Quantum Annealing based Feature Selection in Machine Learning

Bharadwaj Chowdary Mummaneni; Christian Tutschku; Daniel Pranjic

REVIEW 3 major objections 4 minor 47 references

Quantum Annealing based Feature Selection in Machine Learning

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2411.19609 v1 pith:CLLNF33R submitted 2024-11-29 quant-ph

Daniel Pranjic , Bharadwaj Chowdary Mummaneni , Christian Tutschku This is my paper · ORCID

classification quant-ph

keywords featureselectionquantumannealingQUBOmutualinformationconditionalsupportvectorregressionhybridquantum-classicaloptimizationpriceforecasting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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 -MI(X_j;Y|X_i) for i

What 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.

Soft 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.

Who 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.

Recommendation: 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.

Referee Report

3 major / 4 minor

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.

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 (3)

[Section II.B and III, solver validation] 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 III, Fig. 5] 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 II.A and III] 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.

minor comments (4)

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 II.B] 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 II.B, Fig. 3] 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.
[General] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reasoning in the MIQUBO derivation or the MI-vs-CMI comparison.

full rationale

The paper's central claim is an empirical comparison: feature sets selected by maximizing Eq. (7) are evaluated by train/test SVM R2 (Eq. 15), which is independent of the selection objective. The QUBO coefficients are computed directly from MI and CMI estimates, and the selected bitstrings are then used as SVM inputs; no fitted parameter is renamed as a prediction. The self-citations (Ref. [12] for dataset provenance and Ref. [41] for the Ising model) are not load-bearing: the datasets are described independently in Section II.A, and the Ising model citation is a standard background reference. The approximation leading to Eq. (7) is stated explicitly as an assumption, not smuggled in. The lack of validation of the Kerberos solver against exact optima is a correctness or robustness concern, not circularity, because the R2 metric does not depend on the solver's objective. Similarly, the potential mismatch between Eq. (7) and the QUBO coefficients described in Section II.B would be an implementation error, not a circular reduction. No step in the derivation is equivalent to its own input by construction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the CMI approximation in Eq. (7), on the exactness of the QUBO encoding of that approximation, and on the hybrid solver returning high-quality solutions. None of these are validated against exact classical optimization in the paper. The SVM hyperparameters and the 25-feature pre-pruning are hand-chosen inputs that also shape the results.

free parameters (3)

SVM hyperparameters gamma, C, epsilon = gamma=1, C=1, epsilon=1e-3
Fixed by hand for all experiments; they affect R2 and the observed gap but are not fitted to data.
Number of pre-selected features for Caterpillar (all models) = 25
The 67 one-hot features are reduced to the top 25 by MI before QUBO solving; this hand-chosen threshold constrains both selection methods.
Number of train-test splits = 100 (Cat-308), 15 (Cat-All)
Arbitrary experimental choices; the low split count for Cat-All weakens statistical confidence.

assumptions (4)

standard math Definitions of MI, entropy, and SVR dual formulation are standard and correctly applied.
Treated as known background from Refs. [13,44,47]; no issue.
domain assumption Conditional independence approximation p(Fi|Fj;Fk) = p(Fi|Fk), restricting CMI to triples (Eq. 7).
The QUBO objective is only an approximation to the full CMI feature selection problem; if the approximation is poor, the selected feature sets may not maximize true CMI.
ad hoc to paper QUBO coefficients Qii = -MI(Xi;Y) and Qi,j = -MI(Xj;Y|Xi) exactly encode Eq. (7) under the solver's QUBO convention.
The paper does not specify how the asymmetric CMI terms are placed in an upper-triangular QUBO matrix; the encoding is essential for the solver to represent the stated objective.
domain assumption D-Wave Kerberos returns sufficiently optimal solutions to the QUBO.
The empirical claim treats the solver output as a good solution; no optimality gap is reported.

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Cite this review

Pith. "Pith review of Quantum Annealing based Feature Selection in Machine Learning." pith.science (2026). https://pith.science/paper/CLLNF33R

@misc{pith2026241119609,
  author       = {Pith},
  title        = {Pith review of: Quantum Annealing based Feature Selection in Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CLLNF33R}},
  note         = {Machine review of arXiv:2411.19609}
}

read the original abstract

Feature selection is crucial for enhancing the accuracy and efficiency of machine learning (ML) models. This work investigates the utility of quantum annealing for the feature selection process in an ML-pipeline, used for maximizing the mutual information (MI) or conditional mutual information (CMI) of the underlying feature space. Calculating the optimal set of features that maximize the MI or CMI is computationally intractable for large datasets on classical computers, even with approximative methods. This study employs a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) formulation, enabling its solution on a quantum annealer. We demonstrate the capability of this approach to identify the best feature combinations that maximize the MI or CMI. To showcase its real-world applicability, we solve the MIQUBO problem to forecast the prices of used excavators. Our results demonstrate that for datasets with a small MI concentration the MIQUBO approach can provide a significant improvement over MI-only based approaches, dependent on the dimension of the selected feature space.

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