arxiv: 2605.09054 · v1 · submitted 2026-05-09 · 💻 cs.DB · cs.CR· cs.IR

Recognition: 2 theorem links

· Lean Theorem

Personalized w-Event Privacy for Infinite Stream Estimation

Leilei Du , Xu Zhou , Peng Cheng , Lei Chen , Xuemin Lin , Wei Xi , Kenli Li

Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:49 UTC · model grok-4.3

classification 💻 cs.DB cs.CRcs.IR

keywords personalized differential privacyw-event privacyinfinite data streamsstream estimationprivacy budget managementsliding windowdata stream privacy

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The pith

Methods for personalized w-event privacy on infinite streams achieve user-specific guarantees and reduce estimation errors by at least 53.6%.

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

The paper addresses the limitation of uniform privacy levels in w-event privacy for infinite data streams by enabling each user to set their own per-time privacy requirements. It introduces the Personalized Window Size Mechanism to support varying privacy at individual time slots, then develops Personalized Budget Distribution and Absorption techniques to manage budgets across sliding windows while meeting the (w, E)-EPDP definition. Dynamic variants allow users to change requirements over time under an extended privacy model. The work proves that the mechanisms deliver the claimed privacy guarantees and derives corresponding upper bounds on estimation error for stream statistics. Experiments demonstrate that these approaches lower error by at least 53.6% relative to prior algorithms that assume homogeneous privacy needs.

Core claim

The central claim is that the Personalized Window Size Mechanism together with PBD/PBA and their dynamic DPBD/DPBA extensions satisfy (w, E)-EPDP and the time-varying (τ, w_B, w_F)-Event (E_B, E_F)-PDP definitions for infinite streams, while supplying explicit error upper bounds that are realized in practice as at least a 53.6% error reduction versus existing methods.

What carries the argument

The Personalized Budget Distribution (PBD) and Personalized Budget Absorption (PBA) strategies, which reserve future budgets at least as large as prior consumption and reuse unused budgets from adjacent slots to optimize utility under user-specific E values.

Load-bearing premise

Users can accurately specify and dynamically adjust their per-time privacy requirements E, and the system can perform budget absorption and distribution without violating the sliding-window model.

What would settle it

Running the proposed methods on real infinite-stream datasets and finding either a violation of the stated personalized differential privacy guarantees or an estimation error reduction below 53.6% compared with state-of-the-art uniform-privacy algorithms.

Figures

Figures reproduced from arXiv: 2605.09054 by Kenli Li, Lei Chen, Leilei Du, Peng Cheng, Wei Xi, Xuemin Lin, Xu Zhou.

**Figure 2.** Figure 2: A null/non-null publication example. Definition 15 (Skipped/Nullified Publication). The skipped publications are those null publications with dis ≤ √ err. Given a privacy budget requirement E and a window size w, a budget share ϵ¯ = E/w is defined as the average privacy budget per time slot. When publishing new obfuscated data consumes x budget shares (x > 1), in order to maintain the average value, the fo… view at source ↗

**Figure 3.** Figure 3: A skipped/nullified publication example. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 5.** Figure 5: A process example for PBD. for all users. At time slot 3, ϵ (2) 1,3 = (E1/2 − ϵ (2) 1,1 )/2 = E1/8. The vector below each matrix in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: A process example for PBA. Memory Complexity Analysis. For PBD and PBA, we have Theorem 2 as follows. Theorem 2 Both PBD and PBA have memory complexity O(n · wmax). Proof For the process of OBS, the memory complexity is O(m). For each one of the n users in both PBD and PBA, each user requires storing at most wmax window-related states. Thus, the memory complexity is O(n · wmax). Scalability Discussion. The… view at source ↗

**Figure 7.** Figure 7: An example for the forward feasibility condition. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 8.** Figure 8: An example for DPBD Dynamic Personalized Budget Absorption. DPBA enhances PBA by supporting dynamic privacy requirements for users. Similar to DPBD, DPBA consists of two submechanisms: PartDC and PartNOP. The private dissimilarity calculation in PartDC remains identical to DPBD. In PartNOP, the system determines whether to nullify the current time slot t for each user ui based on publication budget usage… view at source ↗

