{"id":"19e0ad89-98db-46d5-ae62-16536e696140","arxiv_id":"2411.17859","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Sparse XY-PLS, formed by soft-thresholding weight vectors in both blocks, outperforms dense XY-PLS and PLS2 in simulations and chemometric applications with uninformative variables.","lead":"This paper adds a sparsity step to the XY-PLS algorithm so that both predictor and response variable blocks are compressed and have uninformative variables dropped at once. The method is tested in simulations and two chemometric datasets, where it predicts better than ordinary multivariate PLS in most settings.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Masking loadings in Algorithm 1 steps vi–vii breaks the deflation orthogonality, so successive scores can remain correlated; the reported gains may be an artifact of this implementation choice.","rationale":"The central claim is empirical superiority of the sparse twoblock estimator, but the estimator's internal mechanics must be coherent for that superiority to mean anything. The masked deflation is a concrete, checkable break: it violates the orthogonality that the rest of the algorithm assumes, and the paper's own Equations (3) and (7) depend on that orthogonality. The reader identified the same area as the weakest assumption; this analysis localizes the failure to the Hadamard mask in steps vi and shows algebraically why the residuals retain covariance with the preceding score. A simple unmasked-deflation variant would settle whether the published results are driven by the sparse two-block idea or by this implementation defect. Because the fix is easy and the evidence can be regenerated, the conditional verdict remains appropriate; if the test shows a large difference, the paper would need to be revised or rejected in its current form. I focus on this issue rather than the missing dense-XY-PLS simulation baseline because the deflation problem threatens the validity of the method itself, not just the completeness of the comparison.","tokens_in":9103,"tokens_out":9714,"duration_ms":84568,"concrete_test":"Run Algorithm 1 as published on one Section 3.1 dataset (e.g., n=100, p1=100, p2=200, q1=3, q2=2, h=3, g=1, eta=kappa=0.5) and compute the residual-score covariances u_1^T F_1 and t_1^T E_1, and the correlations between u_1 and u_2 and between t_1 and t_2. Nonzero values demonstrate the broken orthogonality. Then repeat the full Figure 1 simulation with step 1(b)vi and 2(b)vi changed to unmasked OLS loadings (q_j = F_{j-1}^T u_j/(u_j^T u_j), p_i = E_{i-1}^T t_i/(t_i^T t_i)), keeping all other steps and hyperparameters identical. If MSEB and FP/FN rates are essentially unchanged, the masking is not the source of the gains; if they differ materially, the reported advantage is an artifact of the invalid masking.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Algorithm 1, step 1(b)vi computes q_j = (F_{j-1}^T u_j)/(u_j^T u_j) ⊙ m_j, and step 2(b)vi computes p_i analogously with n_i. The mask is intended only to align the nonzero pattern of loadings with the sparse weights, but it changes the deflation. In dense XY-PLS, q_j is the OLS loading, so u_j^T F_j = 0 and the residuals are orthogonal to the score. With the mask, u_j^T F_j = a^T(1-m_j), where a = F_{j-1}^T u_j: every variable excluded by the mask retains its full covariance with u_j. The same holds for t_i^T E_i in the predictor block. As a result, the next weights v_{j+1}, w_{i+1} are computed from residuals that still contain the previous score direction, so successive scores are not guaranteed to be uncorrelated. Equations (3) and (7), and the regression-coefficient formula (8), all rely on this orthogonality. The paper explicitly calls the estimator 'postulated ad hoc' and defers theory, but the issue here is not a missing population proof; the algorithm is internally inconsistent with its own deflation equations. Consequently the reported improvements over dense XY-PLS and PLS2 may be caused by this masking rather than by sparse two-block dimension reduction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces a sparse version of the XY-PLS algorithm for simultaneous dimension reduction in two blocks. It applies soft-thresholding to the weight vectors of each block, masks the loadings to the selected variables, and derives sparse regression coefficients. The method is evaluated in a simulation study and on two chemometric data sets, and is claimed to outperform dense XY-PLS and multivariate PLS2. The paper explicitly acknowledges that the estimator is postulated ad hoc and defers theoretical analysis to future work.","tokens_in":92,"tokens_out":11251,"duration_ms":156013,"significance":"If the empirical claims hold, the paper offers a practical algorithm for multivariate calibration with variable selection in both X and Y blocks, and it usefully extends the less-cited XY-PLS approach. The manuscript is clearly written, the algorithm is concrete, and the two real-data examples use appropriate independent test splits. However, the simulation evidence is narrower than the abstract claims, and the masked deflation creates a technical inconsistency that needs to be resolved before the reported improvements can be attributed to