{"id":"3360e426-371d-4eae-a6f8-23dbc8c97011","arxiv_id":"2506.02410","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A privacy-preserving test based on Laplace-perturbed sample eigenvalues is asymptotically distribution-free and detects n^{-1/2} local alternatives to Sigma = I.","lead":"This paper builds a privacy-protected statistical test for whether a high-dimensional covariance matrix equals the identity, using sample eigenvalues with added random noise. It gives formulas for how much noise is needed for sub-Gaussian data and proves the test's error rates and power.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 1 uses the noisy estimate \\hatγ as the Laplace scale; under H0, \\hatγ<γ with probability approaching 1/2, so the implemented mechanism is not ε-DP with the probability claimed in Theorem 2, even when σ=1 and γ≤γtilde.","rationale":"The paper makes a plausible start: the LSS CLT in Lemma 5 and the null/alternative asymptotics are nontrivial, the simulations are extensive, and the idea of perturbing eigenvalues rather than raw data is natural. I do not see a problem with the statistical CLT itself; the load-bearing gap is in the privacy guarantee. Theorem 2 is an oracle statement about a scale that uses the true γ. Algorithm 1 replaces γ by \\hatγ, and this substitution is invalid in DP: the noise scale must be an upper bound on sensitivity, not an estimate, and \\hatγ is an underestimate with probability about 1/2 even in the null case. The reader's weakest assumption identified the dependence on σ=1 and γtilde; my concern is sharper because it arises even when those are correct. It is addressable—for example, use a private upper confidence bound for γ or the preset γtilde for both noise stages—so the paper should remain conditional rather than accepted as written. Since the reader already gave CONDITIONAL, I keep that verdict unchanged.","tokens_in":35351,"tokens_out":15436,"duration_ms":157727,"concrete_test":"Analytic check: in the Step-4 mechanism, the privacy-loss bound for a neighboring pair is exp(Δ/s) with s=2.01\\hatγ d/(nε) and Δ≤2.01γd/n; thus the theorem's proof requires \\hatγ≥γ. To falsify the claimed probability, simulate Algorithm 1 with n=d=400, Gaussian null, ε=1, γtilde=2 over 10^4 replicates and record P(\\hatγ<1). The oracle theorem's failure probability 2exp(−n^{1−2r}) is ≤2exp(−20) for r=1/4, whereas the simulation should show P(\\hatγ<1)≈1/2. This directly demonstrates that the implemented noise scale is too small with non-negligible probability.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Theorem 2 proves ε-DP for an oracle that adds Laplace noise with scale 2.01σ²γd/(nε), where γ=Tr(Σ)/d. Algorithm 1 cannot use the unknown γ: Step 3 sets \\hatγ = d^{-1}|Σ_{i=1}^K(λ_i+ℓ*_i)| and Step 4 draws ℓ_i with scale 2.01\\hatγ d/(nε). A Laplace mechanism with ℓ1 sensitivity bounded by Δ is ε-DP only if its scale is at least Δ/ε. Since Δ≤2.01γd/n, the implemented scale is too small whenever \\hatγ<γ. Under H0, γ=1 and \\hatγ=|1+U|, where U is a centered noise of order O_p(1/√n) with a symmetric continuous distribution; consequently P(\\hatγ<1)→1/2, not the claimed 1−2exp(−n^{1−2r}). For any neighboring pair whose sensitivity attains the bound, and any realization with \\hatγ<γ, the Laplace density ratio can exceed e^ε, so the two-stage mechanism is not ε-DP. Remark 3 adds the further unverified assumptions σ=1 and γ≤γtilde, but the \\hatγ issue is internal and occurs even in the simulations' setting.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes differentially private tests for the high-dimensional hypothesis H0: Sigma = I_d when d/n -> y in (0, inf). The test statistics (1.4)-(1.6) are built from Laplace-perturbed sample eigenvalues, with the noise scale derived from a high-probability bound on the l1 sensitivity of the eigenvalue map for sub-Gaussian data (Theorem 1 and Theorem 2). The authors claim an asymptotically distribution-free null limit (Theorem 3), consistency against local alternatives at rate 1/sqrt(n) (Section 3.3), and support this with simulations and a real-data example. The statistical core is an original combination of random matrix theory and DP, but the privacy guarantee as implemented in Algorithm 1 is not