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arxiv: 2606.03878 · v1 · pith:CRHLGY37new · submitted 2026-06-02 · 📊 stat.ML · cs.LG

Privacy-Robust Incrementality Measurement for Advertising Systems under Signal Loss

Prashant Shekhar , Caroline Howard This is my paper

Pith reviewed 2026-06-28 07:55 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords privacy-preserving measurementincrementalitycausal inferencerobust statisticsadvertising experimentssignal lossdecision frontierlift testing
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The pith

Privacy-induced signal losses create a sharp decision frontier separating certifiable from unresolvable incrementality claims in advertising experiments.

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

The paper models ad incrementality measurement under privacy rules that degrade data through match-rate loss, linkability loss, attribution windows, aggregation thresholds, noise, and heterogeneous loss. It treats the problem as a robust causal decision task: an ambiguity set encodes all clean experimental worlds consistent with a given degraded report, and the framework projects this fiber onto the incrementality value to decide certification, rejection, or unresolved status. The central result is a sharp frontier in report space; outside it, any observed report permits a uniformly valid decision about whether lift exceeds a threshold, while inside it no procedure can make that distinction for all compatible worlds. This matters for platforms that must justify ad spend when privacy constraints limit what can be observed.

Core claim

Given a randomized experiment and an ambiguity set for privacy-induced degradation, the framework projects the observation-compatible fiber of clean experimental worlds onto the incrementality functional and returns certified, rejected, and unresolved decisions. The main result gives a sharp decision frontier. Reports outside the frontier support uniformly valid certification or rejection, whereas reports inside it contain too little information for any method to uniformly distinguish above-threshold incrementality from non-incrementality.

What carries the argument

The decision frontier obtained by projecting the observation-compatible fiber onto the incrementality functional under the ambiguity set for privacy-induced signal losses.

If this is right

  • Finite-sample procedures exist that certify or reject incrementality for reports outside the frontier.
  • Sample-complexity bounds quantify the data volume required to reach a decision outside the frontier.
  • A minimax lower bound establishes that greater signal loss strictly reduces the information available for any inference method.
  • A reporting-granularity tradeoff shows how coarser privacy-preserving reports increase the measure of the unresolved region.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Platforms could compute the frontier on incoming reports to decide whether to accept the result or request less-degraded data at added privacy cost.
  • The same projection technique might apply to other causal settings where privacy or missingness creates an ambiguity set around observed outcomes.
  • Empirical checks on large uplift datasets indicate that mild degradation often leaves population-level claims certifiable while combined noise and uncertainty push most finite-sample cases into the unresolved region.

Load-bearing premise

The chosen ambiguity set correctly contains every clean experimental world that could have produced the observed degraded report.

What would settle it

A statistical procedure that, for some report inside the computed frontier, produces a uniformly valid certification or rejection across every world in the ambiguity set would falsify the claimed sharpness.

Figures

Figures reproduced from arXiv: 2606.03878 by Caroline Howard, Prashant Shekhar.

Figure 1
Figure 1. Figure 1: Privacy-robust incrementality measurement as a decision problem. A randomized advertising experiment identifies clean lift before reporting constraints are applied (as summarized in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Population and finite-sample certification frontiers under auditable signal-loss stress layers. The purple curve is the population lower bound, which applies signal-loss uncertainty while treating the degraded arm means as exactly known. The green curve is the finite-sample lower bound, which adds simultaneous randomization uncertainty and randomized reporting-noise uncertainty to the same signal-loss band… view at source ↗
Figure 3
Figure 3. Figure 3: Sample-complexity and minimax scaling under privacy signal loss. The left panel evaluates the finite-sample radius Radn from Eq. (9) as the per-arm sample size and reportable-retention lower bound qmin vary. The right panel evaluates the implemented constant-scaled minimax curve 0.08 B/√qn, corresponding to the universal-constant lower￾bound rate in Theorem 5.3. Lower retention enlarges both quantities, sh… view at source ↗
Figure 4
Figure 4. Figure 4: Reporting granularity diagnostics. The horizontal axis is the number of reported cells in the partition. The left panel compares the share of cells that clear the population signal-loss lower bound with the share that clear the finite-sample lower bound after simultaneous uncertainty and reporting noise are added. The middle panel reports aggregation-threshold suppression with fixed threshold m = 100. The … view at source ↗
Figure 5
Figure 5. Figure 5: Sharp compatibility fiber for a controlled degraded-report example. This diagnostic is not dataset-specific. It fixes degraded treated and control means µe1 = 0.12 and µe0 = 0.08, with retention ambiguity q ∈ [0.5, 1.0]. The shaded interval is the full set of clean incrementality values compatible with the same released report and ambiguity set. A business threshold below the interval is certifiable, a thr… view at source ↗
Figure 6
Figure 6. Figure 6: Privacy-aware minimum detectable effects. Reporting noise increases the detectable-effect floor [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Heterogeneous signal loss can reverse segment decisions. Two clean segment-level worlds induce [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
read the original abstract

