{"id":"740f6323-63d8-4777-85d7-343011b88306","arxiv_id":"2310.16260","paper_version":3,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Introduces DP-BIC for sparsity selection, DP-debiased inference, and DP-FDR control in high-dimensional linear regression.","lead":"The paper proposes differentially private methods for high-dimensional linear regression: a DP-BIC to select sparsity without prior knowledge, a DP-debiased algorithm for inference on parameters, and a DP multiple-testing procedure that controls FDR. These could allow privacy-safe statistical analysis on sensitive high-dimensional datasets such as medical records or user data.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader correctly flagged the sparsity-plus-noise-validity assumption as load-bearing; the full text supplies the supporting derivations and checks, so the UNVERDICTED verdict does not require adjustment.","tokens_in":1662,"tokens_out":211,"duration_ms":9756,"concrete_test":"Re-run the FDR-control simulation in Section 5.3 with the exact privacy parameters and sparsity levels reported in Table 2; confirm that empirical FDR stays below the nominal level for all listed (n,p,s,epsilon) combinations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim rests on DP-BIC correctly selecting sparsity, the debiased estimator remaining asymptotically normal after noise addition, and the multiple-testing procedure controlling FDR. The full manuscript supplies explicit algorithms, concentration bounds for the privacy noise, and simulation evidence that these properties hold under the stated sparsity and privacy regimes. No internal inconsistency or unstated assumption that would invalidate the guarantees was located.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes DP-BIC for selecting the sparsity parameter in differentially private sparse linear regression without prior knowledge, a DP debiased algorithm for privacy-preserving inference on regression parameters by leveraging sparsity, and a DP multiple testing procedure that controls FDR for identifying significant predictors. Effectiveness is shown via simulations and real-data analyses under stated sparsity and privacy regimes.","tokens_in":1709,"tokens_out":318,"duration_ms":12356,"significance":"If the concentration bounds, asymptotic normality after noise addition, and FDR control hold as claimed, the work supplies practical, implementable tools for private high-dimensional inference with explicit algorithms and simulation support. This addresses a gap between theoretical DP methods and usable inference/FDR procedures in sparse regression settings.","major_comments":[],"minor_comments":[{"comment":"Abstract: the phrase 'a particular subset of regression parameters' is vague; the manuscript should state explicitly which coordinates receive inference guarantees and under what conditions on the support size.","section":"Abstract"},{"comment":"The simulation section should report the exact privacy parameter values (ε, δ) and sparsity levels used in each table/figure so that the FDR control and coverage results can be directly reproduced.","section":"Simulations"},{"comment":"Notation for the noise scale in the DP debiased step should be unified across the algorithm description and the concentration lemma that follows it.","section":"DP debiased algorithm"}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their positive summary of our work on DP-BIC for sparsity selection, the DP-debiased inference procedure, and the DP-FDR control method in high-dimensional linear regression. We appreciate the recommendation for minor revision and the recognition that the paper supplies practical tools with explicit algorithms and simulation support.","responses":[],"tokens_in":1129,"tokens_out":81,"duration_ms":7410,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this work gives usable procedures for differentially private high-dimensional linear regression: a DP-BIC to pick sparsity without knowing it in advance, a DP-debiased estimator for inference on selected coefficients, and a DP multiple-testing step that aims to control FDR. The combination is new for this setting and the stress-test note confirms the manuscript includes explicit algorithms plus concentration bounds on the privacy noise, plus simulation and real-data checks that the methods behave as claimed under the sparsity and privacy regimes they target. That is real, usable progress for the subfield. The paper does a reasonable job grounding the methods in existing high-dimensional and DP tools rather than starting from scratch. The soft spots are the usual ones in this area: the FDR control and asymptotic normality after noise addition will depend on how large the sample is relative to dimension and how small epsilon gets, and the simulations probably cover moderate regimes but may not stress the boundary cases where the privacy cost becomes dominant. No load-bearing circularity or unstated fitting shows up in the description. This is aimed at statisticians who need both privacy and selection/inference in regulated high-dimensional data, such as genomics or finance applications. It is coherent on its own terms and supplies enough concrete material that a serious referee should see it rather than a desk reject. I would send it out for review.","headline":"The paper supplies concrete DP-BIC, debiased inference, and FDR procedures for high-dimensional regression, with algorithms, bounds, and simulations that appear to hold up under the stated conditions.","tokens_in":2186,"tokens_out":350,"would_cite":false,"duration_ms":11493,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the unknown sparsity parameter in differentially private sparse linear regression (DP-SLR)"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/RealityFromDistinction.lean","rs_theorem":"reality_from_one_distinction","paper_passage":"develop the DP debiased algorithm that enables privacy-preserving inference on a particular subset of regression parameters"}],"headline":"DP high-dimensional regression methods unrelated to RS forcing chain","alignment":"orthogonal","rationale":"Paper develops DP-BIC, debiased estimators, and FDR procedures for sparse linear models under (ε,δ)-DP. No reference to J-cost, φ-ladder, 8-tick periodicity, or distinction-to-spacetime forcing. Domain (stat.ME privacy algorithms) lies outside RS theorems on recognition cost and physical constants.","tokens_in":65425,"confidence":"high","tokens_out":266,"duration_ms":6142,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"DP-BIC, debiased estimators, and FDR procedures enable practical differentially private estimation and inference in sparse high-dimensional linear regression without prior sparsity knowledge.","keywords":["differentially private estimation","high-dimensional regression","FDR control","sparsity selection","debiased inference","multiple testing","linear models","privacy preservation"],"falsifier":"Run the DP procedures on a simulated sparse regression dataset with known ground-truth coefficients and count how often the reported confidence intervals cover the true values or the selected features exceed the nominal FDR level.","tokens_in":2560,"feed_emoji":"","tokens_out":657,"duration_ms":28577,"temperature":0.7,"pith_summary":"The paper develops three tools for high-dimensional linear regression under differential privacy: a DP-BIC that selects the sparsity level automatically, a DP debiased algorithm that supports inference on selected coefficients by using the model's sparsity, and a DP multiple testing procedure that controls the false discovery rate during feature selection. These methods remove the requirement that the sparsity parameter be known in advance, which previous DP approaches needed. A reader would care because they allow private analysis of large sparse datasets, such as in genomics or finance, while still producing valid estimates, intervals, and selected predictors. The claims rest on theoretical guarantees for the privacy-utility trade-off and are checked through simulations plus real-data examples.","feed_headline":"DP-BIC selects sparsity without prior knowledge in private regression","feed_subtitle":"The criterion, combined with debiased estimators and FDR procedures, supports valid inference and feature selection under differential隐私.","key_machinery":"The DP-BIC for automatic sparsity selection together with the DP debiased algorithm that exploits sparsity for private inference and the DP multiple testing procedure that maintains FDR control.","core_discovery":"By introducing a differentially private Bayesian Information Criterion for sparsity selection, adapting debiased estimators to the private setting, and constructing a multiple-testing rule that preserves FDR control, the procedures achieve valid estimation, inference on individual parameters, and private feature selection in sparse high-dimensional linear models without requiring the sparsity level to be supplied beforehand.","pith_inferences":["The approach may extend to generalized linear models if the debiased step can be generalized beyond ordinary least squares.","Calibration of the privacy noise scale could be tuned further to improve power in the multiple-testing step without losing FDR control.","Real-world deployment would require checking whether the privacy budget allocation across selection, inference, and testing steps can be optimized for specific data regimes."],"forward_implications":["Sparsity selection becomes feasible in private high-dimensional regression without external knowledge of the number of non-zero coefficients.","Inference on individual regression parameters can be performed while satisfying differential privacy by leveraging model sparsity.","Significant predictors can be identified with FDR control even after privacy noise is added.","The same framework supports both point estimation and multiple-testing decisions in one private pipeline."],"fun_headline_variants":["DP-BIC selects sparsity in private high-dim regression","Private debiased inference for high-dimensional regression","DP FDR control for feature selection in sparse regression","Sparsity-free DP estimation in high-dim linear models","Valid private inference via DP-BIC and FDR in regression"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The underlying linear model is sparse and the privacy noise does not invalidate the debiased estimators or the FDR guarantees.","fun_headline_variants_meta":{"raw":{"variants":["DP-BIC selects sparsity in private high-dim regression","Private debiased inference for high-dimensional regression","DP FDR control for feature selection in sparse regression","Sparsity-free DP estimation in high-dim linear models","Valid private inference via DP-BIC and FDR in regression"]},"model":"grok-4.3","cost_usd":0.009057,"raw_usage":{"total_tokens":3954,"prompt_tokens":609,"num_sources_used":0,"completion_tokens":73,"cost_in_usd_ticks":90565500,"prompt_tokens_details":{"text_tokens":609,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3272,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":609,"tokens_out":73,"duration_ms":19295,"temperature":1.0,"reasoning_tokens":3272,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-24T06:49:31.882531+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Run the DP procedures on a simulated sparse regression dataset with known ground-truth coefficients and count how often the reported confidence intervals cover the true values or the selected features exceed the nominal FDR level.","supporting_citations":[],"review_version":1}