and all three missingness mechanisms.","feed_headline":"Imputation-free kernel tops missing-data benchmarks","feed_subtitle":"Handles mixed feature types and MCAR, MAR, and MNAR missingness without ever imputing.","key_machinery":"The engine is the m0-dissimilarity, a data-dependent measure that defines the dissimilarity between two instances as the average log probability mass of the region they occupy in each feature; dense regions count as more dissimilar than sparse ones. HI-PMK adds two components to this base: the H-component computes the region probability mass for ordinal features by summing label frequencies between the two values and for nominal features by taking the probability of either label, while the I-component handles missing entries by putting all missing values of a feature into a separate bucket Bk and applying MaxU, which replaces an unobserved value with the largest plausible region mass. The m0 score is then normalized by the self-dissimilarities to produce a symmetric similarity matrix; the paper asserts this normalization satisfies the Mercer kernel condition.","core_discovery":"The central claim is that HI-PMK consistently ranks at or near the top in classification F1 and clustering NMI across more than fifteen benchmark datasets, under all three missingness mechanisms and across missing rates up to 80%. The kernel computes pairwise similarity from the observed part of the data, so no imputation is needed; numerical features are discretized into bins, categorical features use label frequencies, and missing entries are represented by a dedicated bucket whose size feeds into a worst-case dissimilarity adjustment. The paper argues that this design lets the kernel capture structured missingness under MAR and MNAR while remaining stable as missingness increases, where imputation-based and generative baselines degrade.","pith_inferences":["A testable extension is to replace the hand-set MaxU worst-case rule with a learned or calibrated uncertainty weight; the paper's ablations show MinU and AvgU underperform, but a data-driven interpolation is not explored.","The same probability-mass-plus-missing-bucket construction could be lifted onto other data-dependent kernels, such as isolation kernels, to see whether the missingness-aware adjustment transfers beyond the m0 base.","The quadratic O(m^2 n) kernel matrix limits scale; a Nyström-style or minibatch approximation is the obvious next step, though the paper does not propose one.","On naturally incomplete datasets the true missingness mechanism is unknown, so a controlled mechanism-switching study on a single dataset could separate how much of the gain comes from MaxU's conservative prior versus the kernel's density adaptation."],"forward_implications":["If HI-PMK's kernel is valid, SVMs can be trained on incomplete mixed-type data directly, eliminating the privacy risk and bias that come from exposing imputed values.","The method provides a single kernel that works under MCAR, MAR, and MNAR, so practitioners do not need to know or model the missingness mechanism in advance.","Clustering methods using HI-PMK as the similarity measure inherit the same missingness awareness, as the NMI and ARI gains on naturally incomplete datasets show.","Because the kernel matrix costs O(m^2 n) time and O(m^2) space, it is a practical drop-in replacement for Euclidean or RBF kernels on small-to-medium tabular datasets.","The separate missing-value bucket Bk gives structured missingness a representation that imputation-free alternatives lack, which the ablations attribute to the gains under MAR and MNAR."],"supporting_citations":[{"why":"Supplies the m0-dissimilarity measure that HI-PMK extends.","marker":"[4]"},{"why":"Provides the Gower (Gow) similarity baseline for clustering comparisons.","marker":"[28]"},{"why":"Defines the MCAR/MAR/MNAR missingness taxonomy used throughout.","marker":"[30]"},{"why":"Grounds the MaxU strategy in the maximum entropy principle.","marker":"[18]"},{"why":"Supplies the genRBF kernel baseline for incomplete data.","marker":"[34]"},{"why":"Is the MICE imputation baseline used across experiments.","marker":"[40]"},{"why":"Is the GAIN generative imputation baseline.","marker":"[41]"},{"why":"Is the MissForest mixed-type imputation baseline.","marker":"[36]"},{"why":"Supplies the strategy used to generate MAR missingness in synthetic experiments.","marker":"[24]"}],"fun_headline_variants":["Imputation-free kernel beats missing-data baselines","No imputation needed: kernel tops 15 missing-data sets","HI-PMK: data-dependent kernel wins without imputation","Kernel for incomplete heterogeneous data skips imputation","Missing data kernel outperforms imputation pipelines"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the normalized similarity scores form a valid kernel matrix (positive semi-definite), a property stated but not proved, and the classification gains would be unsupported if the matrix is not positive semi-definite.","fun_headline_variants_meta":{"raw":{"variants":["Imputation-free kernel beats missing-data baselines","No imputation needed: kernel tops 15 missing-data sets","HI-PMK: data-dependent kernel wins without imputation","Kernel for incomplete heterogeneous data skips imputation","Missing data kernel outperforms imputation pipelines"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000505,"raw_usage":{"total_tokens":2448,"prompt_tokens":914,"completion_tokens":1534,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":530,"completion_tokens_details":{"reasoning_tokens":1458}},"tokens_in":530,"tokens_out":1534,"duration_ms":9770,"temperature":1.0,"reasoning_tokens":1458,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:36:06.940968+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the eigenvalues of the HI-PMK Gram matrix on a published dataset configuration, such as Banknote at 20% MCAR missingness; if any eigenvalue is negative, the kernel is not positive semi-definite and the SVM-with-precomputed-kernel results are not supported.","supporting_citations":[{"cited_title":"Hi- pmk: A data-dependent kernel for incomplete heterogeneous data representation, 2025","cited_arxiv_id":null,"evidence_quote":"Supplies the m0-dissimilarity measure that HI-PMK extends."}],"review_version":1}