{"id":"81c42a0c-77d8-4ede-8297-eea5330e1e23","arxiv_id":"2505.20787","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"An influence-function debiased objective for ill-posed regression achieves second-order nuisance bias, with finite-sample rate bounds, cross-validated tuning, and root-n inference conditions for linear functionals.","lead":"Statistical problems from nonparametric instrumental variables to proximal causal inference require solving a conditional moment equation that is an ill-posed inverse problem. This paper adds an influence-function debiasing step to the standard projection-error objective and proves second-order bias, finite-sample rates, and root-n conditions for linear functionals.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 4's proof relies on a loss-Lipschitz bound that appears to require sup-norm boundedness of H and g1, not the stated L2 boundedness; this gap should be resolved before the quartic-rate claim is accepted.","rationale":"The reader's CONDITIONAL verdict is appropriate, and the paper has real strengths: Proposition 2's bias structure is correctly derived, the comparison to Li et al. (2024) is explicit, and the cross-validation analysis in Theorems 6 and 7 is a serious attempt to address hyper-parameter selection. However, I believe the single most load-bearing issue is not Assumption 4 itself, though that assumption is indeed fragile and self-referential in the way Remark 8 concedes. The more fundamental concern is that Theorem 4, the key rate result advertised in the abstract and used in Section 4, has a proof gap in its Lipschitz verification. The proof invokes Lemma 2 on a loss function whose Lipschitz constant in L2(P0) is only established by dropping terms that require L-infinity-type control on H, g1, and the estimated conditional expectation operator. Assumption 3(ii), as written, does not supply that control. This is an internal inconsistency in the proof as stated, not a disagreement with external consensus. The reader flagged the same step as needing clarification, but assigned Assumption 4 as the weakest assumption; my read is that the Theorem 4 proof gap is chronologically and logically prior, since Theorem 4 is the central claim and Corollaries 2 and 3 inherit it. A concrete analytical check can settle the matter: attempt to reproduce the Lipschitz bound under the stated assumptions; if it fails, add the minimal sup-norm or multiplier-boundedness condition and confirm that the quartic-rate theorem then follows. This does not change the verdict from CONDITIONAL; it sharpens one of the conditions the authors must satisfy.","tokens_in":42518,"tokens_out":8579,"duration_ms":85466,"concrete_test":"Independently re-derive the Lipschitz inequality in the proof of Theorem 4 using only Assumption 3(ii). Specifically, test the term ||2 g1(V) (T_hat h1)(Vq) (h1 - h2)(Vh)||_2 for a class H with sup_{h in H} ||h||_2 <= C but not uniformly bounded in L-infinity. Construct g1 and T_hat h1 as unbounded L2 functions and take h1 - h2 = 1_A / ||1_A||_2 on a set A where T_hat h1 is large; if the ratio ||...||_2 / ||h1 - h2||_2 is unbounded, the claimed L-Lipschitz property fails and Lemma 2 cannot be applied. Then re-run the proof of Theorem 4 with the strengthened assumption sup_{h in H} ||h||_infty < C and, for the contraction step, |g1| <= 1, to verify that the stated rate follows; if it does, the concern is resolved by an explicit amendment to Assumption 3.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative claim is Theorem 4, which replaces the quadratic dependence on ||T - T_hat|| in Li et al. (2024) with a quartic dependence, and this bound underlies Corollaries 2 and 3. In the proof of Theorem 4 (Appendix A), the localization argument requires Lemma 2, which needs the loss l(V;h) to be Lipschitz in h with respect to the L2(P0) norm. The displayed verification of Lipschitzness bounds terms such as ||2 g1(V) (T_hat h1)(Vq) (h1 - h2)(Vh)||_2 and ||2 g1(V) h2(Vh) (T_hat(h1 - h2))(Vq)||_2 by C ||h1 - h2||_2. This step is valid only if the multipliers g1, T_hat h1, T_hat h2, and h2 are uniformly bounded in L-infinity, or if some comparably strong product-structure condition holds. Assumption 3(ii) only asserts uniform boundedness of H and R in L2(P0) norm, which does not control such products in L2. The final comparison also invokes 'T is a contraction', which requires a bound on the known function g1 (e.g., |g1| <= 1) that is not stated as a general assumption, even though it holds in the two examples. Without these extra conditions, the empirical-process step leading to the (1/lambda^2) max{delta_n^2, ||T - T_hat||^4, ||T - T_hat||^2 ||r_hat - r0||^2} bound is not justified. Proposition 2's second-order bias statement remains correct as a bias calculation for the projected error of a fixed h, but Theorem 4's rate consequence is the load-bearing bridge to root-n inference, and a repair or a stated strengthening of Assumption 3 is needed before that bridge is secure.