{"id":"12f450eb-d986-4231-be17-bfaccace0c84","arxiv_id":"2411.19609","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Using a mutual-information QUBO solved on a D-Wave hybrid annealer, conditional-mutual-information feature selection improves SVM price forecasts on a large excavator dataset for small feature subsets.","lead":"This paper recasts the task of picking a small set of predictive features as a QUBO optimization problem solved with D-Wave's hybrid quantum-classical annealer, and tests it on two used-excavator price datasets. For the larger, less information-concentrated dataset, selecting features by conditional mutual information outperforms simple mutual-information ranking when few features are used.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The QUBO mapping in Section II.B appears to encode only one directional CMI per feature pair, so the executed objective may not be Eq. (7); this undermines the central R² comparison before solver optimality is even considered.","rationale":"The paper's stated contribution is conditional: MIQUBO can improve over MI-only on low-MI-concentration data because it optimizes Eq. (7). For this to be true, the QUBO actually executed must maximize Eq. (7). Section II.B maps Eq. (7) by setting Q_ij=-MI(X_j;Y|X_i). Because Eq. (7) contains both ordered CMI terms per pair, the quadratic coefficient for the unordered pair should be -[MI(X_j;Y|X_i)+MI(X_i;Y|X_j)] under the upper-triangular convention stated in Eq. (11). The text gives only one of these terms. Unless the implementation builds a full asymmetric Q matrix and the solver consumes both directional contributions, the optimized objective is order-dependent: permuting one-hot feature columns would change the selected sets. This is an internal consistency issue, not a disagreement with external consensus. The reader's solver-optimality concern is plausible but secondary: if the encoding is wrong, exact optimization would still optimize the wrong function, and if the encoding is right, classical optimality checks are straightforward to add. The concrete test (rebuild the QUBO, solve both asymmetric and symmetrized versions, and check index-permutation invariance) settles the matter. Because the central empirical R² result is the only positive evidence and it hinges on this mapping, the authors should supply the Q matrix or reproducible code. I keep the CONDITIONAL verdict: the ambiguity could be resolved in the authors' favor if their code symmetrizes or stores both directional terms, but as written the paper does not establish that the CMI curves in Fig. 5 test Eq. (7).","tokens_in":11636,"tokens_out":13077,"duration_ms":120892,"concrete_test":"Reconstruct the Cat-All QUBO exactly as described (top-25 MI pre-pruning, Q_ii=-MI_i, Q_ij=-MI(X_j;Y|X_i) for i<j). (1) Solve this QUBO and the symmetrized version Q'_ij=-(MI(X_j;Y|X_i)+MI(X_i;Y|X_j)) for i<j, using an exact branch-and-bound or high-quality classical QUBO solver on the 25-variable problem, and compare the selected feature sets for k=2,...,10. (2) As a cheaper invariant check, permute the feature indices, rebuild the stated QUBO, and re-solve; if the selected set changes, the objective is order-dependent and cannot equal Eq. (7). (3) If the sets differ, recompute the SVM R² curves in Fig. 5c/d with the symmetrized QUBO. If the gap persists, the empirical claim may survive with corrected coefficients; if it vanishes, the reported improvement is an artifact of the asymmetric encoding. Either way, the paper must report this check before the claim is accepted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (7) defines the objective as sum_{i in F} [MI(X_i;Y) + sum_{j in F, j != i} MI(X_j;Y|X_i)]. For an unordered pair {i,j}, this includes both MI(X_j;Y|X_i) and MI(X_i;Y|X_j); these are not equal in general because CMI is symmetric in its first two arguments, not in the conditioning variable. Section II.B maps Eq. (7) to a QUBO by setting Q_ii -> -MI(X_i;Y) and Q_ij -> -MI(X_j;Y|X_i), and Eq. (11) and Table 2 use the standard upper-triangular form sum_i q_i x_i + sum_{i<j} q_ij x_i x_j. Under that convention, a selected pair contributes only MI(X_j;Y|X_i) with i<j fixed by feature order, so the reverse term MI(X_i;Y|X_j) is dropped. The minimization therefore maximizes a different, order-dependent objective rather than Eq. (7). The text does not say that the edge coefficient is symmetrized to -(MI(X_j;Y|X_i)+MI(X_i;Y|X_j)), and no code or Q matrix is provided; the remark in Fig. 3 that only the upper triangular matrix is shown is consistent with one coefficient per pair. If this is what was run, the central empirical claim that sets maximizing the sum of MI and CMI improve SVM R² over MI-only selection (Fig. 5c/d) is not actually tested, even if Kerberos returns exact optima. This is an internal correctness issue in the formulation, distinct from and more fundamental than the unverified solver optimality raised by the reader.