Inferentially-Private Private Information

Shuaiqi WangShuran ZhengZinan LinGiulia FantiZhiwei Steven Wu

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Establishes a geometric framework and efficient algorithms to construct Blackwell-optimal data release mechanisms that maximize utility while bounding information leakage against Bayesian adversaries.

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Organizations often need to share public information that is statistically correlated with sensitive, private data. For instance, quarterly earnings reports may inadvertently reveal proprietary business strategies. Strict privacy standards that forbid any leakage of secrets often destroy the utility of the released data, whereas releasing raw data compromises confidentiality. Inferential privacy addresses this balance by formally bounding the Bayesian inferential power an observer can gain about sensitive secrets after seeing a released signal.

The article aims to design optimal information disclosure mechanisms that maximize the informativeness and utility of released signals for downstream decision-makers while rigorously adhering to inferential privacy constraints.

To achieve this, the authors used a mathematical and geometric approach grounded in the classical Blackwell ordering framework, which ranks information structures by how well they serve arbitrary convex decision-making utility functions. They evaluated scenarios involving a binary target state, known prior probability distributions, and both binary and multi-valued secret states. The analysis establishes structural bounds and optimality conditions without relying on empirical data collection.

The investigation produced four key findings. First, the authors geometrically proved that any Blackwell-optimal release mechanism needs at most three times the number of secrets plus one distinct output signals, dramatically bounding an otherwise infinite search space. Second, for binary secrets, the authors derived an exact, closed-form disclosure mechanism that requires at most four signals and universally maximizes decision-maker utility across all convex reward functions. Third, relaxing a zero-leakage perfect privacy constraint to a modest inferential privacy parameter yields massive utility gains, demonstrating utility improvements of two- to five-fold under common settings. Fourth, for non-binary secrets, the article shows that optimal release mechanisms can be computed in polynomial time via linear programming.

These findings demonstrate that organizations do not need to choose between total confidentiality and severe utility loss. By adopting a calibrated inferential privacy threshold, data holders can dramatically boost the usefulness of shared data—cutting operational inefficiencies—while maintaining strict mathematical bounds on privacy risks. Furthermore, the universal optimality of the binary solution means institutions can deploy a single signal mechanism that remains optimal regardless of the diverse reward structures of downstream users.

Decision-makers facing privacy-constrained data sharing should evaluate their tolerance for inferential leakage and transition away from zero-leakage requirements toward tunable inferential privacy bounds. For settings with binary secrets, organizations can immediately deploy the closed-form mechanism. For complex, multi-secret settings, technical teams should implement the linear programming framework.

Confidence in these mathematical findings is high, but practical deployment requires noting two key boundary conditions. The models assume that the prior joint distribution between states and secrets is known precisely, and they focus primarily on binary target states. Organizations should verify the stability of their prior correlation estimates or conduct pilot evaluations before applying the mechanisms in environments where data distributions are highly uncertain or non-stationary.

Carnegie Mellon University Microsoft Tsinghua University bayesian methods differential privacies individual privacy inferential privacy private Blackwell optimal information structure differential privacy

arXiv: 2410.17095

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Abstract

Information disclosure can compromise privacy when revealed information is correlated with private information. We consider the notion of inferential privacy, which measures privacy leakage by bounding the inferential power a Bayesian adversary can gain by observing a released signal. Our goal is to devise an inferentially-private private information structure that maximizes the informativeness of the released signal, following the Blackwell ordering principle, while adhering to inferential privacy constraints. To achieve this, we devise an efficient release mechanism that achieves the inferentially-private Blackwell optimal private information structure for the setting where the private information is binary. Additionally, we propose a programming approach to compute the optimal structure for general cases given the utility function. The design of our mechanisms builds on our geometric characterization of the Blackwell-optimal disclosure mechanisms under privacy constraints, which may be of independent interest.