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies estimation of the L2-minimal solution h0 of a conditional moment restriction T h = r0, covering nonparametric IV and proximal causal inference as leading examples. It proposes an influence-function-debiased estimator h_hat^IF_{lambda,2} that minimizes a debiased version of the projected squared error plus an iterated Tikhonov penalty. The central claims are: (i) the debiasing induces a second-order bias in the nuisance estimates (Proposition 2); (ii) under a beta-source condition the source error depends on max{delta_n^2, ||T - T_hat||^4, ||T - T_hat||^2 ||r_hat - r0||^2}, replacing the quadratic dependence on ||T - T_hat|| of the non-debiased estimator (Theorem 4 and Remark 1); (iii) a cross-validation procedure for the hyper-parameter has a projected-error oracle bound (Theorem 6) and, under an alpha-error condition, a source-error bound (Theorem 7); and (iv) these rates imply root-n consistency for linear functionals in the parameter class of Ghassami et al. (2022), with an application to proximal causal inference (Corollaries 2-3). The paper contains detailed proofs of the bias calculations and of the rate algebra.","tokens_in":42751,"tokens_out":14848,"duration_ms":135864,"significance":"If the rate claims survive a repair of the localization argument, the paper makes a substantial contribution: it proposes a debiased estimator for ill-posed conditional moment models with second-order bias in both the operator and the r-nuisance, and it quantifies a genuine robustness improvement over Li et al. (2024) in the dependence on the operator estimation error. The influence-function derivation (Theorem 2) and the bias-structure calculation (Proposition 2) are clean and appear correct. The treatment of hyper-parameter selection is also valuable, as the rate loss from not knowing the optimal lambda is rarely analyzed in inverse problems. The root-n conditions in Corollary 2 are concrete and checkable given the rates. However, the central rate theorem currently rests on an unjustified Lipschitz claim, and the cross-validated root-n claim rests on an unverifiable alpha-error condition; both need to be addressed before the main results can be accepted.","major_comments":[{"comment":"The claimed L2-Lipschitz bound for the loss function l(V;h) is not a consequence of Assumption 3. In the displayed verification, terms such as ||2 g1(V)(T_hat h1)(Vq)(h1 - h2)(Vh)||_2 and ||2 g1(V) h2(Vh)(T_hat(h1 - h2))(Vq)||_2 are bounded by a constant times ||h1 - h2||_2 only if the multipliers g1, T_hat h1, and h2 are uniformly bounded in L-infinity; Assumption 3(ii) provides only L2(P0) boundedness, and products of L2 functions are not controlled in L2. The subsequent inequality also drops the term ||T_hat - T|| ||h1 - h2||_2 and invokes \"T is a contraction\", which requires a bound such as |g1| <= 1 that is not stated as a general assumption in Theorem 4. Because Lemma 2 is applied to this l, the empirical-process step leading to the (1/lambda^2) max{delta_n^2, ||T - T_hat||^4, ||T - T_hat||^2 ||r_hat - r0||^2} bound is not justified. The same issue affects the proof of Theorem 3, where Lemma 2 is invoked for the same loss. This is load-bearing for Theorem 4 and, through it, for Corollaries 2 and 3.","section":"Sec. 3.1 and Appendix A, proof of Theorem 4 (also Theorem 3)"},{"comment":"The variance bound in the proof of Theorem 6 is derived by expanding E[(l(h*,eta_hat) - l(h*,eta0) - l(h,eta_hat) + l(h,eta0))^2] into products such as 2 g1(V) h*(Vh)((T_hat - T)h*)(Vq) and 2 g0(V)((T - T_hat)(h* - h))(Vq), and then asserting the expectation is O(||T - T_hat||^2 ||h - h*||_2^2 + ||r0 - r_hat||_2^2 ||h - h*||_2^2). Bounding the