sparse two-block dimension reduction.","major_comments":[{"comment":"Masking q_j and p_i with m_j and n_i breaks the deflation orthogonality. In dense XY-PLS, q_j = F_{j-1}^T u_j/(u_j^T u_j) gives u_j^T F_j = 0; with q_j ⊙ m_j, u_j^T F_j = (F_{j-1}^T u_j)^T(1-m_j), which is generally nonzero. The same holds for t_i^T E_i. The sparse algorithm therefore does not satisfy Equations (3) and (4), and Equation (8) is inherited from the dense derivation without justification. Since the paper itself calls the estimator 'postulated ad hoc' and says the loadings masking is 'strictly speaking not necessary,' the authors should either prove that the masked deflation preserves the needed orthogonality, remove the masking and verify that sparse coefficients still result, or add a comparison that isolates the effect of the masking. Without this, the reported gains over dense XY-PLS may be an artifact of the implementation rather than of sparse two-block dimension reduction.","section":"Section 2.2, Algorithm 1, steps 1(b)vi-vii and 2(b)vi-vii; Eq. (7)"},{"comment":"The abstract claims that in the simulation study the new method outperforms its dense counterpart, but the simulation compares only Sparse Twoblock with PLS2; dense XY-PLS is never included in the simulation. Figures 1 and 2 and the accompanying text describe two estimators only. The central claim 'outperforms dense XY-PLS' is therefore unsupported by the simulation and should be either substantiated by adding dense XY-PLS to the simulation or removed from the abstract.","section":"Abstract and Section 3.3"},{"comment":"The MSEB definition appears to have a dimension mismatch. B is p×q, and the text says the metric compares coefficients for the informative dependent variables, so the slice should be \\`hat B[:,1:q1]\\` (or the rows should be restricted to the p1 informative predictors). As printed, the expression \\`hat B[:,1:p1]\\` uses p1 in the column index. Please correct the notation; this metric drives all simulation conclusions.","section":"Section 3.1, Eq. (12)"},{"comment":"The simulation fixes η=κ=0.5, h=3, g=1 and reports only point averages over 1000 runs. No error bars, standard errors, or sensitivity analysis around the sparsity parameters are provided. Because the proposed method has four tuning parameters and the text draws a general conclusion that it 'increasingly outperforms PLS2,' the simulation evidence should include at least a small grid over (η,κ) and (h,g), or report variability, to show the result is not an artifact of the single chosen setting.","section":"Section 3.3"}],"minor_comments":[{"comment":"The subscript in E_j is undefined in the predictor loop; it should be E_{i-1} (and similarly for step 2(b)vi's E_i).","section":"Algorithm 1, step 2(b)i"},{"comment":"The sentence 'Loadings are composed of ... P = [p0, ⋯, pp10⋯p2]' is garbled; please restate the construction of the true loading matrix.","section":"Section 3.1"},{"comment":"The typesetting of the formula is corrupted; please use a standard norm notation such as \\\\| \\cdot \\\\|_F^2.","section":"Section 3.2, Eq. (12)"},{"comment":"The text reports MSE values (0.95, 1.73, 0.34) that do not appear in Table 2, which reports R2 values; use one metric consistently or give both.","section":"Section 4.2"},{"comment":"The number of wavelengths selected by Cook et al. is given as both 63 and 64; please make the count consistent.","section":"Section 4.2"},{"comment":"Minor typographical issues: 'reported in in Cook et al.' (Section 4.1), 'compositions pf seven' (Section 4.1), and the missing word 'in which' in Section 3.3.","section":"Sections 3.3 and 4.1"},{"comment":"The manuscript does not provide code or a data availability statement; for an algorithmic paper, sharing the implementation would improve reproducibility.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"I am not recommending rejection because the core problem is fixable: the authors can add dense XY-PLS to the simulation, correct or justify the masked deflation, and report tuning sensitivity. The paper is within the scope of the journal, but the current version overclaims what the simulation shows and needs a substantive revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new thing here is an algorithm that puts the SNIPLS soft-thresholding rule onto XY-PLS, giving sparse dimension reduction in both X and Y with separate sparsity parameters. That combination is new, and the two real-data examples are genuinely encouraging: sparse twoblock beats PLS1, PLS2, and dense XY-PLS on the slump test set and gets better or comparable R2 on the NIR biscuit data. The paper is also honest about what it does not prove: it calls the estimator \"postulated ad hoc\" and defers population theory to future work. Those are points in its favor.\n\nThe soft spots are real, and one of them is load-bearing. The simulation section only compares against PLS2, not dense XY-PLS, even though the abstract promises the new method outperforms its dense counterpart. The averages are over 1000 runs but there are no error bars; the sparsity parameters are fixed at 0.5 with no sensitivity analysis; no code or data are supplied. The citation pattern is fine: XY-PLS and SNIPLS are properly attributed, and the self-citations are disclosed and relevant.