established, and the null CLT is proved only under a support-separation condition that fails at y=1 and y>1.","tokens_in":35673,"tokens_out":7437,"duration_ms":72735,"significance":"If the results were correct as stated, this would be a valuable first contribution to DP-based testing of large-dimensional covariance structures, and the sensitivity analysis for unbounded sub-Gaussian data is a useful technical step. The paper is also commendable for stating detailed proofs of the sensitivity bound and of the CLT, and for providing extensive simulations. However, the central privacy claim is not supported by the algorithm actually implemented: the noise scale is data-dependent in a way that is not analyzed, and the simulations include a model whose sub-Gaussian parameter is not the assumed sigma=1. The asymptotic null distribution is also unproved for the important cases y=1 and y>1. These are load-bearing issues for the paper's main advertised contributions.","major_comments":[{"comment":"Theorem 2 proves a privacy guarantee for an oracle mechanism that adds Laplace noise with scale 2.01*sigma^2*gamma*d/(n*epsilon), where gamma=Tr(Sigma)/d. Algorithm 1 instead uses the data-dependent estimate hat(gamma) = d^{-1}|sum_i (lambda_i + ell*_i)| from Step 3 to set the scale in Step 4. Under H0, gamma=1 and hat(gamma)=1+O_p(K^{-1/2}) with a symmetric centered distribution, so P(hat(gamma)<1) tends to 1/2. Whenever hat(gamma)<gamma, the Laplace scale is strictly smaller than the sensitivity bound in Theorem 2, and for neighboring datasets whose sensitivity attains the bound, the output density ratio can exceed e^epsilon. Thus the mechanism in Algorithm 1 is not epsilon-DP with the probability claimed in Theorem 2. No composition argument or adaptive-sensitivity analysis is provided for the two-stage release of hat(gamma) and the subsequent eigenvalues.","section":"Algorithm 1, Steps 3-4; Theorem 2"},{"comment":"The algorithm's privacy guarantee relies on the unverified assumptions sigma=1 and gamma <= gamma_tilde. In the simulations, Model II generates z from Unif([-sqrt(3), sqrt(3)]^d), which is sub-Gaussian with sigma > 1 (Hoeffding's lemma gives sigma=sqrt(3) up to constants). With gamma_tilde=2, the scale used in Algorithm 1 is smaller than 2.01*sigma^2*gamma*d/(n*epsilon) under H0, so the privacy claim in Theorem 2 does not cover the reported Model II results. The paper should either treat sigma as a known upper bound and use it in the scale, or provide a privacy-preserving procedure to estimate or conservatively bound sigma; the current Remark 3 simply assumes the problem away.","section":"Remark 3 and Model II in Section 4.1"},{"comment":"Theorem 3 is stated under only Assumptions 1-2 for all y in (0,inf), but its proof invokes Lemma 5, whose proof requires Assumption 4, in particular that the support of the limiting spectral distribution is bounded away from zero. Under H0 with y=1, the Marcenko-Pastur left edge is 0, and for y>1 the support includes 0. Hence Assumption 4 fails exactly in the regimes y=1 and y>1 that are included in the theorem's statement and in the simulations (y=1 and y=5). The asymptotic distribution-free null limit is therefore not proved for these cases; a separate treatment of the zero edge, or a restricted statement of Theorem 3, is needed.","section":"Theorem 3 and Lemma 5/Assumption 4"},{"comment":"The statement that the privatized statistics are 'epsilon-DP with probability at least 1 - 2exp(-n^{1-2r})' is not the standard worst-case guarantee of Definition 1. The probability is over the random data, whereas DP requires the inequality to hold for every fixed neighboring pair. If the intended guarantee is (epsilon,delta)-DP with delta=2exp(-n^{1-2r}), the proof must spell out the conditioning on the sensitivity event and how the failure event is handled uniformly over all neighboring datasets. As written, the privacy semantics are ambiguous and weaker than the formal definition used elsewhere in the paper.","section":"Theorem 2 and Definition 1"}],"minor_comments":[{"comment":"The phrase 'detects local alternatives distinct from the null at the fastest rate of 1/sqrt(n)' is imprecise: the argument shows power tending to 1 when sqrt(K)|mu0_m - mu1_m| -> inf, and only