Topics

bayesian methods differential privacies individual privacy private information utility functions optimal structures inference

Keywords

inferential privacy private Blackwell optimal information structure differential privacy optimal information disclosure Pufferfish privacy Bayesian persuasion Blackwell optimality mean-preserving spread secret-state structure

1 Introduction
2 Problem Formulation
2.1 Privacy Metric
2.2 Informativeness and Utility
3 Geometric Visualization of Information Structures
4 Geometric characterization of IP Blackwell-Optimal Solutions
4.1 Geometric characterization of ℙ⁡(Y|S,T)\mathbb{P}\left(Y|S,T\right)
4.2 Geometric characterization of ℙ⁡(T|S)\mathbb{P}\left(T|S\right)
4.3 Upper left characterization
4.4 Cardinality of the Output Signal Set
5 Mechanism Design with Binary Secret
5.1 Geometric characterization with binary secret
5.2 Mechanism design
5.2.1 Step 1: Determine the Blackwell-Optimal Solution
5.2.2 Step 2: Determine the information disclosure mechanism
5.2.3 Utility gains under inferential privacy
6 Mechanism Design for n>2n>2 Secrets
7 Conclusion
References
A Proof of Lemma 4.1
B Proof of Lemma 4.2
C Proof of Lemma 4.3
D Proof of Lemma 5.1
E Proof of Lemma 5.2
F Proof of Theorem 5.1

Knowls

Knowl 1 — Closed-Form Inferentially-Private Blackwell-Optimal Information Structure for Binary Secrets
theoretical result
Let $Y \in \{0, 1\}$ be a binary state of interest and $S \in \{s_0, s_1\}$ be a binary sensitive secret with known joint prior distribution $\mathbb{P}(S, Y)$ . Assume without loss of generality that $q_{s_0} \ge q_{s_1}$ , where $q_s = \mathbb{P}(Y = 1 \mid S = s)$ for each $s \in \{s_0, s_1\}$ . Let privacy budget be $\varepsilon > 0$ . Define the likelihood ratios:

$R_1 = \frac{q_{s_0}}{q_{s_1}}, \qquad R_2 = \frac{1 - q_{s_1}}{1 - q_{s_0}}$

Let $l_i^{(j)} = \mathbb{P}(T = t_i \mid S = s_j)$ for output signals $t_i \in \mathcal{T} = \{t_1, t_2, t_3, t_4\}$ and $j \in \{0, 1\}$ . The boundary conditional probabilities are fixed to $l_1^{(1)} = q_{s_1}$ and $l_4^{(0)} = 1 - q_{s_0}$ , and the inferential privacy constraints bind on intermediate signals via $l_2^{(0)} = e^\varepsilon l_2^{(1)}$ and $l_3^{(1)} = e^\varepsilon l_3^{(0)}$ .