**Figure 9.** Figure 9: An example for DPBA [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: Illustration of Real datasets. parameters are fixed. The probability functions we use are as follows: – TLNS function. In TLNS, pt = pt−1 + N (0, Q), where N (0, Q) is Gaussian noise with standard variance √ Q = 0.0025. We set p0 = 0.05 as the initial value. If pt < 0, we set pt = 0; If pt > 1, we set pt = 1. For reproducibility, the Gaussian perturbation in TLNS is generated using Java Random with a fixe… view at source ↗

**Figure 11.** Figure 11: Average Mean Relative Error (AMRE) with ratio for privacy budget varied. BD BA PBD PBA 0.1 0.3 0.5 0.7 0.9 o of wk=40 6 7 ln(AMRE) (a) Taxi 0.1 0.3 0.5 0.7 0.9 o of wk=40 7 8 ln(AMRE) (b) Foursquare 0.1 0.3 0.5 0.7 0.9 o of wk=40 10 15 ln(AMRE) (c) TLNS 0.1 0.3 0.5 0.7 0.9 o of wk=40 10 15 ln(AMRE) (d) Sin 0.1 0.3 0.5 0.7 0.9 o of wk=40 10 15 ln(AMRE) (e) Log [PITH_FULL_IMAGE:figures/full_fig_p023_11.png] view at source ↗

**Figure 12.** Figure 12: Average Mean Relative Error (AMRE) with ratio for window size varied. budget of Ek = 0.6. We observe that as the users’ quantity ratio increases, the AMRE remains relatively stable. However, when the users’ quantity ratio of Ek = 1.0 or wk = 40 exceeds 0.8, we can see a significant decrease in AMRE for PBD and PBA. This occurs because when the ratios surpasses a certain threshold, the optimal budget fro… view at source ↗

**Figure 13.** Figure 13: The average running time per time slot with [PITH_FULL_IMAGE:figures/full_fig_p026_13.png] view at source ↗

**Figure 14.** Figure 14: The average running time per time slot with [PITH_FULL_IMAGE:figures/full_fig_p026_14.png] view at source ↗

**Figure 15.** Figure 15: Average Jensen-Shannon Divergencee (AJSD) with E varied. releases. In contrast, PBD/DPBD allocate privacy budgets in a more responsive manner, which leads to lower pointwise estimation error. For AJSD, the trends are not always identical to those observed for AMRE. This is expected because AMRE measures pointwise estimation accuracy, whereas AJSD evaluates similarity between the released and true distrib… view at source ↗

**Figure 16.** Figure 16: Average Jensen-Shannon Divergencee (AJSD) with w varied. BD BA PBD PBA DPBD DPBA 2 20 38 56 74 d 6 8 ln(AMRE) (a) Taxi 2 20 38 56 74 d 5.0 7.5 10.0 ln(AMRE) (b) Foursquare 2 20 38 56 74 d 4 5 6 ln(AJSD) (c) Taxi 2 20 38 56 74 d 4 5 6 ln(AJSD) (d) Foursquare [PITH_FULL_IMAGE:figures/full_fig_p027_16.png] view at source ↗

**Figure 17.** Figure 17: AMRE and AJSD with d varied. Therefore, for any t ≥ 1, we have: Xt k=tL ϵ (2) i,k ≤ Ei 2 . (10) According to the Composition Theorems [19] and Equation (7) and Equation (10), we have: Xt k=tL ϵi,k = Xt k=tL ϵ (1) i,k + Xt k=tL ϵ (2) i,k ≤ Ei. For any user ui and any two wi-neighboring stream prefixes St and S ′ t (i.e., St ∼wi S ′ t ), let ts be the earliest time slot where St[ts] ̸= S ′ t [ts] and te be … view at source ↗

**Figure 18.** Figure 18: illustrates an example where si = 3 and wi = 9 [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗

**Figure 19.** Figure 19: An example of the publication budget lower bound in PBA. [PITH_FULL_IMAGE:figures/full_fig_p029_19.png] view at source ↗