second moments of these products again requires L-infinity bounds on g0, g1, h*, T_hat h*, and r_hat, which Assumption 3 does not provide. Without these bounds, the Bernstein step that yields the log(2M/zeta)/n term is unsupported. Since Theorem 6 is the basis for the hyper-parameter selection guarantee and for Corollary 3, this is a second load-bearing gap that must be repaired, either by strengthening Assumption 3 or by a different argument.","section":"Sec. 3.2 and Appendix A, proof of Theorem 6"},{"comment":"The alpha-error condition is not verifiable from primitive conditions. Remark 8 concedes that a finite alpha is guaranteed only once source-error convergence is already known, so the condition cannot be checked in advance. Theorem 7 and Corollary 3 therefore depend on an assumption whose verification is essentially the source-error convergence that the theorem is meant to establish. The paper should either prove, for its examples, that Assumption 4 holds under the beta-source condition used in Theorems 4-5, or state explicitly that Corollary 3 is a conditional result and does not provide verifiable root-n inference under cross-validated hyper-parameter selection. As written, the cross-validated source-error claim collapses if Assumption 4 fails, leaving only the oracle-lambda results (Theorems 3-5, Corollary 2).","section":"Sec. 3.2, Assumption 4 and Remark 8"}],"minor_comments":[{"comment":"There are several typographical errors: \"in the filed of causal inference\" should be \"in the field of causal inference\", \"Correspondance\" should be \"Correspondence\" in the footnote, and \"underscore the importance\" should be \"underscores the importance\" in the abstract.","section":"Abstract and Introduction"},{"comment":"In the final display of Proposition 2, the term \"||r - r_hat0||_2\" should be \"||r0 - r_hat||_2\" or equivalently \"||r_hat - r0||_2\" for consistency with the rest of the paper.","section":"Proposition 2"},{"comment":"Lemma 2 states that the loss is Lipschitz with respect to the L2(P0) norm, but the proof of Theorem 4 verifies a bound on the L2 norm of the difference l(V;h1) - l(V;h2). The paper should clarify which Lipschitz notion the lemma requires, since the pointwise and L2 versions lead to different sufficient conditions.","section":"Appendix B, Lemma 2"},{"comment":"The sentence \"We assume that the debiasing succeed in the sense that delta_n^2 = Delta_n and delta_{M,n}^2 = Delta_{M,n}\" introduces a strong assumption about the candidate set and the nuisance estimates; this should be stated as an explicit assumption in Theorems 6 and Corollary 1 rather than appearing as an informal remark, because the subsequent oracle bound depends on it.","section":"Sec. 3.2"},{"comment":"The Cauchy-Schwarz step in Example 1 bounds sum_i (mu_i^(n))^alpha <e_n, phi_i>^2 by n^{-alpha/10} (sum_i i^{-6alpha})^{1/2} (sum_i <e_n, phi_i>^4)^{1/2}; the final bound should involve ||e_n||_2^2 rather than ||e_n||_2, so the displayed conclusion \"||e_n||_2 <= n^{alpha/10 - 1/3}\" does not follow as written and the numerical value alpha = 10/3 should be re-derived.","section":"Example 1"},{"comment":"The notation X_1 <= X_2 is defined, but in several displays the paper writes \"<=+\" or \"≲+\" without explanation; please define these symbols or avoid them.","section":"Sec. 3.1, definitions"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely to become a useful contribution if the localization gap is repaired. I recommend requesting a revision that either strengthens Assumption 3 to include L-infinity boundedness of H and R and a contraction-type bound on T, or provides a different proof of the Lipschitz and variance bounds. The comparison with Li et al. (2024) is reasonable in spirit, but Theorem 4's proof must be corrected before the central claim can be accepted. The alpha-error condition should also be clarified as a limitation of the cross-validated results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version. The paper proposes a debiased estimator of the projected error for conditional moment restrictions (NPIV, proximal causal inference), and claims that the source-error rate depends on ||T - T_hat||^4 instead of ||T - T_hat||^2 as in Li et al. 2024. That's a genuinely useful improvement if it holds. The clean part is Proposition 2: the bias of the debiased objective is second-order in the operator and r0 estimation errors, and it's robust to misspecification of r0. Theorem 2's influence function derivation is straightforward and correct.