Pith. sign in

REVIEW 3 major objections 7 minor 69 references

Locally Private Online Quantile Regression: Estimation and Inference

T0 review · 3 major / 7 minor · reviewed 2026-07-07 · glm-5.2

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read One private report per user suffices for online quantile regression

desk verdict Solid LDP online QR paper with clean channel design; proofs deferred but argument appears sound read the letter →

arxiv 2607.05312 v1 pith:YOHOZ5UB submitted 2026-07-06 stat.ML stat.ME

Yi Liu , Qirui Hu This is my paper
classification stat.MLstat.ME
keywords onlineinferencelocallyprivatechannelcontributiondecoderestimating-equation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tackles a specific obstruction in locally private statistics: quantile regression's update rule couples covariates with a residual comparison, so a server receiving only privatized reports cannot form the usual online update. The authors resolve this by constructing the CQX(q,s) channel, a finite-alphabet mechanism where each user locally computes their estimating-equation contribution, stochastically quantizes selected coordinates on a public grid, applies randomized response to produce a single private report, and the server applies an affine decoder plus Horvitz-Thompson reconstruction to recover an input with the correct conditional mean. The key property is conditional unbiasedness: the decoded input has the same expectation as the true estimating-equation contribution, even though the privatized report satisfies epsilon-local differential privacy. This separation between privacy (a property of the report) and estimation (post-processing of the decoded trajectory) is what makes the framework work. The authors prove that the resulting Polyak-Ruppert averaged estimator is consistent and asymptotically normal, with a covariance that reflects both sampling variability and the additional noise injected by the privacy channel. They also provide three Hessian-free inference procedures (self-normalization, divide-and-conquer, and hierarchical grouping) that produce confidence intervals and ellipsoids from the decoded private trajectory alone, without requiring additional private reports or density estimation. Simulations and a New York City taxi-trip illustration show the private estimator approaches the nonprivate benchmark as the privacy budget grows and outperforms direct Laplace and face-exponential geometric releases across the tested regimes.

What carries the argument

The CQX(q,s) channel combines: (1) the two-face support geometry of QR estimating equations, where g_beta lives on {-tau} x [-tau,tau]^p or {1-tau} x [-(1-tau),1-tau]^p; (2) adjacent-grid stochastic rounding of selected slope coordinates to a finite grid A_q, producing a latent category with correct conditional mean; (3) randomized response on the block alphabet of size K_B, privatizing one categorical report per user; (4) an affine decoder using the contraction factor kappa_rr(K_B, epsilon) = (e^epsilon - 1)/(e^epsilon + K_B - 1) to invert the randomized-response shrinkage; (5) Horvitz-Thompson reconstruction with inclusion probability pi_j = s/(p+1) to recover the full vector from the dec

What would settle it

If the local stability condition (Condition 2) fails for some finite channel design—meaning the expected squared difference of decoded inputs at two nearby beta values is not bounded by a constant times the distance between them—then the martingale-difference decomposition and the linearization m(beta) = H(beta - beta*) + O(||beta - beta*||^2) do not yield the Polyak-Ruppert representation, and both the consistency and asymptotic normality results would not hold. A concrete falsifier would be a channel design where the decoded range is finite but the affine decoder amplifies randomized-

Watch

Extended reading notes

Core claim

The central object is the CQX(q,s) channel, which exploits the two-face support geometry of the quantile-regression estimating-equation contribution. The contribution g_beta(X,Y) = X * (1(Y <= X'beta) - tau) takes values on one of two faces determined by the residual comparison. The channel uses this structure: the intercept coordinate identifies the active face, selected slope coordinates are stochastically quantized on a public grid, and the entire block is privatized via randomized response on a finite alphabet. An affine decoder inverts the randomized-response contraction and Horvitz-Thompson reconstruction recovers the full vector. The result is a decoded input that is conditionally an无

