{"id":"4895f66c-c4a7-4e8a-8e0f-be4a4c59131b","arxiv_id":"2506.06861","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"New differentially private iterative hard thresholding algorithms for high-dimensional sparse linear regression with heavy-tailed responses, with a claimed bound for the l1 variant that does not depend on the tail index.","lead":"This paper proposes two differentially private algorithms for sparse linear regression when the response has heavy-tailed noise with only a bounded (1+ζ)-th moment, a case standard DP regression methods do not cover. If the bounds hold, the second algorithm's error does not grow as the tails get heavier, which would help privacy-preserving analysis of biomedical and financial data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proof of Theorem 5 rests on a false gradient-norm bound: with K-clipped features, ||G_t||_2 can be K√d ≫ n c_u^{1/2} when d≫n, so the contraction argument in Theorem 4 collapses and the ζ-independent O((s*)^{3/2} log d/(nε)) bound is unsupported.","rationale":"The reader correctly rejects the paper, but the single most load-bearing defect is not the privacy accounting. The algorithms split data into disjoint chunks and each iteration uses only its own chunk; standard parallel composition (plus post-processing for later rounds) can make the whole procedure (ε,δ)-DP even if the proof in Appendix A is imprecise. The decisive problem is in the utility proof of the headline ζ-independent result. Appendix D's proof of Theorem 4 relies on ||G_t||_2 ≤ n c_u^{1/2}, where G_t is the subgradient used in the update. For the algorithm's own clipped features, each coordinate of G_t is bounded by K=O(log d), so the ℓ2 norm is at most K√d. In the high-dimensional regime d≫n this bound is incomparably larger than n√c_u, and the step-size choice that the proof uses to guarantee contraction is invalid. The same false norm bound supports both phases of Theorem 4 and therefore the global error rate of Theorem 5. A correct analysis would need a step size smaller by roughly a factor of K√d/n, which in turn would inflate the Peeling noise and destroy the claimed logarithmic dependence on d. Hence the central contribution is unsupported by the proof as written, and the REJECT verdict is appropriate. I mark agreement as 'disagree' because the reader's identified weakest assumption (adaptive composition of full-budget Peeling rounds) is not the actual fatal flaw: the paper's data-splitting structure makes that concern addressable, whereas the gradient-norm error is not.","tokens_in":22814,"tokens_out":15996,"duration_ms":181557,"concrete_test":"Independently recompute the Phase One contraction inequality in Appendix D with the bound ||G_t||_2 ≤ K√d implied by Algorithm 3's clipping, instead of ||G_t||_2 ≤ n c_u^{1/2}. Instantiate d=n^2, K=log n, and the stated step size η_t ≈ D_t/n; verify that the quadratic term η_t^2||G_t||_2^2 exceeds the linear decrease term, so the displayed induction step fails. Then check whether any step size small enough to restore contraction keeps the Peeling noise scale λ=2ηK/(n/T) small enough to preserve the claimed logarithmic-in-d error; if not, Theorem 5 cannot hold as stated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central ζ-independent bound (Theorem 5) depends on Theorem 4, whose proof in Appendix D asserts: 'By Lemma 1 in [38], there exists a constant c_l > 0 such that f(β_t)−f(β*) ≥ n/4 c_l^{1/2} ||β_t−β*||_2, and, moreover, ||G_t||_2 ≤ n c_u^{1/2}.' This gradient-norm bound is false for Algorithm 3. The algorithm clips each covariate coordinate to K=O(log d), so every entry of G_t = (1/|D_t|)∑_{i∈D_t} sign(\\tilde x_i^T β_t − y_i)\\tilde x_i is bounded by K, giving ||G_t||_2 ≤ K√d by triangle inequality. In the regime d≫n, e.g., d=n^2 and K=log n, this is ||G_t||_2 ≤ n log n, which is not O(n c_u^{1/2}). The proof uses the asserted bound to select η_t ∈ n^{−1}√(c_l/c_u)[D_t/8, 3D_t/8] and to argue that the quadratic term η_t^2||G_t||_2^2 is dominated by the negative linear term in the displayed contraction