The unique (up to equivalent signal mergers) $\varepsilon$ -inferentially-private Blackwell-optimal information structure universally maximizes the expected utility $\mathbb{E}_T[u(q_T)]$ for every convex utility function $u$ of the posterior $q_t = \mathbb{P}(Y = 1 \mid T = t)$ , with values of $(l_2^{(1)}, l_3^{(1)})$ partitioned into four parameter regimes:
1. Regime 1 ( $R_1 \le e^\varepsilon$ and $R_2 \le e^\varepsilon$ ): $l_2^{(1)} = 0, \qquad l_3^{(1)} = 0$ (Only 2 signals needed: $\mathcal{T} = \{t_1, t_4\}$ , with $l_1^{(0)} = q_{s_0}$ and $l_4^{(1)} = 1 - q_{s_1}$ ).
2. Regime 2 ( $R_1 \le e^\varepsilon, R_2 > e^\varepsilon$ , or $R_1 > e^\varepsilon, R_2 > e^\varepsilon, q_{s_1} \ge \frac{1}{1 + e^\varepsilon}$ ): $l_2^{(1)} = 0, \qquad l_3^{(1)} = 1 - q_{s_1} - e^\varepsilon (1 - q_{s_0})$ (3 signals needed: $\mathcal{T} = \{t_1, t_3, t_4\}$ , with $l_1^{(0)} = 1 - e^{-\varepsilon}(1 - q_{s_1})$ and $l_4^{(1)} = e^\varepsilon(1 - q_{s_0})$ ).
3. Regime 3 ( $R_1 > e^\varepsilon, R_2 \le e^\varepsilon$ , or $R_1 > e^\varepsilon, R_2 > e^\varepsilon, q_{s_0} \le \frac{1}{1 + e^{-\varepsilon}}$ ): $l_2^{(1)} = e^{-\varepsilon} q_{s_0} - q_{s_1}, \qquad l_3^{(1)} = 0$ (3 signals needed: $\mathcal{T} = \{t_1, t_2, t_4\}$ , with $l_1^{(0)} = e^\varepsilon q_{s_1}$ and $l_4^{(1)} = 1 - e^{-\varepsilon} q_{s_0}$ ).
4. Regime 4 ( $R_1 > e^\varepsilon, R_2 > e^\varepsilon, q_{s_0} > \frac{1}{1 + e^{-\varepsilon}}$ , and $q_{s_1} < \frac{1}{1 + e^\varepsilon}$ ): $l_2^{(1)} = \frac{1}{e^\varepsilon + 1} - q_{s_1}, \qquad l_3^{(1)} = e^\varepsilon q_{s_0} - \frac{e^{2\varepsilon}}{e^\varepsilon + 1}$ (All 4 signals needed: $\mathcal{T} = \{t_1, t_2, t_3, t_4\}$ , with $l_1^{(0)} = e^\varepsilon q_{s_1}$ and $l_4^{(1)} = e^\varepsilon(1 - q_{s_0})$ ).
Knowl 2 — Universally Optimal Disclosure Mechanism for Binary Secrets
model/method
For a binary state $Y \in \{0, 1\}$ and binary secret $S \in \{s_0, s_1\}$ with known prior $\mathbb{P}(S, Y)$ satisfying $q_{s_0} \ge q_{s_1}$ where $q_s = \mathbb{P}(Y = 1 \mid S = s)$ , the universally optimal $\varepsilon$ -inferentially-private disclosure mechanism releases a signal $T \in \{t_1, t_2, t_3, t_4\}$ according to the conditional distribution $\mathbb{P}(T \mid S, Y)$ :

$\mathbb{P}(T = t_1 \mid S = s_1, Y = 1) = 1$

$\mathbb{P}(T = t_i \mid S = s_0, Y = 1) = \frac{l_i^{(0)}}{q_{s_0}}, \quad \forall i \in \{1, 2, 3\}$

$\mathbb{P}(T = t_4 \mid S = s_0, Y = 0) = 1$

$\mathbb{P}(T = t_i \mid S = s_1, Y = 0) = \frac{l_i^{(1)}}{1 - q_{s_1}}, \quad \forall i \in \{2, 3, 4\}$

where the cell conditional widths $l_i^{(j)} = \mathbb{P}(T = t_i \mid S = s_j)$ are determined by the closed-form Blackwell-optimal information structure for binary secrets. This mechanism fully reveals the state ( $Y=1$ deterministically on $t_1$ , and $Y=0$ deterministically on $t_4$ ) when $(S = s_1, Y = 1)$ or $(S = s_0, Y = 0)$ , and is unique up to merging equivalent output signals.
Knowl 3 — Geometric Characterization of Inferentially-Private Blackwell-Optimal Information Structures
theoretical result
Let $Y \in \{0, 1\}$ be a binary state and $S \in \mathcal{S} = \{s_1, \dots, s_n\}$ be a finite secret set ordered such that $q_{s_1} \ge q_{s_2} \ge \dots \ge q_{s_n}$ , where $q_s = \mathbb{P}(Y = 1 \mid S = s)$ . Let $T \in \mathcal{T} = \{t_1, \dots, t_k\}$ be the output signal set ordered by decreasing state posteriors $q_{t_1} \ge q_{t_2} \ge \dots \ge q_{t_k}$ , where $q_t = \mathbb{P}(Y = 1 \mid T = t)$ . Let $\tilde{\mathcal{T}} = \{t \in \mathcal{T} : q_t \notin \{0, 1\}\}$ be the set of uncertain output signals.