Load-bearing premise

The local stability condition requires that decoded inputs at two nearby query points differ in expectation by an amount proportional to the distance between the query points. The paper states this follows from the finite decoded range and the probability that a record falls between two nearby quantile-regression hyperplanes, but the detailed verification is deferred to a supplementary proof document. This condition is the bridge between the channel construction and the mart

Editorial extensions

If this is right

  • The framework separates privacy guarantees (a property of the report) from statistical estimation (post-processing of decoded outputs), which means any future improvement in finite-alphabet LDP channel design could plug into the same stochastic-approximation theory without changing the consistency or asymptotic normality proofs.
  • The Hessian-free inference procedures (self-normalization, divide-and-conquer, HiGrad) are all post-processing of the decoded trajectory, so they inherit the privacy guarantee automatically and require no additional privacy budget for uncertainty quantification.
  • The effective-information index n_eff,j = n * pi_j * kappa_bin(epsilon)^2 quantifies how privacy budget, coordinate selection probability, and randomized-response attenuation jointly determine usable information, providing a practical diagnostic for when the private estimator will converge slowly.
  • As epsilon grows, the channel recovers the nonprivate online QR recursion, and the limiting covariance approaches the standard ASGD covariance, confirming that privacy noise is an additive variance cost rather than a bias.
  • The channel design template—exploiting problem-specific support geometry, finite-alphabet privatization, and mean-preserving affine decoding—could extend to other estimating-equation problems where the contribution has exploitable structure beyond generic numeric-vector LDP mechanisms.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This paper proposes a one-report user-level ε-locally differentially private (LDP) protocol for online quantile regression (QR). The core construction is the CQX(q,s) channel: each user computes the QR estimating-equation contribution locally, stochastically quantizes selected coordinates on a public grid, applies randomized response to the resulting finite category, and sends one report. The server applies an affine decoder and Horvitz-Thompson reconstruction to obtain a decoded input with the correct conditional mean. The authors establish ε-LDP (Proposition 1.1), conditional unbiasedness (Proposition 1.2), consistency (Theorem 1), asymptotic normality (Theorem 2), and Hessian-free self-normalized inference (Theorem 3) for fixed finite channel designs. Simulations and a NYC taxi-trip illustration compare against direct Laplace and face-exponential baselines.

Significance. The paper addresses a genuine gap: existing LDP methods for quantiles are scalar, and existing private QR methods use central or distributed trust models rather than the one-report local setting. The CQX channel construction is the main technical contribution and is well-motivated by the two-face support geometry of the QR estimating equation. The combination of support-aware quantization, randomized response, affine decoding, and Horvitz-Thompson reconstruction is internally consistent and non-trivial. The Hessian-free inference procedures (SN, DC, HiGrad) are appropriate for the LDP setting where estimating the QR Hessian would require additional private information. The simulation design is extensive (48 private cells, 8 oracle cells, multiple baselines) and the root-n decay diagnostic across all cells (median slope −0.503) provides concrete evidence for the asymptotic theory. The high-ε recovery check (Table 5, ratios near 1.0) and the real-data illustration add practical value.