\n\nThe deeper problem is the masking of loadings in Algorithm 1. In dense XY-PLS, q_j is the OLS loading F_{j-1}^T u_j/(u_j^T u_j), so the deflation F_j = F_{j-1} - u_j q_j^T removes all covariance between u_j and the residual. In the sparse version, q_j is elementwise multiplied by the mask m_j. Variables excluded by the mask keep their full covariance with u_j, so the next score can remain correlated with the previous one. The same happens in the predictor block with p_i. Equations (3), (7), and the regression-coefficient formula (8) all rely on that orthogonality. This is not a missing population theorem; the algorithm as written is inconsistent with its own deflation equations. The reported gains over dense XY-PLS and PLS2 could therefore be an artifact of the masking rather than evidence for sparse two-block dimension reduction. This is fixable, but it needs to be fixed, not deferred.\n\nWho is this for: chemometricians and practitioners who want automatic variable selection in multivariate calibration. I would send it to a serious referee, but with a clear request to address the deflation orthogonality, add dense XY-PLS to the simulations, report variability, and release code and data. As it stands, the central claim is not supported.","headline":"A promising but unproven sparse XY-PLS variant whose load-bearing flaw is that masking loadings breaks the deflation orthogonality.","tokens_in":9935,"tokens_out":3245,"would_cite":false,"duration_ms":28733,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Sparse two-block dimension reduction simultaneously compresses and selects variables in both blocks, and the paper shows it predicts multivariate responses better than dense XY-PLS and PLS2.","keywords":["sparse PLS","two-block dimension reduction","variable selection","multivariate regression","XY-PLS","soft-thresholding","chemometrics","partial least squares"],"falsifier":"A simulation with a known sparse coefficient structure in which the sparse twoblock estimator selects a large fraction of uninformative variables and yields higher prediction error than dense XY-PLS, or a direct check that the thresholded weights produce nonzero covariances between residual blocks, would refute the method's core claim.","tokens_in":8902,"feed_emoji":"🧪","tokens_out":5753,"duration_ms":43787,"temperature":0.7,"pith_summary":"The paper introduces a sparse version of the two-block dimension reduction method XY-PLS, which finds linear combinations of the independent variables and of the dependent variables simultaneously. By soft-thresholding the weight vectors in each block, the method performs intrinsic variable selection in both X and Y blocks. The author claims that, when uninformative variables are present, this sparse estimator estimates regression coefficients more accurately than dense XY-PLS and than multivariate PLS (PLS2), and that the advantage grows with the number of irrelevant predictors. Two chemometric applications, concrete slump and NIR biscuit dough data, are used to show improved overall predictive performance. The paper also provides an explicit algorithm, so the method can be implemented directly.","feed_headline":"Sparse two-block PLS outperforms dense XY-PLS and PLS2","feed_subtitle":"Variable selection in both blocks sharpens multivariate predictions on simulations and two chemometric datasets.","key_machinery":"The central object is Algorithm 1, the sparse twoblock PLS algorithm. It takes the dense XY-PLS weight vectors, normalizes them, applies the soft-thresholding rule of Equation (9) with sparsity parameters kappa for the response block and eta for the predictor block, and masks the corresponding loadings so that each latent direction has a single nonzero pattern. Each block is deflated separately as in XY-PLS, preserving the zero-covariance conditions of Equation (3) among scores, and the final multivariate regression coefficients are assembled from the sparse weights and loadings by Equation (8). This mechanism ties variable selection directly to the dimension-reduction step, so the same selected variables appear in weights, loadings, and coefficients.","core_discovery":"The paper claims that applying a soft-thresholding operation to the XY-PLS weighting vectors, with separate tunable sparsity parameters for the predictor and predictand blocks, yields an estimator that simultaneously reduces dimension and deselects uninformative variables in both blocks. The resulting sparse twoblock PLS algorithm computes sparse weights, sparse loadings, and sparse regression coefficients that remain consistent in their nonzero patterns, and the deflation steps guarantee uncorrelated scores. The author argues that this estimator outperforms dense XY-PLS and PLS2 in simulation studies, especially as the proportion of uninformative predictors increases, and that it gives better overall prediction errors on the concrete slump and NIR biscuit dough datasets. The regression coefficients are still computed by the XY-PLS formula, with sparse weights in place of the dense ones.","pith_inferences":["The soft-thresholding rule is one of many possible sparsity-inducing schemes; lasso-type or adaptive