Every $\varepsilon$ -inferentially-private Blackwell-optimal information structure $\mathbb{P}(S, Y, T)$ satisfies the following structural properties:
1. Deterministic state posteriors given secret and signal: For every secret $s \in \mathcal{S}$ and signal $t \in \mathcal{T}$ , $\mathbb{P}(Y = 1 \mid S = s, T = t) \in \{0, 1\}$
2. Binding privacy bounds on uncertain signals: For every $t \in \tilde{\mathcal{T}}$ , let $L_t = \min_{s \in \mathcal{S}} \mathbb{P}(T = t \mid S = s)$ and $H_t = \max_{s \in \mathcal{S}} \mathbb{P}(T = t \mid S = s)$ . Then $H_t = e^\varepsilon L_t$ , and for all $s \in \mathcal{S}$ , $\mathbb{P}(T = t \mid S = s) \in \{L_t, H_t\}$
3. Monotonic regions in grid space: Define the cell sets $\mathcal{A} = \{(s, t) : \mathbb{P}(Y = 1 \mid S = s, T = t) = 1, s \in \mathcal{S}, t \in \mathcal{T}\}$ $\mathcal{B} = \{(s, t) \in \mathcal{A} : \mathbb{P}(T = t \mid S = s) = H_t, s \in \mathcal{S}, t \in \tilde{\mathcal{T}}\}$ $\mathcal{C} = \{(s, t) \notin \mathcal{A} : \mathbb{P}(T = t \mid S = s) = H_t, s \in \mathcal{S}, t \in \tilde{\mathcal{T}}\}$ Then:
  - $\mathcal{A}$ is $\mathcal{T}$ -upper-left: $(s_i, t_j) \in \mathcal{A} \implies (s_k, t_l) \in \mathcal{A}$ for all $k \le i, l \le j$ .
  - $\mathcal{B}$ is $\tilde{\mathcal{T}}$ -upper-left: $(s_i, t_j) \in \mathcal{B} \implies (s_k, t_l) \in \mathcal{B}$ for all $k \le i, l \le j$ .
  - $\mathcal{C}$ is $\tilde{\mathcal{T}}$ -lower-right: $(s_i, t_j) \in \mathcal{C} \implies (s_k, t_l) \in \mathcal{C}$ for all $k \ge i, l \ge j$ .
Knowl 4 — Signal Set Cardinality Bound for IP Blackwell-Optimal Information Structures
theoretical result
For any joint distribution $\mathbb{P}(S, Y)$ over a binary state $Y \in \{0, 1\}$ and a finite secret $S \in \mathcal{S}$ , and for any inferential privacy level $\varepsilon > 0$ , every $\varepsilon$ -inferentially-private Blackwell-optimal information structure has an equivalent information structure $\mathbb{P}(S, Y, T)$ whose output signal space satisfies:

$|\mathcal{T}| \le 3|\mathcal{S}| + 1$

Equivalence means the compressed structure is obtained by merging signals $t \in \mathcal{T}$ that share identical state posteriors $\mathbb{P}(Y = 1 \mid T = t)$ and conditional secret probabilities $\mathbb{P}(S = s \mid T = t)$ for all $s \in \mathcal{S}$ , preserving Blackwell dominance and expected utility under all convex utility functions.
Knowl 5 — Inferential Privacy Definition for Information Disclosure
definition
An information disclosure structure $\mathbb{P}(S, Y, T)$ —where $Y \in \{0, 1\}$ is the target state, $S \in \mathcal{S}$ is a finite sensitive secret with known prior $\mathbb{P}(S, Y)$ , and $T \in \mathcal{T}$ is the released signal—is $\varepsilon$ -inferentially-private ( $\varepsilon$ -IP) about $S$ for privacy parameter $\varepsilon \ge 0$ if for all secrets $s_1, s_2 \in \mathcal{S}$ and all output signals $t \in \mathcal{T}$ :