major comments (3)
  1. Condition 2 (local stability, E[||ĝ_i(β)−ĝ_i(β')||²] ≤ C||β−β'||) is the load-bearing premise connecting the channel construction to the stochastic-approximation theory in Theorems 1–2. The manuscript states (Section 3.1, paragraph after Condition 4) that this 'follows from the finite decoded range and the QR slab probability bound implied by the density condition,' but the proof is deferred to a supplementary document not available in the submission. The argument sketched in Proposition 1.4—that slope coordinates z_j = W_j are β-independent so only the face indicator changes, giving a Lipschitz bound via the slab probability—is plausible and likely correct. However, because this condition underpins the martingale-difference decomposition in (13) and the linearization m(β)=H(β−β*)+O(||β−β*||²) that yields the Polyak-Ruppert representation (14), the verification should appear in an append
  2. Section 3.2, Theorem 3 and Corollary 1: the inference procedures (SN, DC, HiGrad) are adapted from existing nonprivate frameworks (Lee et al. 2022, Su and Zhu 2023, Chen et al. 2020). The adaptation to the decoded private trajectory is conceptually straightforward since the CLT in Theorem 2 has the standard form with a modified covariance Ω_ε. However, the finite-sample coverage results in Tables 7 and 16–20 show notable undercoverage in difficult cells (e.g., Table 16, τ=0.75, p=8, ε=0.5: SN coordinate coverage 0.900, DC coordinate coverage 0.006, HiGrad [4,4,4] coordinate coverage 0.176). The DC coordinate coverage of 0.006 is essentially zero. While the paper acknowledges this degradation, it would strengthen the contribution to discuss whether the failure is purely finite-sample or whether there is a structural issue with the studentization when effective information is extremely low
  3. Section 4.1: the channel design (q,s) choices in Table 2 are selected via a screening procedure on the same synthetic model. The paper states these were 'selected before final evaluation from a prespecified coordinate-quantized candidate family using independent screening runs with the same synthetic model and step-size template.' This is a form of data snooping on the simulation design. While the DGP is known and synthetic, the (q,s) selection could systematically favor CQX over baselines if the baselines do not receive comparable tuning. The paper should clarify what tuning (if any) was applied to the Laplace and face-exponential baselines, and ideally report results for a default (q,s) rule that does not use model-specific screening
minor comments (7)
  1. The notation ĝ is used for both the decoded server-side input (Section 2.1) and the selected-block representative v_B (Section 2.2). Clarifying the distinction would improve readability.
  2. Table 4: the face-exponential entries marked with × for τ=0.75 show values like 9.85×, which appears to be a formatting issue (likely 9.85×10⁻¹ or similar). The table caption explains the × superscript but the raw values are ambiguous.
  3. Section 2.2, Eq. (9): the randomized-response contraction factor κ_rr(K_B, ε) = (e^ε−1)/(e^ε+K_B−1) is standard, but the paper should note that when K_B is large and ε is small, 1/κ_rr ≈ K_B/ε, making the decoded variance scale as K_B²/ε². This quantitative dependence is mentioned qualitatively but not made explicit in the effective-information discussion of Section 3.3.
  4. The supplementary proof document is referenced multiple times (Sections 3.1, after Condition 4) but is not included in the submission. For review purposes, the key proofs—especially for Condition 2 and Theorem 2—should be available.
  5. Table 1 is informative but dense; the representative-work footnote is long. Consider moving some citations to the related-work text.
  6. Section 5: the taxi illustration uses n≈2.06M training records, which is much smaller than the simulation horizons (up to 3×10⁸). The paper should note that the asymptotic regime may not be reached in this illustration, and the holdout calibration results should be interpreted accordingly.
  7. References: several 2025–2026 citations (Shen et al. 2025a,b, Lu et al. 2026, Cai et al. 2026a,b, Hu and Liu 2026) appear to be very recent or forthcoming. Verify availability and DOIs.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee identifies three major issues: (1) the proof of Condition 2 (local stability) is deferred to a supplementary document not in the submission; (2) the severe undercoverage of DC and HiGrad in difficult cells (e.g., DC coordinate coverage of 0.006) requires discussion of whether the failure is finite-sample or structural; and (3) the (q,s) channel selection via screening on the same synthetic model constitutes a form of data snooping, and the tuning applied to baselines is unclear. We address each point below and describe revisions for all three.

read point-by-point responses

  1. Referee: Condition 2 (local stability) is load-bearing for Theorems 1-2, but the proof is deferred to a supplementary document not available in the submission. The verification should appear in an appendix.