\n\nThe problem is Theorem 4, the bridge to the headline rate. The proof's Lipschitz verification for the loss requires bounding terms like ||g1 (T_hat h1)(h1 - h2)||_2 by C||h1 - h2||_2. That's valid only if g1, T_hat h1, h2 are uniformly bounded in L∞, or a comparable product-structure condition holds. Assumption 3 only gives uniform boundedness in L2. The 'T is a contraction' step also needs a stated |g1| ≤ 1 bound. So the quartic dependence isn't established as written. It's probably fixable by adding L∞ assumptions, but it's a real gap in the central argument.\n\nOther soft spots: Assumption 4 (alpha-error condition) is strong; Remark 8 admits that a finite alpha is only known after source-error convergence, making it hard to verify. The cross-validated source-error results (Theorem 7, Corollary 3) collapse without it. Corollaries 2 and 3, which carry the root-n results, are stated without proofs. And the claim that 'without debiasing, asymptotic normality may not be feasible' is supported only by an extrapolated rate in Example 2, not a lower bound.\n\nOn the plus side, the paper is honest about its limitations, the cross-validation analysis is a nice addition, and the comparison to Li et al. 2024 is explicit. No fitted constants, no circularity. The citations look appropriate. If you work on NPIV or proximal causal inference, the debiased objective is worth knowing about.\n\nVerdict: this is worth a serious referee. The idea is sound and the paper is readable, but Theorem 4 needs a repair or a strengthened assumption, and the missing proofs for Corollaries 2 and 3 should be supplied. I'd send it out, with a referee explicitly asked to check the Lipschitz step and the unsupported corollaries.","headline":"Interesting influence-function debiasing idea for ill-posed regression, but the central rate theorem's proof has a gap that needs fixing before the quartic-rate claim is accepted.","tokens_in":43515,"tokens_out":5013,"would_cite":true,"duration_ms":43624,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62G05","62G20","62G08","65J22"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper shows that debiasing the projected error via its influence function makes the estimator's bias second-order in the nuisances, so slow operator estimation costs only its squared error and root-n inference on linear functionals…","keywords":["ill-posed regression","conditional moment restriction","influence function debiasing","second-order bias","iterative Tikhonov regularization","hyper-parameter selection","nonparametric instrumental variable","proximal causal inference"],"falsifier":"Run a simulation of the nonparametric instrumental variable model with a compact operator whose singular system is known, so the truth is computable. Make the operator estimator converge at a controlled slow rate, say $\\|T-\\widehat T\\|\\asymp n^{-1/4}$, and let $\\widehat r$ converge at a different rate; the theorem predicts the debiased source error contains $\\|T-\\widehat T\\|^4$ while the non-debiased estimator contains $\\|T-\\widehat T\\|^2$. If the observed scaling of $\\|\\widehat h-h_0\\|^2$ with $\\|T-\\widehat T\\|$ at the optimal $\\lambda$ is quadratic rather than quartic, the central second-order-bias claim is falsified.","tokens_in":42101,"feed_emoji":"📐","tokens_out":10654,"duration_ms":94989,"temperature":0.7,"pith_summary":"The paper studies estimation of a function $h_0$ that solves a conditional moment restriction, an ill-posed inverse problem covering nonparametric instrumental variables and proximal causal inference. The standard approach minimizes an estimated projected mean-squared error; the paper shows this is fragile because the operator estimate enters linearly. It constructs a new objective by adding the influence-function debiasing term of the projected error, which makes the bias second-order in the nuisance estimators. The central result is a finite-sample bound in which the cost of operator-estimation error is the fourth power of $\\|T - \\widehat T\\|$ rather than its square, with a robustness guarantee: misspecifying one of the two nuisance functions costs no more than reverting to the undebiased rate. It then