nontrivial power bounded away from alpha when the limit is a finite positive constant. The finite-constant case is not 'detection' in the usual consistency sense and should be stated as such.","section":"Section 3.3"},{"comment":"In the 'Power 1' columns, the row label (400,200) is repeated three times and the rows (600,300) and (800,400) appear to be missing. This makes the power comparison hard to read and should be corrected.","section":"Table 3 and Table 4"},{"comment":"There are several typographical errors, including 'covariance matrice' in Section 5, 'covairates' in Section 4.2, and inconsistent notation for the tilde/gamma parameters in Remark 3 and Algorithm 1. These should be cleaned up.","section":"Throughout"},{"comment":"The statement that any (epsilon+delta,0)-DP algorithm is also (epsilon,delta)-DP is true but the choice of epsilon+delta seems arbitrary and does not by itself justify the focus on Laplace noise; a clearer discussion of the relation between pure and approximate DP would help.","section":"Section 2.2, Remark 1"}],"recommendation":"major_revision","confidential_remarks":"The core difficulty is not the statistical CLT but the mismatch between the privacy theorem and Algorithm 1. This is fixable in principle (for example, by using a prespecified public upper bound on gamma for the Laplace scale, or by a careful adaptive-sensitivity argument), but as it stands the paper's headline privacy guarantee is not valid for the implemented procedure. The missing edge case y>=1 in the null CLT is also serious because the simulations rely on those cases. I would encourage the authors to address these points; the paper has useful ideas and the sensitivity analysis is nontrivial."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper before citing it: it is the first to tackle differentially private testing for large-dimensional covariance structure, and it contains a genuinely useful technical contribution in the high-probability sensitivity bound for sample eigenvalues of unbounded sub-Gaussian data. The theoretical machinery is a DP adaptation of the Bai–Silverstein CLT for linear spectral statistics, and the paper works out the null asymptotics in detail, showing the privatized statistic is asymptotically distribution-free and can detect local alternatives at rate 1/sqrt(n). The simulations are extensive and the method appears to control Type I error and achieve reasonable power. That is real work, and the authors deserve credit for it.\n\nBut there is a load-bearing flaw in the privacy guarantee, and it is internal to the algorithm. Theorem 2 proves epsilon-DP for an oracle that adds Laplace noise with scale determined by the unknown true gamma = Tr(Sigma)/d. Algorithm 1 cannot do that, so it first adds noise with a preset scale, computes a noisy estimate hat-gamma from the already-perturbed eigenvalues, and then adds a second round of Laplace noise with scale proportional to hat-gamma. The problem is that under H0 hat-gamma is a symmetric noisy version of gamma, so with probability approaching 1/2 it is below gamma. Whenever that happens, the Laplace scale is smaller than the sensitivity bound requires, and the two-stage mechanism is not epsilon-DP with the probability claimed in Theorem 2. This is not a minor technicality; the privacy guarantee is the point of the paper. The stress-test note is correct, and the issue even occurs in the simulations' setting where sigma=1 and gamma<=gamma_tilde.\n\nA second soft spot is that Theorem 3 is stated for all y in (0,infinity), but the proof relies on Assumption 4, which requires the limiting spectral density to be bounded away from zero. At y=1 the Marcenko-Pastur left edge touches zero, so Assumption 4 fails exactly in the range the theorem claims to cover. This might be repairable with a separate argument for y=1, but as written the theorem's scope is wider than the proof supports.\n\nThere are also the preset assumptions sigma=1 and gamma<=gamma_tilde, which are not validated in a privacy-preserving way; if sigma>1 or gamma>gamma_tilde, even the oracle mechanism would not be DP.