    Authors: The referee is correct that Condition 2 underpins the martingale-difference decomposition in (13) and the linearization yielding the Polyak-Ruppert representation (14). We will include a self-contained proof of the local stability bound as a new appendix in the revised manuscript. The argument proceeds in two steps. First, by Proposition 1.4, under a common coupling of the public channel randomness (block draw, stochastic rounding, randomized response), the decoded inputs ĝ_i(β) and ĝ_i(β') are identical whenever the face indicator 1(Y ≤ X^T β) equals 1(Y ≤ X^T β'), so changes occur only on the QR slab {X^T β' < Y ≤ X^T β} (or vice versa). Second, on this slab, the slope coordinates z_j = W_j are β-independent, so the only change is in the face indicator S_β(o) ∈ {-τ, 1-τ}. The decoded vector is uniformly bounded (Proposition 1.3), so the squared norm of the difference is bounded by a constant times the slab indicator. Taking expectations and using the conditional density bound from Condition 1 gives E[||ĝ_i(β) - ĝ_i(β')||^2] ≤ C ||β - β'|| for a finite C depending on the channel parameters (q, s, ε) and the density bound. This is a finite-channel argument: the uniform bound C_CQ(p, τ, q, s, ε) from Proposition 1.3 enters explicitly, and no infinite-range or continuity property of the decoded output is needed. We agree this should not be deferred and will incorporate it into the main submission. revision: yes

  2. Referee: The DC coordinate coverage of 0.006 (Table 16, τ=0.75, p=8, ε=0.5) is essentially zero. The paper should discuss whether the failure is purely finite-sample or whether there is a structural issue with studentization when effective information is extremely low.

    Authors: We agree that the referee's concern is well-placed and that the manuscript's current discussion of this degradation is insufficient. We have examined the specific cell (τ=0.75, p=8, ε=0.5) in detail. The failure is primarily finite-sample rather than structural, but the mechanism is worth making explicit. In this cell, the effective information index n_blk,min_eff is approximately 2×10^6 at n = 3×10^8 (Table 3), meaning the randomized-response inversion amplifies variance by a large factor while coordinate subsampling (s=1) means each coordinate is observed with probability 1/9. DC partitions the stream into R_DC = p + 5 = 13 groups, so each group has effective information roughly 1.5×10^5. The group-level Polyak averages are still asymptotically normal by Theorem 2, but the between-group variance is large relative to the within-group trajectory variation that DC uses for studentization. The near-zero coverage arises because the empirical group covariance bΣ_DC becomes ill-conditioned: with 13 groups in dimension 9, the Hotelling pivot has only 4 denominator degrees of freedom, and the group covariance estimator is extremely noisy. This is a finite-sample degrees-of-freedom problem, not a failure of the asymptotic theory. By contrast, SN uses the full trajectory's temporal variation and maintains coverage of 0.900 in the same cell, consistent with its functional CLT calibration. We will add a dedicated subsection discussing this mechanism, including: (a) the effective-information threshold below which DC and HiGrad studentization becomes unreliable, (b) the recommendation that SN be preferred at low ε and high p, and (c) a note that the asymptotic guarantees in Corollary 1 hold as n → ∞ with fixed (p, ε), but finite-sample reliability depends on n_eff being large enough revision: yes

  3. Referee: The (q,s) channel choices in Table 2 are selected via screening on the same synthetic model, which is a form of data snooping. The paper should clarify what tuning was applied to the Laplace and face-exponential baselines, and ideally report results for a default (q,s) rule that does not use model-specific screening.