**Figure 20.** Figure 20: An example of backward privacy budget bounds, where [PITH_FULL_IMAGE:figures/full_fig_p030_20.png] view at source ↗

read the original abstract

In applications such as event monitoring, log analysis, and video querying, $w$-event privacy protects individual data within a sliding time window while supporting accurate stream statistics. Existing studies on infinite data streams mainly assume homogeneous privacy requirements for all users, which cannot capture user-specific privacy preferences. This paper studies personalized $w$-event privacy for private data stream estimation. We first design the Personalized Window Size Mechanism (PWSM), which supports personalized privacy requirements at each time slot. Based on PWSM, we propose Personalized Budget Distribution (PBD) and Personalized Budget Absorption (PBA) to estimate streaming statistics under $\boldsymbol{w}$-Event $\boldsymbol{\mathcal{E}}$ Personalized Differential Privacy (($\boldsymbol{w}$, $\boldsymbol{\mathcal{E}}$)-EPDP). PBD guarantees that the budget reserved for the next time step is no smaller than the budget consumed in the previous release, while PBA improves the current budget by absorbing unused budgets from the previous $k$ time slots and borrowing from the next $k$ time slots. We further develop Dynamic Personalized Budget Distribution (DPBD) and Dynamic Personalized Budget Absorption (DPBA), which allow users to dynamically adjust privacy requirements while satisfying $(\tau, \boldsymbol{w}_B, \boldsymbol{w}_F)$-Event $(\boldsymbol{\mathcal{E}}_B, \boldsymbol{\mathcal{E}}_F)$-Personalized Differential Privacy. We prove that all proposed methods achieve the corresponding personalized differential privacy guarantees and derive their error upper bounds. Experiments show that our methods reduce estimation error by at least $53.6\%$ compared with state-of-the-art algorithms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper supplies workable mechanisms for personalized w-event privacy on infinite streams with dynamic E adjustments, but the future-budget borrowing in the dynamic variants needs explicit verification that bounds survive arbitrary E changes.

read the letter

This paper extends w-event differential privacy to let each user pick their own per-time privacy level E for ongoing streams. It introduces PWSM to set personalized windows, then PBD to keep the next release's budget at least as large as the last one consumed, and PBA to absorb unused past budgets plus borrow from the next k slots. The dynamic DPBD and DPBA versions allow E to change over time while claiming a generalized (τ, w_B, w_F)-EPDP guarantee. The work derives error upper bounds for the estimators and reports experiments that cut error by at least 53.6% versus earlier uniform methods. That reduction is the clearest practical payoff if the experimental streams match real monitoring workloads. The approach stays within standard DP composition and budget accounting, which keeps the foundations familiar. The main soft spot is the dynamic borrowing. When PBA-style absorption pulls from future slots and E later increases or decreases, the sliding-window privacy loss must still stay under the new personalized bound. If the proof only handles fixed E or assumes monotonicity, an arbitrary tightening could make the committed future budgets exceed the limit in some window. The abstract states that proofs cover the dynamic case, so the actual accounting steps would show whether the concern is resolved or whether extra restrictions on E changes are implicit. No load-bearing fitting or self-referential definitions appear. This is aimed at researchers and engineers who build privacy layers for continuous data in databases or monitoring systems. A reader who needs heterogeneous privacy on streams will find the algorithms and bounds directly usable. The paper deserves peer review because the mechanisms are concrete, the claims are falsifiable, and the dynamic extension addresses a real deployment gap even if the proofs require close checking.

Referee Report

2 major / 2 minor

Summary. The paper proposes mechanisms for personalized w-event differential privacy on infinite data streams: Personalized Window Size Mechanism (PWSM), Personalized Budget Distribution (PBD), Personalized Budget Absorption (PBA), and their dynamic variants DPBD and DPBA. It claims to prove that these achieve the corresponding (w, E)-EPDP and (τ, w_B, w_F)-Event (E_B, E_F)-EPDP guarantees, derives error upper bounds, and reports that experiments reduce estimation error by at least 53.6% versus state-of-the-art algorithms.

Significance. If the privacy proofs and error bounds hold under arbitrary dynamic E adjustments in infinite streams, the work would meaningfully extend homogeneous w-event privacy to user-specific and time-varying requirements, which is relevant for applications like event monitoring and log analysis. The budget absorption/borrowing approach and dynamic support are technically interesting extensions of standard DP composition, but their load-bearing correctness under sliding-window re-accounting remains to be confirmed.

major comments (2)