\n\nWho is this for? Researchers working on private high-dimensional inference will want to know about this paper because it opens a new direction and contains reusable analytic ideas. But it needs major revision before the privacy claim can stand. I would send it to peer review because the problem is important and the mistakes are identifiable and likely fixable, but I would insist that the authors confront the calibration issue head-on.\n\nRecommendation: send to a serious referee, but expect heavy revision.","headline":"First DP test for high-dimensional covariance structure with a real sensitivity bound, but the two-stage noise calibration in Algorithm 1 breaks the advertised privacy guarantee.","tokens_in":36148,"tokens_out":2118,"would_cite":false,"duration_ms":21459,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62H15","62H10","62F03","60B20","68P27"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that testing whether a large covariance matrix equals the identity can be made differentially private by adding Laplace noise to sample eigenvalues, with no bounded-data assumption, while staying asymptotically…","keywords":["differential privacy","random matrix theory","likelihood ratio statistics","covariance matrix testing","high-dimensional data","sub-Gaussian distribution","eigenvalue sensitivity","local alternatives"],"falsifier":"Run Algorithm 1 on data whose sub-Gaussian parameter is $\\sigma = 2$ (for example, standardized two-point or narrowly supported sub-Gaussian vectors) while the algorithm assumes $\\sigma = 1$ and takes $\\tilde{\\gamma}$ equal to the true $\\gamma$. If the empirical Type I error at $\\varepsilon = 8$ diverges from the nominal level as $n$ grows, or if a finite-sample attack on the released eigenvalues can detect a single changed row with probability exceeding the $\\varepsilon$-DP bound, the sensitivity calibration premise is false.","tokens_in":35162,"feed_emoji":"🔒","tokens_out":11790,"duration_ms":97624,"temperature":0.7,"pith_summary":"The paper proposes the first differentially private test for the high-dimensional null hypothesis $H_0: \\Sigma = I_d$, where the dimension $d$ and the sample size $n$ grow together with $d/n \\to y \\in (0,\\infty)$. The central move is to query only the sample eigenvalues, perturb each one with Laplace noise calibrated by a new high-probability bound on the $\\ell_1$ global sensitivity of the eigenvalue map, valid for unbounded sub-Gaussian data. The privatized statistic is the maximum of three eigenvalue-based loss statistics — an entropy-like loss, a quadratic loss, and an absolute-deviation loss — and it is shown to be asymptotically distribution-free under the null, with critical values from a known Gaussian maximum distribution, and to detect local alternatives at the rate $1/\\sqrt{n}$. If correct, a data curator can test $\\Sigma = I_d$ without releasing eigenvectors or raw eigenvalues and, with high probability, without any bounded-data assumption.","feed_headline":"Differentially private covariance test works without bounded data","feed_subtitle":"Laplace noise on sample eigenvalues keeps the test distribution-free and the 1/√n detection rate.","key_machinery":"The proof rests on two pillars. The first is the sensitivity analysis: using the tail bound for quadratic forms of sub-Gaussian vectors of Hsu et al. (2012), the paper shows that replacing one row of the design matrix changes the $\\ell_1$ distance between the eigenvalue vectors by at most $(x_1^\\top x_1 + \\tilde{x}_1^\\top \\tilde{x}_1)/n$, and bounds this quantity in probability. The second is a DP version of the classical CLT for linear spectral statistics: eigenvalue rigidity lets the authors replace each $\\lambda_i$ by its classical location $\\alpha_i$ at a cost of $o_p(K^{-1/2})$, after which a Lyapunov CLT applies to $g_m(\\alpha_i + \\ell_i)$ because the independent Laplace noise $\\ell_i$ provides a non-degenerate variance. The mean and covariance terms are then evaluated as Riemann sums against the generalized Marcenko-Pastur density. The Laplace noise, of order $d/n$, dominates the $O(K^{-1})$ fluctuations of the sample eigenvalues, so the asymptotic variance is non-zero, is governed by the noise, and does not depend on the unknown covariance under the null, which is what makes the test distribution-free.","core_discovery":"On its own terms, the paper establishes that