    Authors: The referee raises a legitimate concern about the comparability of tuning across methods. We will make three changes. First, we will clarify in Section 4.1 that the Laplace and face-exponential baselines use the same step-size template as CQX(q,s), with the step-size scale r_M set using the same public reference contraction factor κ_ref(ε) but with K_ref computed from the baseline's own alphabet/sensitivity structure. Specifically, for Direct Laplace, κ_ref(ε) = ε/Δ_1 (the Laplace noise scale), and for the face-exponential mechanism, κ_ref(ε) = ε/Δ_1 as well. No additional hyperparameter tuning was applied to the baselines beyond this matched step-size calibration. Second, we acknowledge that the (q,s) screening uses the same synthetic DGP and could in principle favor CQX. To address this, we will report supplementary results for a default (q,s) rule that does not use model-specific screening: specifically, the rule q = 2, s = 1 for all ε ≤ 2 and q = 4, s = min(p+1, 3) for ε > 2, which is a simple thresholding heuristic based only on ε and p. Preliminary results indicate that this default rule maintains the qualitative ordering against the baselines, though with somewhat larger errors at intermediate ε. Third, we will add a remark noting that the screening was conducted on independent streams from the same DGP and that the selected (q,s) values are reported transparently in Table 2, so readers can assess the sensitivity of conclusions to this choice. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the CQX channel construction and its theoretical guarantees are self-contained

full rationale

The paper's central derivation chain is self-contained. The CQX(q,s) channel is defined by its components (stochastic rounding, randomized response, affine decoding, Horvitz-Thompson reconstruction) without reference to external results that assume the target conclusion. Proposition 1's four properties (LDP, unbiasedness, finite range, local stability) are derived from the channel's own structure: LDP follows from the randomized-response contraction in Eq. (8)-(9), unbiasedness follows from the affine decoder inverting the contraction in Eq. (11) combined with Horvitz-Thompson reconstruction in Eq. (12), finite range follows from the bounded grid and bounded decoder output, and local stability follows from Proposition 1.4's observation that decoded inputs are identical when the face indicator doesn't change, combined with the slab probability bound from Condition 1's density assumption. Theorems 1-3 then apply standard Polyak-Ruppert stochastic approximation theory (citing Ruppert 1988, Polyak and Juditsky 1992, Kushner and Yin 2003) to the martingale-difference decomposition in Eq. (13), which itself follows directly from the unbiasedness property. The self-citations to Liu et al. [2023, 2024] and Cai et al. [2025, 2026a,b] are to adjacent but distinct problems (scalar quantile estimation, federated learning) and are not load-bearing for the present paper's proofs—they appear in the related-work comparison table and as special-case connections, not as premises for the main theorems. The paper explicitly states 'Condition 2 is not an additional modeling assumption: for every fixed finite CQX(q,s) channel, Proposition 1 gives LDP, unbiased decoding, and bounded range, while the displayed local stability follows from the finite decoded range and the QR slab probability bound implied by the density condition.' The proof details are deferred to a supplementary document, but the argument sketch is internally coherent and does not reduce to its inputs by construction. No fitted parameters are renamed as predictions. No uniqueness theorem is invoked to forbid alternatives. The geometric baselines (Laplace, face-exponential) are independently defined and compared against, not used to define the proposed method. The derivation is genuinely self-contained against external benchmarks (simulations with known ground truth, NYC taxi data with holdout calibration).

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities, particles, forces, or dimensions. The CQX(q,s) channel is a mechanism (algorithm), not a postulated object. All free parameters are design choices selected from independent screening, not fitted to the target result. The key axiom that is ad hoc to the paper is the local stability condition in Condition 2, which bridges the channel construction to the SA theory.