inequality. With the correct bound, the quadratic term is approximately D_t^2 K^2 d/n^2 and, for d≫ n^2/K^2, it swamps the decrease term, so the Phase One contraction cannot be concluded. Phase Two inherits the same norm bound, so the two-phase convergence proof fails. Thus Theorem 5's Õ((s*)^{3/2} log d/(nε)) guarantee does not follow from the supplied analysis. This is an internal inconsistency, not merely a disagreement with prior work. The reader's privacy-composition concern is secondary: because each round uses a fresh disjoint data chunk and later rounds are post-processing of earlier outputs, the (ε,δ) claim can likely be repaired by a parallel-composition argument; the false gradient bound cannot be repaired without changing the rate.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies differentially private sparse linear regression under heavy-tailed responses, assuming sub-Gaussian features and responses with only a finite (1+ζ)-th moment. It proposes two iterative hard-thresholding algorithms: DP-IHT-H, which uses a Huber loss and claims an estimation error of order Õ(√s* (log d/n)^{ζ/(1+ζ)} + (s*)^{(1+2ζ)/(2+2ζ)} (log^2 d/(nε))^{ζ/(1+ζ)}), and DP-IHT-L, which uses an ℓ1 loss with clipped features and claims a ζ-independent bound of order Õ((s*)^{3/2} log d/(nε)) under an additional local Bernstein condition on the noise density. The paper also reports synthetic and real-data experiments comparing the methods with DP-SLR and non-private adaHuber.","tokens_in":23333,"tokens_out":9696,"duration_ms":104789,"significance":"If the theorems were correct, the paper would be a meaningful step: it targets a realistic heavy-tailed regime in high-dimensional sparse linear regression, and the ζ-independent rate for DP-IHT-L would match the best known sub-Gaussian-rate dependence on n and ε. The algorithmic design (clipping, data splitting, Peeling-based sparse selection) is natural and the experiments are relevant. However, the paper's central proofs contain load-bearing gaps, including a false gradient-norm bound in the proof of Theorem 4 and an incorrect privacy composition argument in Appendix A, so the advertised guarantees are not established by the manuscript as written.","major_comments":[{"comment":"The proof asserts, by reference to 'Lemma 1 in [38]', that f(β_t)−f(β*) ≥ (n/4)c_l^{1/2}||β_t−β*||_2 and moreover ||G_t||_2 ≤ n c_u^{1/2}. The second bound is false for Algorithm 3. Because every feature coordinate is clipped to |\\tilde x_{i,j}| ≤ K, the subgradient G_t (either the sum or the normalized average used in the update) satisfies a triangle-inequality bound of the form ||G_t||_2 ≤ |D_t| K √d (or K√d after normalization), which is dimension-dependent and can exceed n√c_u by a large factor when d≫n, e.g., d=n^2 and K=log d. The subsequent step-size choice η_t ∈ n^{−1}√(c_l/c_u)[D_t/8, 3D_t/8] is derived from the false bound, and the quadratic term η_t^2||G_t||_2^2 is not shown to be dominated by the negative linear term. Consequently the two-phase contraction in Theorem 4, and therefore the ζ-independent rate in Theorem 5, do not follow from the supplied analysis.","section":"Appendix D (proof of Theorem 4)"},{"comment":"The privacy proof states that each iteration of the algorithm is (ε,δ)-DP because the Peeling step is (ε,δ)-DP and the per-iteration influence of one sample is bounded, and then concludes that the entire procedure is (ε,δ)-DP. This is not a valid composition argument: applying a mechanism with budget (ε,δ) in each of T adaptive iterations would only yield (Tε,Tδ)-DP under standard sequential composition. A parallel-composition argument could repair the claim because the T rounds use disjoint data chunks, and for a neighboring dataset differing in one record only one chunk changes; however, that argument is not supplied, and the fact that the iterate β_t carries information from earlier chunks through the adaptively chosen inputs to later Peeling steps must be handled explicitly.","section":"Appendix A (proofs of Theorems 1 and 3)"},{"comment":"The proof of Lemma 6 invokes 