thresholding could yield different selection properties, but the paper does not compare them.","The claim that thresholding preserves the zero-covariance deflation structure is not proven theoretically; if a future proof fails, the advantages may be specific to the simulation design or require additional constraints.","In applications where both blocks are large and sparse, the method could serve as an exploratory tool to map which predictors relate to which responses, beyond its predictive role.","The comparison to sparse CCA in the outlook suggests the method could be recast as a sparse alternative to canonical correlation with per-block complexity control."],"forward_implications":["Variable selection in both X and Y blocks becomes automatic via cross-validation of the two sparsity parameters, removing the need for manual wavelength or feature selection.","The method can be applied to settings with p > n, since the simulation shows stable coefficient estimation when the number of predictors exceeds the sample size.","Because Y-block variables can be deselected, the estimator can flag response variables that carry no joint information, which the paper notes is relevant for genomics and metabolomics.","The sparse estimator outperforms PLS2 more as uninformative predictors increase, suggesting it is particularly suited to high-dimensional data with many irrelevant variables.","The explicit algorithm allows straightforward implementation and adaptation to other PLS-family variants."],"supporting_citations":[{"why":"Provides the dense XY-PLS algorithm that the sparse method builds on and whose regression coefficient formula is reused.","marker":"Cook et al. (2023)"},{"why":"Contributes the SNIPLS soft-thresholding rule that is applied to the weight vectors in Equation (9).","marker":"Hoffmann et al. (2016)"},{"why":"Supplies the NIPALS algorithm used to compute the PLS2 baseline that sparse twoblock outperforms.","marker":"Wold (1966)"},{"why":"Establishes that PLS scores estimate the central subspace, the theoretical basis for treating PLS-type dimension reduction as sufficient.","marker":"Cook et al. (2013)"},{"why":"Provides the concrete slump dataset used as the first chemometric application.","marker":"Yeh (2007)"},{"why":"Provides the NIR biscuit dough dataset used as the second chemometric application.","marker":"Osborne et al. (1984)"}],"fun_headline_variants":["Two-block sparse PLS beats dense XY-PLS and PLS2","Sparse PLS selects variables in both blocks, beats PLS2","Joint sparsity in PLS improves prediction over dense and PLS2","Sparse two-block reduction outperforms PLS2 and dense XY-PLS","Variable selection in both blocks sharpens PLS forecasts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that applying soft-thresholding to the weight vectors and then masking the loadings does not break the deflation steps or the regression-coefficient formula, so the estimator still obeys the zero-covariance constraints; the paper does not prove this and calls the method 'postulated ad hoc'.","fun_headline_variants_meta":{"raw":{"variants":["Two-block sparse PLS beats dense XY-PLS and PLS2","Sparse PLS selects variables in both blocks, beats PLS2","Joint sparsity in PLS improves prediction over dense and PLS2","Sparse two-block reduction outperforms PLS2 and dense XY-PLS","Variable selection in both blocks sharpens PLS forecasts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000931,"raw_usage":{"total_tokens":3910,"prompt_tokens":796,"completion_tokens":3114,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":412,"completion_tokens_details":{"reasoning_tokens":3035}},"tokens_in":412,"tokens_out":3114,"duration_ms":19357,"temperature":1.0,"reasoning_tokens":3035,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:46:59.638805+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A simulation with a known sparse coefficient structure in which the sparse twoblock estimator selects a large fraction of uninformative variables and yields higher prediction error than dense XY-PLS, or a direct check that the thresholded weights produce nonzero covariances between residual blocks, would refute the method's core claim.","supporting_citations":[{"cited_title":"D., Forzani, L., and Liu, L","cited_arxiv_id":null,"evidence_quote":"Provides the dense XY-PLS algorithm that the sparse method builds on and whose regression coefficient formula is reused."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Contributes the SNIPLS soft-thresholding rule that is applied to the weight vectors in Equation (9)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the NIPALS algorithm used to compute the PLS2 baseline that sparse twoblock outperforms."},{"cited_title":"D., Helland, I., and Su, Z","cited_arxiv_id":null,"evidence_quote":"Establishes that PLS scores estimate the central subspace, the theoretical basis for treating PLS-type dimension reduction as sufficient."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the concrete slump dataset used as the first chemometric application."},{"cited_title":"G., Fearn, T., Miller, A","cited_arxiv_id":null,"evidence_quote":"Provides the NIR biscuit dough dataset used as the second chemometric application."}],"review_version":1}