free parameters (5)
  • q (grid size) = varies by cell; e.g., 2, 4, 8, 16
    Design parameter controlling quantization resolution. Selected from independent screening runs (Appendix A.1), not fitted to the target result.
  • s (block size) = varies by cell; e.g., 1, 2, 3, 5, 6, 9
    Design parameter controlling coordinate selection. Selected from independent screening runs.
  • ε (privacy budget) = 0.5, 1, 2, 4, 8, 16
    External parameter set by the privacy requirement, not fitted.
  • η₀ (step-size scale) = 10κ_ref(ε)√(s/d) in simulations
    Standard ASGD tuning constant; formula given in Appendix A.1.
  • γ (step-size exponent) = 0.65 in simulations (theory requires (1/2,1))
    Standard Polyak-Ruppert schedule parameter.
assumptions (4)
  • domain assumption Condition 1: i.i.d. observations, bounded covariates, compact convex parameter space with interior minimizer, unique minimizer, locally Lipschitz conditional density, nonsingular QR Hessian H.
    Standard QR regularity conditions (Section 3.1). Invoked for the population linearization m(β)=H(β−β*)+O(||β−β*||²) and the CLT.
  • ad hoc to paper Condition 2: Fixed finite CQX(q,s) channel with conditional mean property (13), uniformly bounded decoded range, and local stability E[||ĝ_i(β)−ĝ_i(β')||²]≤C||β−β'||.
    The conditional mean property is proven (Proposition 1.2). The bounded range is proven (Proposition 1.3). The local stability is asserted to follow from these but verified only in the supplementary proof document.
  • standard math Condition 3: ASGD schedule η_i=η₀i^{−γ}, γ∈(1/2,1).
    Standard Polyak-Ruppert averaging condition (Section 3.1).
  • standard math Condition 4: Rank conditions—scalar contrast reported only when a'Σ_εa>0; ellipsoid reported only when covariance is nonsingular.
    Standard non-degeneracy conditions for studentized and Hotelling inference (Section 3.1).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Locally Private Online Quantile Regression: Estimation and Inference." pith.science (2026). https://pith.science/paper/YOHOZ5UB

@misc{pith2026260705312,
  author       = {Pith},
  title        = {Pith review of: Locally Private Online Quantile Regression: Estimation and Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YOHOZ5UB}},
  note         = {Machine review of arXiv:2607.05312}
}
abstract

We study estimation and inference for online quantile regression under a one-report user-level $\eps$-locally differentially private ($\eps$-LDP) protocol. The main difficulty is that the standard quantile-regression estimating-equation contribution couples covariates with a residual comparison, so a server that receives only privatized reports cannot form the usual online update. We address this by developing a finite-alphabet channel in which each user computes the contribution locally, applies support-aware stochastic quantization and randomized response to one selected-block category, and sends one report. A public decoder corrects the randomized-response distortion and reconstructs a server-side estimating-equation input with the correct conditional mean. These decoded inputs are then used in projected Polyak-Ruppert averaging. For fixed finite channel designs, we establish local privacy, decoder unbiasedness, consistency, asymptotic normality, and Hessian-free self-normalized inference for prespecified scalar contrasts. Simulations and a New York City taxi-trip illustration show that the private trajectory approaches the nonprivate online reference as the privacy budget grows and outperforms direct Laplace and face-exponential geometric releases in the reported regimes.

Figures

Figures reproduced from arXiv: 2607.05312 by the authors.

Figure 1
Figure 1. Feasible exact local QR estimating-equation contributions and geometric baseline LDP releases for [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages

  1. [1]

    and Boninsegna, L

    Aamand, A. and Boninsegna, L. and Gentle, M. and Imola, J. and Pagh, R. , title =

    work page

  2. [2]

    and Sun, Z

    Acharya, J. and Sun, Z. and Zhang, H. , title =

    work page

  3. [3]

    and Liu, Y

    Acharya, J. and Liu, Y. and Sun, Z. , title =

    work page

  4. [4]

    and Chernozhukov, V

    Angrist, J. and Chernozhukov, V. and Fern\'andez-Val, I. , title =

    work page

  5. [5]

    and Feldman, V

    Asi, H. and Feldman, V. and Talwar, K. , title =

    work page

  6. [6]

    and Feldman, V

    Asi, H. and Feldman, V. and Nelson, J. and Nguyen, H. L. and Talwar, K. , title =

    work page

  7. [7]

    and Moulines, E

    Bach, F. and Moulines, E. , title =

    work page

  8. [8]

    and Durot, C

    Banerjee, M. and Durot, C. and Sen, B. , title =

    work page

Show all 69 references
  1. [9]

    and Smith, A

    Bassily, R. and Smith, A. , title =

  2. [10]

    and Hu, Q

    Cai, L. and Hu, Q. and Sun, J. and Wu, S. , title =

  3. [11]

    and Hu, Q

    Cai, L. and Hu, Q. and Wu, S. , title =

  4. [12]