$\frac{\mathbb{P}(S = s_1 \mid T = t)}{\mathbb{P}(S = s_2 \mid T = t)} \le e^\varepsilon \frac{\mathbb{P}(S = s_1)}{\mathbb{P}(S = s_2)}$

This condition is mathematically equivalent to bounding the likelihood ratio of the signal conditioned on any pair of secrets:

$\frac{\mathbb{P}(T = t \mid S = s_1)}{\mathbb{P}(T = t \mid S = s_2)} \le e^\varepsilon, \quad \forall s_1, s_2 \in \mathcal{S}, \; t \in \mathcal{T}$

When $\varepsilon = 0$ , this definition corresponds to perfect inferential privacy (strict statistical independence between $S$ and $T$ ). When the prior distribution $\mathbb{P}(S, Y)$ is fixed and known, $\varepsilon$ -inferential privacy is equivalent to pufferfish privacy with $\delta = 0$ and attribute privacy.
Knowl 6 — Arbitrarily Large Utility Gain of Inferential Privacy over Perfect Privacy
theoretical result
Let $U_0$ denote the maximum achievable expected utility under the perfect privacy constraint ( $\varepsilon = 0$ ), and $U_\varepsilon$ denote the maximum achievable expected utility under an $\varepsilon$ -inferential privacy constraint with $\varepsilon > 0$ .

For any $\varepsilon > 0$ and any constant $\Delta \in \mathbb{R}^+$ , there exists a joint distribution $\mathbb{P}(S, Y)$ and an $L$ -Lipschitz convex utility function $u$ with Lipschitz constant

$L \le 3\Delta \left(1 + \frac{2}{e^\varepsilon - 1}\right)$

such that the expected utility gap satisfies:

$U_\varepsilon - U_0 \ge \Delta$

Specifically, this holds for the symmetric secret prior $\mathbb{P}(S = s_0) = \mathbb{P}(S = s_1) = 1/2$ with conditional probabilities $q_{s_0} = \frac{e^\varepsilon}{1 + e^\varepsilon}$ and $q_{s_1} = \frac{1}{1 + e^\varepsilon}$ , paired with the piecewise linear convex utility $u(q_t) = |L q_t - L/2|$ .
Knowl 7 — Linear Programming Method for Optimal Disclosure with Non-Binary Secrets
algorithm
For general non-binary secrets $\mathcal{S} = \{s_1, \dots, s_n\}$ with $n > 2$ , sorted such that $q_{s_1} \ge \dots \ge q_{s_n}$ , an optimal $\varepsilon$ -inferentially-private disclosure mechanism for a specified convex utility function $u$ is computed by solving a set of linear programs over discrete cell-width indicator patterns $c_{ik}^{(j)} \in \{1, e^\varepsilon\}$ .
Input: utility function $u$ , prior distribution $\mathbb{P}(S, Y)$ , inferential privacy level $\varepsilon$
Output: disclosure mechanism $\mathbb{P}(T \mid S, Y)$
Enumerate all configurations of $c_{ik}^{(j)} \in \{1, e^\varepsilon\}$ for $i \in \{2, \dots, n\}$ , $j \in [n]$ , $k \in [3n]$ satisfying:
     $c_{ik}^{(j)} \le c_{i'k'}^{(j')}$ for all $j \in [n+1-i], j' \le j, i'k' \preceq ik$
     $c_{ik}^{(j)} \le c_{i'k'}^{(j')}$ for all $j \in [n] \setminus [n+1-i], j' \ge j, i'k' \succeq ik$
for each enumerated configuration of $c_{ik}^{(j)}$ do:
    Solve the linear program:
        Maximize $p_{t_1} u(1) + p_{t_{n+1}} u(0) + \sum_{i=2}^n \sum_{k=1}^{3n} p_{t_{ik}} u(q_{t_{ik}})$
        subject to:
             $p_{t_1} = \sum_{j=1}^n \mathbb{P}(S = s_j) l_1^{(j)}$
             $p_{t_{n+1}} = \sum_{j=1}^n \mathbb{P}(S = s_j) l_{n+1}^{(j)}$
             $p_{t_{ik}} = \sum_{j=1}^n \mathbb{P}(S = s_j) l_{ik}^{(j)}$ for all $i \in \{2, \dots, n\}, k \in [3n]$
             $l_1^{(j)} = r_1^{(j)} l_1^{(n)}$ with $l_1^{(n)} = q_{s_n}, r_1^{(j)} \in [e^{-\varepsilon}, e^\varepsilon]$ for $j \in [n-1]$
             $l_{n+1}^{(j)} = r_{n+1}^{(j)} l_{n+1}^{(1)}$ with $l_{n+1}^{(1)} = 1 - q_{s_1}, r_{n+1}^{(j)} \in [e^{-\varepsilon}, e^\varepsilon]$ for $j \in \{2, \dots, n\}$
             $l_{ik}^{(j)} = \frac{c_{ik}^{(j)}}{c_{ik}^{(n)}} l_{ik}^{(n)}$ with $l_{ik}^{(n)} \ge 0$ for all $j \in [n-1]$
             $l_1^{(j)} + l_{n+1}^{(j)} + \sum_{i=2}^n \sum_{k=1}^{3n} l_{ik}^{(j)} = 1$ for all $j \in [n]$
             $l_1^{(j)} + \sum_{i=2}^{n+1-j} \sum_{k=1}^{3n} l_{ik}^{(j)} = q_{s_j}$ for all $j \in [n]$
            where $q_{t_{ik}} = \frac{\sum_{j=1}^{n+1-i} \mathbb{P}(S = s_j) c_{ik}^{(j)}}{\sum_{j=1}^n \mathbb{P}(S = s_j) c_{ik}^{(j)}}$ is constant in each program
Select the solution $(\hat{l}_1^{(j)}, \hat{l}_{n+1}^{(j)}, \hat{l}_{ik}^{(j)})$ that achieves the maximum objective value.
Construct $\mathbb{P}(T \mid S, Y)$ :
     $\mathbb{P}(T = t_1 \mid S = s_j, Y = 1) = \hat{l}_1^{(j)} / q_{s_j}$ for $j \in [n]$
     $\mathbb{P}(T = t_{ik} \mid S = s_j, Y = 1) = \hat{l}_{ik}^{(j)} / q_{s_j}$ for $j \in [n-1], i \in \{2, \dots, n+1-j\}, k \in [3n]$
     $\mathbb{P}(T = t_{n+1} \mid S = s_j, Y = 0) = \hat{l}_{n+1}^{(j)} / (1 - q_{s_j})$ for $j \in [n]$
     $\mathbb{P}(T = t_{ik} \mid S = s_j, Y = 0) = \hat{l}_{ik}^{(j)} / (1 - q_{s_j})$ for $j \in [n] \setminus \{1\}, i \in \{n+2-j, \dots, n\}, k \in [3n]$
return $\mathbb{P}(T \mid S, Y)$
Knowl 8 — Empirical Utility Gains under Relaxed Inferential Privacy
empirical result
Numerical evaluations of the optimal disclosure mechanism for binary secrets $S \in \{s_0, s_1\}$ with prior $\mathbb{P}(S=s_0) = \mathbb{P}(S=s_1) = 0.5$ show substantial utility improvements when relaxing from perfect privacy ( $\varepsilon = 0$ ) to small inferential privacy parameters $\varepsilon$ :
- Moderate imbalance ( $q_{s_0} = 0.75, q_{s_1} = 0.25$ ): Across piecewise linear ( $u(q_t) = |2q_t - 1|$ ), quadratic ( $u(q_t) = (2q_t - 1)^2$ ), and shifted negative binary entropy ( $u(q_t) = q_t \log q_t + (1 - q_t) \log(1 - q_t) + 1$ ) utility functions, relaxing the privacy parameter to $\varepsilon = \ln 3 \approx 1.10$ increases expected utility by up to $1.8\times$ relative to $\varepsilon = 0$ , reaching approximately $2.0\times$ as $\varepsilon \to 2 \ln 3$ .
- High imbalance ( $q_{s_0} = 0.9, q_{s_1} = 0.1$ ): Relaxing privacy to $\varepsilon = \ln 3$ yields utility gains of $2\times$ to $2.8\times$ , and relaxing to $\varepsilon = 2 \ln 3 \approx 2.20$ yields utility gains of up to $5\times$ compared to the perfect privacy baseline.
Knowl 9 — Assumptions and Scalability Limitations of the Privacy Disclosure Framework
limitation
The theoretical and algorithmic framework for inferentially-private information disclosure has several key structural and computational limitations:
1. Known prior assumption: The joint prior distribution $\mathbb{P}(S, Y)$ between the secret and the target state is assumed to be fixed and exactly known a priori to both the data holder and the Bayesian adversary.
2. Binary target state restriction: The universal Blackwell-optimality characterization and closed-form solutions are developed specifically for a single binary target variable $Y \in \{0, 1\}$ .
3. Exponential enumeration for non-binary secrets: For secret spaces with $n = |\mathcal{S}| > 2$ , no closed-form universal Blackwell-optimal mechanism is established; computing the optimal structure for a given utility function requires enumerating indicator configurations whose cardinality grows exponentially in $n$ .