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a quantum-annealing-based feature selection method, MIQUBO, in which a QUBO is built from mutual information (MI) and conditional mutual information (CMI) terms, and solved with D-Wave's Kerberos hybrid solver. The selected feature sets are evaluated by training RBF-SVM regressors to predict used-excavator prices on two Caterpillar datasets: a small MI-concentrated dataset (model 308, 27 one-hot features) and a larger less MI-concentrated dataset (all models, 67 one-hot features, pre-pruned to 25). The central claim is that for datasets with low MI concentration, maximizing the sum of MI and CMI via MIQUBO yields better SVM R2 scores than maximizing MI alone, particularly for small numbers k of selected features. The paper reports R2 means over train-test splits and shows feature-selection maps for k=1,...,25.","tokens_in":11962,"tokens_out":3352,"duration_ms":27530,"significance":"If the central claim were established, the paper would provide a useful practical demonstration of quantum annealing in an ML feature-selection pipeline, with a concrete real-world dataset and a sparse QUBO structure. The application of a hybrid annealer to an information-theoretic feature-selection objective is timely, and the idea that MI concentration governs whether CMI-based selection helps is an interesting and falsifiable prediction. However, the current evidence is not yet convincing: the QUBO formulation appears not to match the stated objective, solver optimality is not validated, and the statistical support is thin. The paper's reproducible-description value is limited by the absence of code or data release, but the feature-selection maps and direct comparison to MI-only selection are potentially useful if the formulation is corrected.","major_comments":[{"comment":"The QUBO mapping does not encode the objective in Eq. (7). Eq. (7) contains, for each unordered feature pair {i,j}, both MI(X_j;Y|X_i) and MI(X_i;Y|X_j). The paper sets Q_ij = -MI(X_j;Y|X_i) and then uses the standard upper-triangular QUBO form sum_{i<j} q_ij x_i x_j, so for a selected pair the objective receives only one of the two CMI terms, with the direction determined by feature ordering. This makes the optimized objective order-dependent and different from Eq. (7). The text nowhere states that the coefficients are symmetrized to -(MI(X_j;Y|X_i)+MI(X_i;Y|X_j)), and Fig. 3's note that only the upper triangular matrix is shown is consistent with one coefficient per pair. Because the central R2 comparison is intended to test feature sets maximizing Eq. (7), this is a load-bearing inconsistency. The authors should state explicitly which Q matrix was used, provide the Q matrix or code, and rerun or re-interpret the experiments if the executed objective was not Eq. (7).","section":"Section II.B and III, solver validation"},{"comment":"No evidence is provided that the Kerberos hybrid solver returns solutions close to the true optimum of the QUBO. Kerberos is heuristic, and the paper reports no optimality gap, no comparison to an exact solver, and no comparison to a classical QUBO solver on the same instances. The feature-selection maps in Fig. 4c/d and the R2 comparisons in Fig. 5 could reflect solver artifacts rather than the choice of MI versus CMI objective. Since the largest dataset is pre-pruned to 25 features, a brute-force or exact classical check for small k is feasible and should be reported. This is necessary to support the claim that the observed gaps are due to the objective rather than to the solver.","section":"Section III, Fig. 5"},{"comment":"The statistical support for the main empirical claim is weak. For the less MI-concentrated Caterpillar-all dataset, the R2 results are based on only 15 train-test splits, no error bars are shown, and no significance test is reported. The text states that 'a statistically relevant gap according to the standard deviation' opens, but the standard deviation is not shown and no test is described. The claim that the improvement is 'dependent on the dimension of the selected feature space' is not quantified. The authors should report per-k means with error bars or confidence intervals, the number of splits, and a significance test (e.g., paired t-test or Wilcoxon across