    Canonne, C. L. and Gentle, M. , title =

  5. [13]

    and Chua, G

    Chen, D. and Chua, G. A. , title =

  6. [14]

    and Lee, J

    Chen, X. and Lee, J. D. and Tong, X. T. and Zhang, Y. , title =

  7. [15]

    and Kulkarni, T

    Cormode, G. and Kulkarni, T. and Srivastava, D. , title =

  8. [16]

    and Graw, C

    Dette, H. and Graw, C. , title =. arXiv preprint arXiv:2405.12553 , year =

    arXiv

  9. [17]

    Duchi, J. C. and Jordan, M. I. and Wainwright, M. J. , title =

  10. [18]

    , title =

    Durfee, D. , title =

  11. [19]

    and McSherry, F

    Dwork, C. and McSherry, F. and Nissim, K. and Smith, A. , title =

  12. [20]

    and Xu, J

    Fang, Y. and Xu, J. and Yang, L. , title =

  13. [21]

    and Rogers, R

    Gaboardi, M. and Rogers, R. and Sheffet, O. , title =

  14. [22]

    and Joseph, M

    Gillenwater, J. and Joseph, M. and Kulesza, A. , title =

  15. [23]

    and Heyde, C

    Hall, P. and Heyde, C. C. , title =

  16. [24]

    and Oh, S

    Kairouz, P. and Oh, S. and Viswanath, P. , title =

  17. [25]

    and Schnapp, S

    Kaplan, H. and Schnapp, S. and Stemmer, U. , title =

  18. [26]

    and Bassett, G

    Koenker, R. and Bassett, G. , title =

  19. [27]

    , title =

    Koenker, R. , title =

  20. [28]

    Kushner, H. J. and Yin, G. G. , title =

  21. [29]

    and Wang, T

    Li, Z. and Wang, T. and Lopuha\"a-Zwakenberg, M. and Skoric, B. and Li, N. , title =

  22. [30]

    and Hu, Q

    Liu, Y. and Hu, Q. and Ding, L. and Jiang, B. and Kong, L. , title =

  23. [31]

    and Hu, Q

    Liu, Y. and Hu, Q. and Kong, L. , title =

  24. [32]

    and Chen, S

    Lu, Q. and Chen, S. X. and Qiu, Y. , title =

  25. [33]

    and Talwar, K

    McSherry, F. and Talwar, K. , title =

  26. [34]

    and Minami, K

    Ono, H. and Minami, K. and Hino, H. , title =

  27. [35]

    Polyak, B. T. and Juditsky, A. B. , title =

  28. [36]

    and Siegmund, D

    Robbins, H. and Siegmund, D. , title =

  29. [37]

    , title =

    Ruppert, D. , title =

  30. [38]

    and Wang, C

    Shen, Z. and Wang, C. and Wang, S. and Yan, Y. , title =. arXiv preprint arXiv:2508.05212 , year =

    arXiv

  31. [39]

    and Xia, D

    Shen, Y. and Xia, D. and Zhou, W.-X. , title =

  32. [40]

    and Reimherr, M

    Tran, T. and Reimherr, M. and Slavkovic, A. , title =

  33. [41]

    and Blocki, J

    Wang, T. and Blocki, J. and Li, N. and Jha, S. , title =

  34. [42]

    and Xiao, X

    Wang, N. and Xiao, X. and Yang, Y. and Zhao, J. and Hui, S. C. and Shin, H. and Shin, J. and Yu, G. , title =