'a lemma from Lemma A.4[?]' to assert ||g^t_{S_t∪S*}||_2^2 − (c_l^2/4)||\\hat β − β^t||_2^2 ≥ (c_l/2)(L_n(β^t) − L_n(\\hat β)). This referenced lemma is not stated or proved anywhere in the manuscript; the placeholder '[?]' explicitly marks it as missing. Since Lemma 6 is the contraction result underlying Theorem 2, the proof of Theorem 2 is incomplete. The same proof also uses undefined notation (e.g., 'I†' in the display after Eq. (3)) and refers to 'Lemma 8.3 and Theorem 4.4 in [41]' without stating the content needed for the argument.","section":"Appendix B (Lemma 6 and proof of Theorem 2)"},{"comment":"The displayed identity G_t = Σ_{i∈D_t} sign(x_i^T β_t − y_i) \\tilde x_i = Σ_{i∈D_t} sign(x_i^T(β_t−β*)) \\tilde x_i − Σ_{i∈D_t} sign(x_i^T ε_i) \\tilde x_i is incorrect in general, because sign(a−b) is not equal to sign(a)−sign(b). This decomposition is used to motivate the two-regime analysis for the ℓ1-loss algorithm, so it should either be replaced by a correct inequality or the proof should be rewritten not to rely on the displayed equality.","section":"Section 5 (display after Assumption 3)"}],"minor_comments":[{"comment":"The final displayed bound in the proof is O((s*)^{3/2} log d (log(1/δ))^{1/2} log(T/n) / ((T/n)ε)), whereas Theorem 5 states O((s*)^{3/2} log d (log(1/δ))^{1/2} log n / (nε)). For T=O(log n), log(T/n) is negative, so the expression in the proof is not even positive; the discrepancy needs to be resolved for the claimed rate to be transparent.","section":"Appendix E (proof of Theorem 5)"},{"comment":"The proof refers to an event E3 and a parameter σ that are not defined in the manuscript; the statement of Theorem 2 uses log(1/δ), while the proof uses log(1/σ). These symbols should be defined and used consistently.","section":"Appendix C (proof of Theorem 2)"},{"comment":"The claim that Assumption 3 is 'quite relaxed' is overstated: the lower bound h_ε(x) ≥ 1/b_0 on an interval around zero excludes densities that vanish near zero, and the upper bound h_ε(x) ≤ 1/b_1 excludes densities with unbounded peaks at zero. The authors should state more precisely which heavy-tailed families are covered.","section":"Assumption 3 and its remark"},{"comment":"The sparsity settings are inconsistent across the paper: Theorem 2 uses s=O(s*), while the proof of Lemma 6 requires s=72(c_u/c_l)^2 s*, and Theorem 4 states s=Ω((c_u/c_l)^8(b_0/b_1)^8 s*). The constants should be reconciled.","section":"Theorem 2 and Theorem 4 constants"},{"comment":"There are numerous typos, including 'adaHuher' instead of 'adaHuber' in Section 6.1, 'imcomparable' instead of 'incomparable' in Section 5, and 'as ϵ decrease' in the caption of Figure 2d.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The manuscript contains multiple explicit proof gaps (a missing 'Lemma A.4[?]', undefined events E3 and σ, and a false gradient-norm bound in the proof of Theorem 4). The ζ-independent claim in Theorem 5 is the paper's headline contribution, and it is not supported by the submitted analysis. The privacy proof can likely be repaired with a parallel-composition argument, but the convergence proof would require substantial new ideas to control the dimension-dependent gradient norm after clipping. I recommend rejection, with encouragement to the authors to resubmit a fully revised version if the results can be established rigorously."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe short version: this is a serious attempt at a real gap—differentially private sparse linear regression when the response has only a finite (1+ζ)-th moment—and the DP-IHT-H half may be salvageable. Do not trust the advertised ζ-independent DP-IHT-L rate as written; the proof of the key contraction theorem uses a gradient-norm bound that is false for the algorithm it analyzes.\n\nWhat is new: the paper is the first to treat (1+ζ)-moment heavy-tailed responses in high-dimensional sparse DP regression, and the specific pairing of private Peeling with Huber and ℓ1 losses is not in the cited literature. The DP-IHT-H bound has the right shape—logarithmic dimension dependence, a non-private statistical term and a DP noise term. The experiments are basic but sensible: they compare against DP-SLR and adaHuber and show the robust losses help under heavy tails.