splits) to support the conclusion.","section":"Section II.A and III"}],"minor_comments":[{"comment":"The notation for mutual information is inconsistent: Eq. (5) defines MI(X;Y|Z) with the target denoted X, while Eq. (7) uses Y for the target and X_i for features. This makes the derivation harder to follow and should be harmonized.","section":null},{"comment":"The sentence 'The restriction that led to Eq. (7) for MI-based feature selection naturally lends itself to being reformulated as a QUBO' is vague; the specific conditional-independence assumption used to derive Eq. (7) from Eq. (5) should be stated more precisely before the QUBO reformulation.","section":"Section II.B"},{"comment":"The caption of Fig. 3 says 'Only upper triangular matrix is shown' but does not say whether the matrix is symmetric; after clarifying the QUBO coefficients, the symmetry or asymmetry should be stated explicitly.","section":"Section II.B, Fig. 3"},{"comment":"There are several typos and grammatical issues, e.g., 'remians' in the introduction and 'probalites' in Eq. (1). These should be corrected in a revision.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The decisive issue is the QUBO mapping in Section II.B: if the executed objective was the asymmetric one-coefficient-per-pair form, the main empirical comparison does not actually test Eq. (7), and the experiments would need to be redone with a corrected, symmetrized Q matrix. The paper may be salvageable if the authors provide the exact Q matrix, validate solver solutions against exact classical optimization, and strengthen the statistical analysis. The lack of code or data release also makes independent verification difficult."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a well-motivated application of QUBO-based feature selection to a real business problem, but I think the central empirical claim is undercut by a likely bug in the QUBO encoding. Eq. (7) includes both MI(X_j;Y|X_i) and MI(X_i;Y|X_j) for every unordered pair {i,j}. The QUBO in Eq. (11) is written with sum_{i<j}, and the mapping in Section II.B sets Q_{ij} -> -MI(X_j;Y|X_i) for i<j. So each selected pair contributes only one of the two conditional terms. The text does not say the coefficient is symmetrized to include both directions, and the Fig. 3 note that only the upper triangle is shown is consistent with one coefficient per pair. That means the solver is not optimizing Eq. (7) unless the reverse CMI is added, which is not stated. Even with an exact solver, the Fig. 5 comparison may be testing an order-dependent objective rather than the stated one. This is a load-bearing problem, not a minor omission.\n\nWhat the paper does well: it is honest about prior work (Refs. [22,29]), describes the D-Wave hybrid workflow concretely, and uses two real datasets with a sensible regression setup. The idea that MI-concentration controls when CMI-based selection helps is interesting and plausible. The data handling and evaluation are described well enough to reproduce with some effort.\n\nSoft spots beyond the mapping: the key positive result on the all-models dataset rests on 15 train-test splits with no significance test or error bars; the 25-feature MI pre-pruning for the larger dataset could bias the comparison; and there is no classical QUBO baseline, so we do not know how close Kerberos comes to the optimum. The reader's concern about solver optimality is valid, but the mapping issue is more fundamental.\n\nWho this is for: practitioners looking to apply quantum annealers to feature selection, and readers who want a concrete example of a subtle QUBO encoding error. As written, I would not accept the central claim. The fix is straightforward—symmetrize the quadratic coefficients—and with that, plus a classical baseline and better statistics, the paper could become a useful empirical study.\n\nRecommendation: I would not desk reject outright, but the paper needs major revision. Send it to peer review only if referees will insist on fixing the encoding and the statistics. The core question is worth one more round.","headline":"The empirical claim is plausible but the QUBO encoding appears to drop half of the conditional mutual information terms, so the paper as written does not test its own objective.","tokens_in":12567,"tokens_out":3871,"would_cite":false,"duration_ms":32658,"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":"The paper claims that solving a mutual-information QUBO on a hybrid quantum annealer selects feature sets that improve SVM price-prediction accuracy over MI-only selection when mutual information is spread thinly across