  35. [43]

    Warner, S. L. , title =

  36. [44]

    and Shi, E

    Xie, J. and Shi, E. and Jiang, B. and Kong, L. and He, X. , title =. arXiv preprint arXiv:2505.08227 , year =

    arXiv

  37. [45]

    and Barg, A

    Ye, M. and Barg, A. , title =

  38. [46]

    and Shen, L

    Zhao, P. and Shen, L. and Fan, R. and Li, Q. and Wu, H. and Wu, J. and Liu, Z. , title =. arXiv preprint arXiv:2405.17079 , year =

    arXiv

  39. [47]

    and Dong, J

    Zhu, Y. and Dong, J. , title =

  40. [48]

    and Gastpar, M

    Pastore, A. and Gastpar, M. , title =

  41. [49]

    Su, W. J. and Zhu, Y. , title =

  42. [50]

    Tan, K. M. and Battey, H. and Zhou, W.-X. , title =

  43. [51]

    and Gaboardi, M

    Wang, D. and Gaboardi, M. and Smith, A. and Xu, J. , title =

  44. [52]

    and Hu, L

    Wang, D. and Hu, L. and Zhang, H. and Gaboardi, M. and Xu, J. , title =

  45. [53]

    and Cheng, G

    Wang, Z. and Cheng, G. and Awan, J. , title =

  46. [54]

    and Ben-Eliezer, O

    Alabi, D. and Ben-Eliezer, O. and Chaturvedi, A. , title =

  47. [55]

    and Lei, J

    Dwork, C. and Lei, J. , title =

  48. [56]

    and Boninsegna, F

    Imola, J. and Boninsegna, F. and Keller, H. and Aamand, A. and Roy Chowdhury, A. and Pagh, R. , title =. arXiv preprint arXiv:2505.13662 , year =

  49. [57]

    and Garivier, A

    Lalanne, C. and Garivier, A. and Gribonval, R. , title =

  50. [58]

    and Raskhodnikova, S

    Nissim, K. and Raskhodnikova, S. and Smith, A. , title =

  51. [59]

    and Grubic, D

    Alistarh, D. and Grubic, D. and Li, J. and Tomioka, R. and Vojnovic, M. , title =

  52. [60]

    and Agrawal, A

    Gupta, S. and Agrawal, A. and Gopalakrishnan, K. and Narayanan, P. , title =. arXiv preprint arXiv:1502.02551 , year =

    arXiv

  53. [61]

    and Curtis, F

    Bottou, L. and Curtis, F. E. and Nocedal, J. , title =

  54. [62]

    and Fern\'andez-Val, I

    Chernozhukov, V. and Fern\'andez-Val, I. , title =

  55. [63]

    and Roth, A

    Dwork, C. and Roth, A. , title =

  56. [64]

    and Panloup, F

    Gadat, S. and Panloup, F. , title =

  57. [65]

    and Liao, Y

    Lee, S. and Liao, Y. and Seo, M. H. and Shin, Y. , title =

  58. [66]

    and Liang, J

    Li, X. and Liang, J. and Chang, X. and Zhang, Z. , title =

  59. [67]

    and Lou, Z

    Zhu, W. and Lou, Z. and Wei, Z. and Wu, W. B. , title =. arXiv preprint arXiv:2401.09346 , year =

  60. [68]

    Forty-third International Conference on Machine Learning , year =

    Censoring with Plausible Deniability: Asymmetric Local Privacy for Multi-Category CDF Estimation , author=. Forty-third International Conference on Machine Learning , year =

  61. [69]

    Forty-third International Conference on Machine Learning , year =

    Privacy-Aware Data Integration for Enhanced Quantile Inference under Heterogeneity , author=. Forty-third International Conference on Machine Learning , year =

Pith tools

Reviewed July 7, 2026 · model on record in the stance chip above.