Coverage note — None was omitted; all key definitions, geometric characterizations, cardinality bounds, closed-form binary solutions, multi-secret linear programs, utility gain bounds, empirical results, and stated limitations are fully covered.

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Citation

MLA

Wang, S., et al. “Inferentially-Private Private Information”. arXiv, 2024, http://arxiv.org/abs/2410.17095v2.

APA

Wang, S., Zheng, S., Lin, Z., Fanti, G., & Wu, Z. S. (2024). Inferentially-Private Private Information. arXiv. http://arxiv.org/abs/2410.17095v2

Chicago

Wang, S., S. Zheng, Z. Lin, G. Fanti, and Z. S. Wu. 2024. “Inferentially-Private Private Information”. arXiv. http://arxiv.org/abs/2410.17095v2.

Harvard

Wang, S. et al. (2024) “Inferentially-Private Private Information”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2410.17095v2.

Vancouver

1. Wang S, Zheng S, Lin Z, Fanti G, Wu ZS (2024) Inferentially-Private Private Information. arXiv

BibTeX

@article{wang2024inferentially,
  title = {Inferentially-Private Private Information},
  author = {Wang, Shuaiqi and Zheng, Shuran and Lin, Zinan and Fanti, Giulia and Wu, Zhiwei Steven},
  year = {2024},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2410.17095v2},
  eprint = {2410.17095}
}

Metadata:arXiv

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Inferentially-Private Private Information

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Closed-Form Inferentially-Private Blackwell-Optimal Information Structure for Binary Secrets

Knowl 2 — Universally Optimal Disclosure Mechanism for Binary Secrets

Knowl 3 — Geometric Characterization of Inferentially-Private Blackwell-Optimal Information Structures

Knowl 4 — Signal Set Cardinality Bound for IP Blackwell-Optimal Information Structures

Knowl 5 — Inferential Privacy Definition for Information Disclosure

Knowl 6 — Arbitrarily Large Utility Gain of Inferential Privacy over Perfect Privacy

Knowl 7 — Linear Programming Method for Optimal Disclosure with Non-Binary Secrets

Knowl 8 — Empirical Utility Gains under Relaxed Inferential Privacy

Knowl 9 — Assumptions and Scalability Limitations of the Privacy Disclosure Framework

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