\n\nThe soft spots are not minor. In Theorem 4’s proof, the authors invoke Lemma 1 of [38] for the bound ||G_t||_2 ≤ n c_u^{1/2}. But Algorithm 3 clips every feature to K, so each coordinate of the subgradient is O(K) and the Euclidean norm can be K√d, which for d ≫ n is far larger than n c_u^{1/2}. The step-size selection then fails: the quadratic term η_t^2 ||G_t||_2^2 can swamp the linear decrease, so the Phase One contraction, and the final O((s*)^{3/2} log d/(nε)) bound in Theorem 5, do not follow from the supplied analysis. This is an internal inconsistency, not just a missing detail.\n\nThere are also local gaps that are repairable. The privacy proof in Appendix A asserts per-round (ε,δ)-DP with the full budget and no composition argument, but because each round uses a disjoint data chunk, a parallel-composition argument should fix it. Lemma 6 depends on a nonexistent 'Lemma A.4[?]', and the step-size choice in Theorem 4 uses the contraction rate being proved. None of these are fatal once noticed; the gradient-norm issue is.\n\nWho gets value from this? A specialist in private high-dimensional estimation can mine the DP-IHT-H construction and the comparison with [10,21,38,41]. A general reader should not take the ζ-independent claim as established. If I were the editor, I would send it to a careful referee—the problem is important enough and the DP-IHT-H part is plausible enough to merit expert scrutiny—but I would expect major revision or removal of the DP-IHT-L theorem.","headline":"A serious attempt at a real gap, but the advertised ζ-independent DP-IHT-L rate rests on a false gradient-norm bound and should not be trusted as written.","tokens_in":23863,"tokens_out":6395,"would_cite":false,"duration_ms":65357,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62J07","68P27","62F35"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper establishes $(\\varepsilon,\\delta)$-DP sparse linear regression under heavy-tailed responses, achieving rates $\\tilde{O}\\big((s^*)^{1/2}(\\log d/n)^{\\zeta/(1+\\zeta)} + (s^*)^{(1+2\\zeta)/(2+2\\zeta)}(\\log^2…","keywords":["differential privacy","sparse linear regression","heavy-tailed data","iterative hard thresholding","Huber loss","l1 loss","Peeling mechanism","finite moments"],"falsifier":"Run DP-IHT-L for $T=O(\\log n)$ rounds on a fixed heavy-tailed dataset with $\\varepsilon=0.5$, $\\delta=1/n^{1.1}$, and track the realized privacy loss of the $T$ adaptive Laplace mechanisms (e.g., via R\\'{e}nyi composition). Standard composition predicts a total budget near $T\\varepsilon$, so if the realized privacy parameter exceeds $(\\varepsilon,\\delta)$ as $T$ grows, the paper's claim that the algorithm is $(\\varepsilon,\\delta)$-DP, and hence the stated rate, is falsified.","tokens_in":22588,"feed_emoji":"🔒","tokens_out":11655,"duration_ms":106879,"temperature":0.7,"pith_summary":"The paper asks whether high-dimensional sparse linear regression can be made differentially private when the response variable has only a finite $(1+\\zeta)$-th moment, so its distribution can be heavy-tailed. It claims yes, and proposes two iterative hard-thresholding algorithms: DP-IHT-H, which uses the Huber loss, and DP-IHT-L, which uses the $\\ell^1$ loss. For general heavy-tailed responses, DP-IHT-H is shown to achieve error $O\\big((s^*)^{1/2}(\\log d/n)^{\\zeta/(1+\\zeta)} + (s^*)^{(1+2\\zeta)/(2+2\\zeta)}(\\log^2 d\\,\\log(1/\\delta)/(n\\varepsilon))^{\\zeta/(1+\\zeta)}\\big)$ under $(\\varepsilon,\\delta)$-DP. Under an additional mild condition on the noise density, DP-IHT-L achieves $O\\big((s^*)^{3/2}\\log d\\,\\sqrt{\\log(1/\\delta)}\\log n/(n\\varepsilon)\\big)$, a rate independent of $\\zeta$ and matching the best known rate for sub-Gaussian responses. If correct, these are the first such high-dimensional sparse DP regression bounds under only a finite $(1+\\zeta)$-th