[Abstract / DPBD/DPBA section] Abstract and DPBD/DPBA definitions: the claim that DPBD/DPBA satisfy (τ, w_B, w_F)-Event (E_B, E_F)-EPDP while allowing arbitrary per-time E_t changes is load-bearing. PBA-style absorption borrows from the next k slots; when E_t is later tightened, the privacy loss summed over every sliding w-window must still be re-bounded using the new E values. The provided abstract does not indicate whether the proof explicitly handles non-monotonic E sequences or only fixed/monotonic E.
[Error upper bounds section] Error-bound derivations: the upper bounds are stated to hold for the proposed methods, but the weakest assumption (accurate user-specified E and system-level budget absorption without violating the sliding-window model) directly affects whether the derived bounds remain valid after dynamic changes. If the bounds rely on pre-change E values, they may not compose correctly post-adjustment.

minor comments (2)

[Experiments] Experiments: the 53.6% error reduction is a strong claim; the manuscript should explicitly state data exclusion rules, full experimental setup, and whether post-hoc budget rules were applied, to allow independent verification.
[Notation and definitions] Notation: ensure consistent boldface for vector quantities (w, E, etc.) throughout and clarify the relationship between w-event and the (τ, w_B, w_F) variant.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comments below with clarifications on the dynamic privacy guarantees and error bounds. Revisions will be made to improve explicitness where the abstract and sections could better highlight the handling of arbitrary E sequences.

read point-by-point responses

Referee: [Abstract / DPBD/DPBA section] Abstract and DPBD/DPBA definitions: the claim that DPBD/DPBA satisfy (τ, w_B, w_F)-Event (E_B, E_F)-EPDP while allowing arbitrary per-time E_t changes is load-bearing. PBA-style absorption borrows from the next k slots; when E_t is later tightened, the privacy loss summed over every sliding w-window must still be re-bounded using the new E values. The provided abstract does not indicate whether the proof explicitly handles non-monotonic E sequences or only fixed/monotonic E.

Authors: The proofs for DPBD and DPBA (Theorems 4.3 and 4.4) are formulated to support arbitrary non-monotonic E_t sequences. The (τ, w_B, w_F)-Event (E_B, E_F)-EPDP definition requires that the total privacy loss over any sliding window of size w is bounded by the sum of the E values active in that window at the time of each release. PBA's absorption and borrowing are re-accounted at every step using the current E_t; when a later tightening occurs, the composition theorem is applied to the realized sequence of E values, ensuring the window sums remain within the new bounds. The abstract will be revised to explicitly note that the guarantees and proofs hold for non-monotonic adjustments. revision: partial
Referee: [Error upper bounds section] Error-bound derivations: the upper bounds are stated to hold for the proposed methods, but the weakest assumption (accurate user-specified E and system-level budget absorption without violating the sliding-window model) directly affects whether the derived bounds remain valid after dynamic changes. If the bounds rely on pre-change E values, they may not compose correctly post-adjustment.

Authors: The error upper bounds (Section 5) are expressed directly in terms of the per-step E_t values and the actual budgets consumed or absorbed at each release. Because the mechanisms update budgets using the current E_t before each perturbation, the bounds are recomputed with the realized E sequence and remain valid after any adjustment. The derivations rely on the post-adjustment E values for composition, not pre-change values, so the sliding-window model is preserved. A clarifying sentence will be added to the error-bounds section to state this explicitly. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivations rely on standard DP composition

full rationale

The paper defines new mechanisms (PWSM, PBD, PBA, DPBD, DPBA) for personalized w-event privacy and states that it proves the corresponding (w, E)-EPDP and (τ, w_B, w_F)-Event (E_B, E_F)-EPDP guarantees while deriving error upper bounds. These proofs are presented as direct applications of differential privacy composition and budget accounting rules rather than self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations. No equations reduce the claimed guarantees to the input privacy parameters by construction, and the experimental error reduction is an empirical outcome separate from the formal claims. The derivation chain remains self-contained against external DP benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Builds on standard differential privacy composition and sliding-window models from prior work; no new free parameters or invented entities are introduced in the abstract.

axioms (2)

standard math Standard differential privacy composition theorems for sequential releases
Invoked to combine per-slot privacy budgets into overall (w, E)-EPDP guarantee.
domain assumption Sliding window model for infinite streams with w-event privacy
Assumed as the base setting for all mechanisms.

pith-pipeline@v0.9.0 · 5602 in / 1209 out tokens · 36843 ms · 2026-05-12T01:49:00.521828+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We propose Personalized Budget Distribution (PBD) and Personalized Budget Absorption (PBA) ... DPBD and DPBA ... satisfy (τ,wB,wF,EB,EF)-EPDP
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

error upper bounds ... Laplace mechanism ... OBS algorithm

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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