provides a cross-validated choice of the regularization parameter and proves that, under an additional smoothness condition, the resulting estimator is accurate enough for root-n inference on linear functionals such as counterfactual means.","feed_headline":"Debiased estimator squares operator error in ill-posed regression","feed_subtitle":"One influence-function debiasing term lets slow or wrong nuisance fits still yield root-n inference on functionals.","key_machinery":"The central object is the influence function of the projected error functional $\\psi(h)=E[(E[g_1(V)h(V_h)|V_q]-g_0(V))^2]$, derived in Theorem 2. The estimator augments the squared projected residual with the debiasing cross term $2\\{(\\widehat T h)(V_q)-\\widehat r(V_q)\\}\\{g_1(V)h(V_h)-(\\widehat T h)(V_q)\\}$, which cancels the first-order nuisance bias. The debiased loss is minimized with two-step iterative Tikhonov regularization, and the analysis combines the second-order bias identity of Proposition 2, localized Rademacher complexity bounds for empirical-process terms, the $\\beta$-source condition for regularization bias, and the $\\alpha$-error condition that converts projected-error bounds into source-error bounds by interpolation in a common basis.","core_discovery":"The paper's central claim is that the $L^2$-minimal solution of the integral equation $T h = r_0$ can be estimated by minimizing a debiased version of the projected error, and that the debiasing fully exploits the structure of the influence function. Concretely, Theorem 4 asserts that with two-step iterative Tikhonov regularization and under the $\\beta$-source condition, the source error of the debiased estimator is bounded by $(1/\\lambda^2)\\max\\{\\delta_n^2, \\|T - \\widehat T\\|^4, \\|T - \\widehat T\\|^2\\|\\widehat r - r_0\\|^2\\} + \\lambda^{\\min\\{4,\\beta\\}}$, and choosing $\\lambda$ optimally yields source error of order $\\Delta_n^{\\min\\{3,\\beta\\}/\\min\\{5,\\beta+2\\}}$. This is the quartic-in-operator-error improvement over the quadratic dependence of the non-debiased estimator. For hyper-parameter selection, the paper claims that a cross-validated choice of $\\lambda$ over a fine grid attains the oracle projected-error rate up to terms that vanish as candidate functions converge, and that under the $\\alpha$-error condition the source error is bounded by a power of the projected error. Finally, for the regular parameter class whose influence functions are products of the two nuisance solutions, the paper claims root-n consistent and asymptotically normal estimation with nonparametric nuisance rates, including for counterfactual means under proximal causal inference.","pith_inferences":["A natural extension is to test whether the quartic dependence on $\\|\\widehat T-T\\|$ persists when the debiasing nuisance $\\widehat r$ is estimated on the same fold, since the analysis assumes separate folds for candidates and nuisances.","The two-layer debiasing template of debiasing the loss for the nuisance and then debiasing the final functional could transfer to other inverse problems, such as density deconvolution or imaging problems where the operator is estimated at slow nonparametric rates.","Because a finite $\\alpha$ in the $\\alpha$-error condition can only be certified after convergence is known, practitioners should treat the cross-validated source-error rate as a heuristic; the oracle-$\\lambda$ results remain the guaranteed ones.","Increasing the number of Tikhonov iterations would replace $\\lambda^{\\min\\{4,\\beta\\}}$ by $\\lambda^\\beta$ at the price of an exponential constant, so benchmarking two-step versus many-step debiasing on simulated data would clarify whether the qualification-limited term binds in realistic sample sizes."],"forward_implications":["With the debiased estimator, the source-error bound depends on $\\|\\widehat T-T\\|^4$ instead of $\\|\\widehat T-T\\|^2$, so a slowly converging operator estimator no longer dominates the rate.","If the debiasing nuisance $\\widehat r$ is misspecified, the error bound degrades at most to that of the non-debiased estimator, making the procedure robust to one misspecified nuisance.","Cross-validated hyper-parameter selection over a fine grid preserves the oracle rates whenever the oracle variance terms dominate; any rate loss comes only from approximation terms that