Advertising platforms use randomized lift tests to measure incrementality, but privacy-preserving reporting systems degrade the observed signal through match-rate loss, linkability loss, attribution-window loss, aggregation-threshold suppression, randomized reporting noise, and segment-heterogeneous signal loss. This paper formulates privacy-constrained advertising measurement as a robust causal decision problem under the mentioned signal losses. Given a randomized experiment and an ambiguity set for privacy-induced degradation, the framework projects the observation-compatible fiber of clean/unfiltered experimental worlds onto the incrementality functional and returns certified, rejected, and unresolved decisions. The main result gives a sharp decision frontier. Reports outside the frontier support uniformly valid certification or rejection, whereas reports inside it contain too little information for any method to uniformly distinguish above-threshold incrementality from non-incrementality. Supporting results give finite-sample certification, sample-complexity guarantees, a minimax lower bound showing that signal loss reduces effective information, and a reporting-granularity tradeoff. On 2.0M Criteo Uplift rows and the 64K-row Hillstrom email experiment, clean conversion lift is positive in both datasets, with lifts 0.00112 and 0.00495, respectively. Population certification survives mild degradation in Criteo and severe degradation in Hillstrom, while all considered finite-sample stress settings in both datasets remain unresolved after simultaneous uncertainty and reporting noise are included. Overall, the research contributes a decision-theoretic layer for privacy-aware incrementality measurement whose output is the strongest causal-claim justified by degraded ads signals.

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.

Referee Report

2 major / 2 minor

Summary. The paper formulates privacy-constrained advertising measurement as a robust causal decision problem under signal losses including match-rate loss, linkability loss, attribution-window loss, aggregation-threshold suppression, randomized reporting noise, and segment-heterogeneous signal loss. Given a randomized experiment and an ambiguity set for privacy-induced degradation, the framework projects the observation-compatible fiber of clean experimental worlds onto the incrementality functional to produce certified, rejected, and unresolved decisions. The main result is a sharp decision frontier outside which uniformly valid certification or rejection is possible; inside the frontier no method can uniformly distinguish above-threshold incrementality from non-incrementality. Supporting results include finite-sample certification, sample-complexity guarantees, a minimax lower bound on information loss, and a reporting-granularity tradeoff. Empirical evaluation on the 2M-row Criteo Uplift and 64K-row Hillstrom datasets shows positive clean lift (0.00112 and 0.00495) with population certification surviving mild/severe degradation but all finite-sample stress settings remaining unresolved.

Significance. If the ambiguity-set construction and projection are valid, the work supplies a decision-theoretic layer that yields the strongest uniformly valid causal claims justifiable from degraded ad signals, together with an explicit minimax lower bound demonstrating that privacy mechanisms strictly reduce effective information. The finite-sample guarantees and real-dataset illustrations on Criteo and Hillstrom provide concrete evidence of applicability to production advertising measurement.