moment.","feed_headline":"DP sparse regression keeps log-d error under heavy tails","feed_subtitle":"Two iterative-hard-thresholding algorithms reach log-d error; one rate is free of the tail parameter ζ.","key_machinery":"The load-bearing mechanism is the combination of feature clipping, a robust loss with bounded gradient, and the private Peeling procedure (Algorithm 2), a coordinate-selection routine that adds Laplace noise before and after choosing the $s$ largest-magnitude entries so that the support itself is protected. Clipping each feature coordinate to $O(\\log d)$ keeps the gradient's $\\ell_\\infty$-sensitivity at $\\tau K/m$, so the Peeling noise scale is $\\lambda\\sqrt{s\\log(1/\\delta)}/\\varepsilon$ rather than something polynomial in $d$. Restricted strong convexity and smoothness of the robust losses drive the IHT contraction, and for DP-IHT-L the proof splits the sub-gradient into a large-deviation regime (fast geometric convergence) and a small-deviation regime (linear contraction dominated by the noise term). The resulting two-phase argument produces the final $\\ell_2$-error bound.","core_discovery":"The paper's central claim is that differential privacy is compatible with heavy-tailed high-dimensional sparse linear regression, provided the estimation procedure is robustified by a bounded-gradient loss and a coordinate-selection step whose sensitivity does not scale with the dimension. The first theorem states that DP-IHT-H, using clipped features, a tuned Huber parameter, and the private Peeling selection, is $(\\varepsilon,\\delta)$-DP and yields $\\|\\beta_T-\\beta^*\\|_2 = O\\big((s^*)^{1/2}(\\log d/n)^{\\zeta/(1+\\zeta)} + (s^*)^{(1+2\\zeta)/(2+2\\zeta)}(\\log^2 d\\,\\log(1/\\delta)/(n\\varepsilon))^{\\zeta/(1+\\zeta)}\\big)$. The second central result states that under Assumption 3, which imposes a local Bernstein lower bound and a uniform upper bound on the noise density, DP-IHT-L achieves $\\|\\beta_T-\\beta^*\\|_2 = O\\big((s^*)^{3/2}\\log d\\,(\\log(1/\\delta))^{1/2}\\log n/(n\\varepsilon)\\big)$, independent of the tail parameter $\\zeta$. The paper positions these as the first bounds of their kind for the case where the response only has a bounded $(1+\\zeta)$-th moment with $\\zeta\\in(0,1]$, and supports the theory with experiments on synthetic and genomic data.","pith_inferences":["The $(\\varepsilon,\\delta)$ guarantee as stated rests on composing $T$ full-budget Peeling runs across adaptive rounds; standard adaptive composition would predict a total budget near $(T\\varepsilon,T\\delta)$, so the advertised rates depend on that composition premise holding.","A clean falsification experiment for the $\\zeta$-independence claim: run DP-IHT-L on noise whose density violates Assumption 3 (e.g., vanishing near zero) but which still has a finite $(1+\\zeta)$-th moment; the theory predicts a degraded, $\\zeta$-dependent rate.","The feature-clipping-plus-Peeling recipe could plausibly extend to other sparse $M$-estimators (e.g., logistic or quantile regression) under heavy-tailed responses, a direction the paper does not explore.","On the real-data benchmark the unknown $\\beta^*$ is approximated by the non-private adaHuber fit; a held-out prediction-error comparison would provide a more neutral evaluation of the DP estimators."],"forward_implications":["Sparse DP regression becomes feasible in $d\\gg n$ settings with heavy-tailed responses, because both error bounds scale as $\\mathrm{poly}(s^*)\\log d$ times a privacy term rather than polynomially in $d$.","With Assumption 3, DP-IHT-L's rate $\\tilde{O}((s^*)^{3/2}\\log d/(n\\varepsilon))$ holds for every $\\zeta\\in(0,1]$, so practitioners do not need to know the tail parameter to deploy the $\\ell^1$-loss version.","The Huber-based bound separates statistical and privacy costs: the first term is the optimal non-private rate, and when $\\zeta=1$ the privacy term becomes $\\tilde{O}((s^*)^{3/4}\\log d/\\sqrt{n\\varepsilon})$, better in sparsity than the $\\ell^1$-loss rate.","For finite $(1+\\zeta)$-th moments with small $\\zeta$, both algorithms should beat DP estimators built for sub-Gaussian or bounded data, matching the paper's synthetic and genomic experiments."],"supporting_citations":[{"why":"Supplies the private Peeling procedure and its contractivity lemmas, the core DP selection tool used in both algorithms.","marker":"[10]"},{"why":"Provides the non-private adaptive Huber estimator and restricted-strong-convexity lemmas that give DP-IHT-H its statistical baseline.","marker":"[41]"},{"why":"Supplies the sub-gradient analysis and two-phase convergence argument for $\\ell^1$-loss high-dimensional regression that DP-IHT-L privatizes.","marker":"[38]"},{"why":"Gives the best prior DP bound for heavy-tailed responses with finite second moment, the baseline that DP-IHT-L's $\\zeta$-free rate is compared against.","marker":"[21]"},{"why":"Names the local Bernstein condition that Assumption 3 invokes to keep the noise density under control.","marker":"[2]"}],"fun_headline_variants":["DP linear regression tames heavy tails in high dimension","Heavy-tailed DP regression: error independent of tail weight","Two private IHT algorithms beat regular-data DP baselines","Tail-agnostic DP rate for sparse linear regression"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The privacy guarantee depends on the premise that $T$ rounds of the full-budget $(\\varepsilon,\\delta)$ Peeling run on disjoint data chunks, with iterates shared across rounds, still compose to an overall $(\\varepsilon,\\delta)$-DP mechanism; standard composition would give roughly $(T\\varepsilon,T\\delta)$.","fun_headline_variants_meta":{"raw":{"variants":["DP linear regression tames heavy tails in high dimension","Heavy-tailed DP regression: error independent of tail weight","Two private IHT algorithms beat regular-data DP baselines","Tail-agnostic DP rate for sparse linear regression"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000209,"raw_usage":{"total_tokens":1517,"prompt_tokens":1166,"completion_tokens":351,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":782,"completion_tokens_details":{"reasoning_tokens":286}},"tokens_in":782,"tokens_out":351,"duration_ms":3785,"temperature":1.0,"reasoning_tokens":286,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T05:48:36.093656+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run DP-IHT-L for $T=O(\\log n)$ rounds on a fixed heavy-tailed dataset with $\\varepsilon=0.5$, $\\delta=1/n^{1.1}$, and track the realized privacy loss of the $T$ adaptive Laplace mechanisms (e.g., via R\\'{e}nyi composition). Standard composition predicts a total budget near $T\\varepsilon$, so if the realized privacy parameter exceeds $(\\varepsilon,\\delta)$ as $T$ grows, the paper's claim that the algorithm is $(\\varepsilon,\\delta)$-DP, and hence the stated rate, is falsified.","supporting_citations":[{"cited_title":"The Annals of Statistics49(5), 2825–2850 (2021)","cited_arxiv_id":null,"evidence_quote":"Supplies the private Peeling procedure and its contractivity lemmas, the core DP selection tool used in both algorithms."},{"cited_title":"Journal of the American Statistical Association115(529), 254–265 (2020)","cited_arxiv_id":null,"evidence_quote":"Provides the non-private adaptive Huber estimator and restricted-strong-convexity lemmas that give DP-IHT-H its statistical baseline."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the sub-gradient analysis and two-phase convergence argument for $\\ell^1$-loss high-dimensional regression that DP-IHT-L privatizes."},{"cited_title":"In: Proceedings of the 41st ACM SIGMOD- SIGACT-SIGAI Symposium on Principles of Database Systems (PODS ’22)","cited_arxiv_id":null,"evidence_quote":"Gives the best prior DP bound for heavy-tailed responses with finite second moment, the baseline that DP-IHT-L's $\\zeta$-free rate is compared against."},{"cited_title":"The Annals of Statistics 47(4), 2117–2144 (2019)","cited_arxiv_id":null,"evidence_quote":"Names the local Bernstein condition that Assumption 3 invokes to keep the noise density under control."}],"review_version":1}