features and few…","keywords":["feature selection","quantum annealing","QUBO","mutual information","conditional mutual information","support vector regression","hybrid quantum-classical optimization","price forecasting"],"falsifier":"Solve Eq. (7) exhaustively on the Caterpillar all-models dataset for the smallest feature-set sizes tested, for example four and five features, and compare the resulting feature sets with Kerberos's selections on the same SVM train-test splits. If the exact CMI-based sets do not yield a higher mean $R^2$ than the MI-only top-k sets, the paper's central claim fails; a supporting check is whether Kerberos's QUBO objective values match the exact optimum on those instances.","tokens_in":11343,"feed_emoji":"⚛️","tokens_out":13889,"duration_ms":104083,"temperature":0.7,"pith_summary":"This paper tries to establish that quantum annealing can beat a standard mutual-information heuristic at feature selection for certain real-world datasets. The authors encode the problem of choosing the most informative features as a QUBO whose objective combines each feature's mutual information with the target and its conditional mutual information given other selected features, then solve it with a hybrid quantum-classical annealer, the Kerberos sampler. They test the selected feature sets in an SVM regression model that forecasts used-excavator prices. Their central empirical finding is that for datasets with low mutual-information concentration, where information about the target is spread across many features rather than concentrated in a few, the conditional-MI-based selection yields better prediction accuracy than selecting the top features by individual MI alone, for small feature-set sizes. For MI-concentrated datasets the two methods perform about the same.","feed_headline":"Quantum annealer feature selection beats MI-only on spread-out MI data","feed_subtitle":"Pairing mutual information with conditional mutual information lifts SVM price forecasts for small feature sets.","key_machinery":"The load-bearing object is the MIQUBO formulation of feature selection. Eq. (7) approximates the optimal feature set by maximizing, over the selected features, each feature's mutual information with the target plus the pairwise conditional mutual information of every other selected feature given it. That objective is turned into a QUBO by setting the diagonal coefficients to the negative individual MI values and the off-diagonal coefficients to the negative CMI values, so that minimizing the QUBO is the same as maximizing the feature-selection objective. The resulting binary quadratic model is solved with the Kerberos hybrid sampler, which runs tabu search, simulated annealing, and QPU sub-problem sampling in parallel. The comparison baseline is the top features by individual MI.","core_discovery":"On its own terms, the paper's central claim is that maximizing the sum of mutual information and conditional mutual information over a selected feature set, the objective in Eq. (7) solved as the MIQUBO on an annealer, selects feature combinations whose information content is more independent, and this translates into better SVM regression performance than MI-only selection when the dataset has low MI concentration and the selected feature set is small. This is demonstrated on two Caterpillar excavator-price datasets. For the model-308 dataset, MI is concentrated in construction year and working hours, and CMI-based and MI-based selections show no visible difference in mean $R^2$. For the all-models dataset, MI is more evenly distributed, and CMI-based selection produces a statistically relevant $R^2$ gap for the smallest feature counts, which narrows as more features are selected. The paper explains the gap by the CMI-selected sets containing more independent information, citing information theory.","pith_inferences":["A natural extension the authors do not run is to verify Kerberos's solutions against exhaustive optimization on the small-k instances; that check would separate the information-theoretic benefit of the CMI objective from solver noise.","Because the paper notes that lower MI concentration would make the QUBO matrices denser, datasets with near-uniform feature informativeness, such as image or audio representations, are a plausible place for annealing-specific gains to grow.","The same QUBO encoding could be applied to other pairwise information-theoretic objectives, such as joint mutual information or interaction information, producing a family of annealer-based feature selectors beyond CMI."],"forward_implications":["On low-MI-concentration