major comments (2)
  1. [§3 (ambiguity set definition) and Theorem 1 (sharp frontier)] The central sharpness claim (abstract and §4) requires that the ambiguity set exactly equals the set of all observation-compatible clean incrementality values under the listed degradations. Without an explicit construction of this set (or the joint distribution over heterogeneous segment losses, attribution-window truncation, and their interaction with aggregation-threshold suppression and randomized noise), it is impossible to verify that the projection yields a frontier whose minimax lower bound matches the upper bound obtained from the fiber projection.
  2. [§5 (finite-sample results) and Table 2/3 (empirical certification outcomes)] The finite-sample certification results (reported in the abstract and §5) are stated to survive mild degradation in Criteo and severe degradation in Hillstrom at the population level, yet all considered finite-sample stress settings remain unresolved once simultaneous uncertainty and reporting noise are included. The paper must clarify whether these unresolved outcomes follow from the information-theoretic bound or from post-hoc choices in the stress-test construction.
minor comments (2)
  1. [§2] Notation for the incrementality functional and the observation-compatible fiber should be introduced with a single running example before the general projection argument.
  2. [§4.3] The reporting-granularity tradeoff result would benefit from an explicit statement of the granularity parameter and how it enters the ambiguity set.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3 (ambiguity set definition) and Theorem 1 (sharp frontier)] The central sharpness claim (abstract and §4) requires that the ambiguity set exactly equals the set of all observation-compatible clean incrementality values under the listed degradations. Without an explicit construction of this set (or the joint distribution over heterogeneous segment losses, attribution-window truncation, and their interaction with aggregation-threshold suppression and randomized noise), it is impossible to verify that the projection yields a frontier whose minimax lower bound matches the upper bound obtained from the fiber projection.

    Authors: The ambiguity set in §3 is defined as the image under the incrementality functional of the fiber of all clean experimental worlds that produce the observed degraded signals when each listed privacy mechanism is applied. The fiber is formed by inverting the channels (match-rate loss, linkability loss, attribution-window truncation, aggregation-threshold suppression, randomized reporting noise, and segment-heterogeneous loss) and taking the product measure over independent components, with the joint over heterogeneous segments obtained by marginalizing the segment-specific loss parameters. The projection then yields the sharp frontier, and the matching minimax lower bound is obtained by exhibiting pairs of incrementality values inside the frontier that induce identical degraded observations. To make verification immediate, the revised manuscript will include explicit pseudocode for constructing the joint distribution and the fiber in §3. revision: yes

  2. Referee: [§5 (finite-sample results) and Table 2/3 (empirical certification outcomes)] The finite-sample certification results (reported in the abstract and §5) are stated to survive mild degradation in Criteo and severe degradation in Hillstrom at the population level, yet all considered finite-sample stress settings remain unresolved once simultaneous uncertainty and reporting noise are included. The paper must clarify whether these unresolved outcomes follow from the information-theoretic bound or from post-hoc choices in the stress-test construction.

    Authors: The unresolved finite-sample outcomes follow directly from the information-theoretic bound of Theorem 1: after degradation the effective sample size lies below the sample-complexity threshold required to resolve the frontier. The stress-test parameters are taken verbatim from the population-level degradation settings; no additional post-hoc adjustments are introduced. The revised §5 will add an explicit comparison of each stress-test sample size against the derived lower bound to make this dependence transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation projects external ambiguity set onto incrementality functional without self-reduction.

full rationale

The paper defines an ambiguity set over listed privacy degradations (match-rate loss, linkability loss, etc.) and projects the observation-compatible fiber of clean experimental worlds onto the incrementality functional to obtain a sharp decision frontier. This is a standard robust decision-theoretic construction; the frontier is the output of the projection, not equivalent to its inputs by definition. No self-citation load-bearing steps, fitted inputs renamed as predictions, or ansatz smuggling appear in the provided text. The minimax lower bound and finite-sample results are presented as supporting derivations independent of the central projection. The framework remains self-contained against external benchmarks for the ambiguity set specification.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling assumption that an ambiguity set can be specified that contains every observation-compatible clean experimental world; no free parameters or invented entities are described in the abstract.

axioms (1)
  • domain assumption An ambiguity set can be specified that contains every observation-compatible clean experimental world under the listed privacy losses.
    Invoked when the framework projects the observation-compatible fiber onto the incrementality functional.

pith-pipeline@v0.9.1-grok · 5805 in / 1236 out tokens · 24667 ms · 2026-06-28T07:55:29.145162+00:00 · methodology

discussion (0)

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