spectral tests for covariance structure can retain their asymptotic properties after differential privacy in the proportional-growth regime $d/n \\to y \\in (0,\\infty)$. The central discovery is that the $\\ell_1$ sensitivity of the sample eigenvalue query is bounded, with probability at least $1 - 2e^{-nt}$, by $\\sigma^2\\{2\\mathrm{Tr}(\\Sigma)/n + 4\\sqrt{\\mathrm{Tr}(\\Sigma^2)}\\sqrt{t/n} + 4\\|\\Sigma\\| t\\}$, where $\\sigma$ is the sub-Gaussian parameter of the standardized population. Taking $t = n^{-2r}$ yields the simplified scale $2.01\\sigma^2\\gamma d/n$, so Laplace noise at this rate makes the released eigenvalues $\\varepsilon$-DP with probability at least $1 - 2\\exp\\{-n^{1-2r}\\}$. For the three loss functions $g_1(x)=|x|-\\log|x|-1$, $g_2(x)=|x-1|^2$, and $g_3(x)=|x-1|$, the perturbed linear spectral statistics $\\frac{1}{K}\\sum_{i=1}^K g_m(\\lambda_i + \\ell_i)$ are jointly Gaussian under $H_0$, with mean and covariance given by convolving the limiting spectral measure with the Laplace density, so $T^{\\mathrm{dp}}_{\\max}$ is asymptotically distribution-free; the same CLT implies power tends to one whenever any coordinate's mean shift exceeds $\\omega(1/\\sqrt{K})$, giving detection at the $1/\\sqrt{n}$ rate.","pith_inferences":["The privacy guarantee is conditional on premises the user cannot verify privately: if the true sub-Gaussian parameter $\\sigma$ exceeds $1$ or the true trace ratio $\\gamma$ exceeds the preset $\\tilde{\\gamma}$, the injected noise is silently too small and the claimed $\\varepsilon$-DP breaks; a two-stage procedure that spends part of the privacy budget to estimate the scale would be a natural extensi","Because the required noise scale is of order $d/n$, the method is confined to the proportional-growth regime; the authors' own concluding remark suggests that as $d/n \\to \\infty$ the same statistics cannot be privatized at this rate, which points toward an information-theoretic price of privacy in ultra-high-dimensional spectral testing worth investigating.","The maximum-of-three integrated statistic offers a template for private high-dimensional testing in general — combining losses with different sensitivity and power profiles can rescue detection when the signal shape is unknown — and the same integration could be ported to sphericity, independence, or two-sample covariance tests.","Releasing privatized eigenvalues rather than a single test decision enables multiple downstream analyses, but the paper does not analyze composition of many queries; repeated releases would require advanced composition or an explicit privacy-loss budget."],"forward_implications":["A data curator can release privatized eigenvalues, and hence a test decision, for $\\Sigma = I_d$ while keeping the data $\\varepsilon$-DP with probability at least $1 - 2\\exp\\{-n^{1-2r}\\}$.","The test is asymptotically distribution-free: critical values come from the distribution of the maximum of three correlated Gaussians, so no Monte Carlo or resampling is needed to set the threshold.","Power tends to one for any alternative whose mean shift in at least one of the three losses is of order $\\omega(1/\\sqrt{n})$, and the test retains non-trivial power at the $1/\\sqrt{n}$ boundary.","Because the released objects are only the noisy eigenvalues, the eigenvectors of the sample covariance matrix are never exposed, so the covariance matrix itself cannot be reconstructed.","The noise-inflated variance is the leading term in the fluctuation of the privatized statistic, so the null distribution does not depend on the unknown $\\Sigma$ under $H_0$ beyond the limit ratio $y$."],"supporting_citations":[{"why":"Supplies the definition of differential privacy, the Laplace mechanism, and the post-processing property on which the entire privacy argument rests.","marker":"Dwork et al. (2014a)"},{"why":"Provides the tail bound for quadratic forms of sub-Gaussian vectors used in the proof of Theorem 1 to control the sensitivity of the eigenvalue query.","marker":"Hsu et al. (2012)"},{"why":"Gives the classical CLT for linear spectral statistics that Lemma 5 extends to the privatized spectrum, including the Riemann-sum variance evaluation technique.","marker":"Bai and Silverstein (2004)"},{"why":"Supplies the eigenvalue rigidity estimates and regularity conditions used to replace sample eigenvalues by their classical locations in the CLT proof.","marker":"Knowles and Yin (2017)"},{"why":"Defines the corrected likelihood ratio statistic and its high-dimensional null distribution, the non-private benchmark the private test extends and is compared against.","marker":"Bai et al. (2009)"},{"why":"Gives the limiting spectral law for sample covariance matrices, used to compute the null mean and variance through the density $f_y$.","marker":"Marchenko and Pastur (1967)"},{"why":"Provides the generalized central limit theorem for sums of non-identical heavy-tailed variables, used to verify the regularity condition for the entropy-type loss $g_1$.","marker":"Shintani and Umeno (2018)"},{"why":"Motivates the quadratic-loss component of the integrated statistic, citing its higher power in specific high-dimensional settings.","marker":"Zheng et al. (2019)"}],"fun_headline_variants":["Private covariance test stays distribution-free at 1/√n rate","No bounded data needed for privatized spectral test","Privatized spectral test detects at optimal rate","Boundedness not required for private covariance tests","DP eigenvalue noise yields distribution-free testing"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the sub-Gaussian parameter of the standardized data equals exactly $1$ and that the user's preset bound $\\tilde{\\gamma}$ truly satisfies $\\tilde{\\gamma} \\ge \\mathrm{Tr}(\\Sigma)/d$; if either fails, the Laplace scale is too small, the high-probability $\\varepsilon$-DP guarantee collapses, and the null variance used for critical values is misspecified.","fun_headline_variants_meta":{"raw":{"variants":["Private covariance test stays distribution-free at 1/√n rate","No bounded data needed for privatized spectral test","Privatized spectral test detects at optimal rate","Boundedness not required for private covariance tests","DP eigenvalue noise yields distribution-free testing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000735,"raw_usage":{"total_tokens":3322,"prompt_tokens":1019,"completion_tokens":2303,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":635,"completion_tokens_details":{"reasoning_tokens":2244}},"tokens_in":635,"tokens_out":2303,"duration_ms":21084,"temperature":1.0,"reasoning_tokens":2244,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T11:25:36.942938+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Algorithm 1 on data whose sub-Gaussian parameter is $\\sigma = 2$ (for example, standardized two-point or narrowly supported sub-Gaussian vectors) while the algorithm assumes $\\sigma = 1$ and takes $\\tilde{\\gamma}$ equal to the true $\\gamma$. If the empirical Type I error at $\\varepsilon = 8$ diverges from the nominal level as $n$ grows, or if a finite-sample attack on the released eigenvalues can detect a single changed row with probability exceeding the $\\varepsilon$-DP bound, the sensitivity calibration premise is false.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the tail bound for quadratic forms of sub-Gaussian vectors used in the proof of Theorem 1 to control the sensitivity of the eigenvalue query."},{"cited_title":"and Yin, J","cited_arxiv_id":null,"evidence_quote":"Supplies the eigenvalue rigidity estimates and regularity conditions used to replace sample eigenvalues by their classical locations in the CLT proof."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the corrected likelihood ratio statistic and its high-dimensional null distribution, the non-private benchmark the private test extends and is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the limiting spectral law for sample covariance matrices, used to compute the null mean and variance through the density $f_y$."},{"cited_title":"and Umeno, K","cited_arxiv_id":null,"evidence_quote":"Provides the generalized central limit theorem for sums of non-identical heavy-tailed variables, used to verify the regularity condition for the entropy-type loss $g_1$."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Motivates the quadratic-loss component of the integrated statistic, citing its higher power in specific high-dimensional settings."}],"review_version":1}