vanish as candidate functions converge.","For linear functionals of solutions, root-n consistency and asymptotic normality hold with nonparametric convergence rates for all nuisance estimators, provided the product of their projected errors is $o_p(n^{-1/2})$.","In the proximal causal inference illustration, this yields root-n inference for counterfactual means using only nonparametric bridge-function estimators, where the undebiased alternative would demand faster-than-parametric rates."],"supporting_citations":[{"why":"Supplies the baseline non-debiased estimator whose quadratic-in-operator-error rate the debiased bound improves upon.","marker":"Li et al. (2024)"},{"why":"Introduces the parameter class and the mixed-bias identity used in Section 4 for root-n inference.","marker":"Ghassami et al. (2022)"},{"why":"Provides the localized concentration inequality used in the proofs of the finite-sample rate theorems.","marker":"Foster and Syrgkanis (2019)"},{"why":"Gives the regularization-bias bounds under the beta-source condition used in Lemma 1.","marker":"Carrasco et al. (2007)"},{"why":"Supplies localized Rademacher complexity and critical-radius machinery used throughout the convergence analysis.","marker":"Wainwright (2019)"},{"why":"Provides the oracle inequalities for cross-validation used in the hyper-parameter selection analysis.","marker":"van der Vaart et al. (2006)"},{"why":"Supports the alpha-error condition and the Jensen-interpolation step converting projected error into source error.","marker":"Florens et al. (2011)"},{"why":"Supplies the iterative Tikhonov regularization theory behind the qualification analysis.","marker":"Engl et al. (1996)"}],"fun_headline_variants":["Debiased ill-posed regression squares operator error","Root-n functionals from debiased conditional moment fits","Cross-validated debiasing for conditional moment estimators","Second-order bias? Debiased estimator makes it robust"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The cross-validated source-error guarantee and the root-n functional results rest on Assumption 4, which requires every candidate error to be uniformly smooth in one common basis with a single unknown constant $\\alpha$ that cannot be verified before one already knows the error converges.","fun_headline_variants_meta":{"raw":{"variants":["Debiased ill-posed regression squares operator error","Root-n functionals from debiased conditional moment fits","Cross-validated debiasing for conditional moment estimators","Second-order bias? Debiased estimator makes it robust"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000276,"raw_usage":{"total_tokens":1733,"prompt_tokens":1118,"completion_tokens":615,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":734,"completion_tokens_details":{"reasoning_tokens":550}},"tokens_in":734,"tokens_out":615,"duration_ms":6413,"temperature":1.0,"reasoning_tokens":550,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:49:20.170180+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a simulation of the nonparametric instrumental variable model with a compact operator whose singular system is known, so the truth is computable. Make the operator estimator converge at a controlled slow rate, say $\\|T-\\widehat T\\|\\asymp n^{-1/4}$, and let $\\widehat r$ converge at a different rate; the theorem predicts the debiased source error contains $\\|T-\\widehat T\\|^4$ while the non-debiased estimator contains $\\|T-\\widehat T\\|^2$. If the observed scaling of $\\|\\widehat h-h_0\\|^2$ with $\\|T-\\widehat T\\|$ at the optimal $\\lambda$ is quadratic rather than quartic, the central second-order-bias claim is falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the parameter class and the mixed-bias identity used in Section 4 for root-n inference."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies localized Rademacher complexity and critical-radius machinery used throughout the convergence analysis."},{"cited_title":"W., Dudoit, S., and van der Laan, M","cited_arxiv_id":null,"evidence_quote":"Provides the oracle inequalities for cross-validation used in the hyper-parameter selection analysis."},{"cited_title":"W., Hanke, M., and Neubauer, A","cited_arxiv_id":null,"evidence_quote":"Supplies the iterative Tikhonov regularization theory behind the qualification analysis."}],"review_version":1}