datasets, CMI-based MIQUBO selection yields higher mean SVM R² values than top-k MI selection for the smallest feature counts, with the gap narrowing as more features are added.","On MI-concentrated datasets, CMI-based selection and MI-only selection converge to essentially the same feature sets and the same R² scores, so the annealing route offers no practical gain there.","The selected features are the original one-hot-encoded inputs, preserving interpretable domain meaning that transformed dimensionality-reduction representations lack.","Because feature selection is written as a QUBO, the search over feature combinations can be delegated to a hybrid annealer instead of enumerating all possible combinations."],"supporting_citations":[{"why":"Supplies the Caterpillar datasets and the SVM price-forecast setup that the experiments extend.","marker":"[12]"},{"why":"Documents the Kerberos hybrid solver used to solve the MIQUBO instances.","marker":"[21]"},{"why":"Proposes an approximate global mutual-information feature-selection approach that underlies Eq. (7).","marker":"[27]"},{"why":"Provides a fast information-theoretic approximation of joint mutual information used alongside [27] to justify the CMI objective.","marker":"[28]"},{"why":"Supports reformulating the MI/CMI feature-selection objective into a QUBO that an annealer can minimize.","marker":"[29]"}],"fun_headline_variants":["Quantum annealer wins feature selection when MI is spread thin","Quantum annealer adds CMI to MIQUBO for better ML forecasts","For low MI concentration, quantum annealer beats MI-only in ML","Quantum annealer selects independent features to beat MI-only","MIQUBO quantum annealing lifts SVM price forecasts with CMI"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The empirical comparison assumes that the Kerberos hybrid solver returns feature sets close enough to the true maximum of the CMI objective that the observed $R^2$ differences come from the choice of objective rather than from solver noise; the paper does not measure how close Kerberos is to that optimum.","fun_headline_variants_meta":{"raw":{"variants":["Quantum annealer wins feature selection when MI is spread thin","Quantum annealer adds CMI to MIQUBO for better ML forecasts","For low MI concentration, quantum annealer beats MI-only in ML","Quantum annealer selects independent features to beat MI-only","MIQUBO quantum annealing lifts SVM price forecasts with CMI"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001229,"raw_usage":{"total_tokens":5027,"prompt_tokens":902,"completion_tokens":4125,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":518,"completion_tokens_details":{"reasoning_tokens":4037}},"tokens_in":518,"tokens_out":4125,"duration_ms":22978,"temperature":1.0,"reasoning_tokens":4037,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T06:00:40.451470+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Solve Eq. (7) exhaustively on the Caterpillar all-models dataset for the smallest feature-set sizes tested, for example four and five features, and compare the resulting feature sets with Kerberos's selections on the same SVM train-test splits. If the exact CMI-based sets do not yield a higher mean $R^2$ than the MI-only top-k sets, the paper's central claim fails; a supporting check is whether Kerberos's QUBO objective values match the exact optimum on those instances.","supporting_citations":[{"cited_title":"Evaluating Quantum Support Vector Regression Meth- ods for Price Forecasting Applications","cited_arxiv_id":null,"evidence_quote":"Supplies the Caterpillar datasets and the SVM price-forecast setup that the experiments extend."},{"cited_title":"D-Wave Ocean Soft- ware Documentation, [Online]","cited_arxiv_id":null,"evidence_quote":"Documents the Kerberos hybrid solver used to solve the MIQUBO instances."},{"cited_title":"E fficient approximate so- lutions to mutual information based global feature selec- tion","cited_arxiv_id":null,"evidence_quote":"Proposes an approximate global mutual-information feature-selection approach that underlies Eq. (7)."},{"cited_title":"A fast information- theoretic approximation of joint mutual information fea- ture selection","cited_arxiv_id":null,"evidence_quote":"Provides a fast information-theoretic approximation of joint mutual information used alongside [27] to justify the CMI objective."},{"cited_title":"E ffective global approaches for mutual information based feature selection","cited_arxiv_id":null,"evidence_quote":"Supports reformulating the MI/CMI feature-selection objective into a QUBO that an annealer can minimize."}],"review_version":1}