A Cross Entropy Interpretation of R{é}nyi Entropy for $α$-leakage
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929226032087040 |
|---|---|
| author | Ding, Ni Zarrabian, Mohammad Amin Sadeghi, Parastoo |
| author_facet | Ding, Ni Zarrabian, Mohammad Amin Sadeghi, Parastoo |
| contents | This paper proposes an $α$-leakage measure for $α\in[0,\infty)$ by a cross entropy interpretation of R{é}nyi entropy. While Rényi entropy was originally defined as an $f$-mean for $f(t) = \exp((1-α)t)$, we reveal that it is also a $\tilde{f}$-mean cross entropy measure for $\tilde{f}(t) = \exp(\frac{1-α}αt)$. Minimizing this Rényi cross-entropy gives Rényi entropy, by which the prior and posterior uncertainty measures are defined corresponding to the adversary's knowledge gain on sensitive attribute before and after data release, respectively. The $α$-leakage is proposed as the difference between $\tilde{f}$-mean prior and posterior uncertainty measures, which is exactly the Arimoto mutual information. This not only extends the existing $α$-leakage from $α\in [1,\infty)$ to the overall R{é}nyi order range $α\in [0,\infty)$ in a well-founded way with $α=0$ referring to nonstochastic leakage, but also reveals that the existing maximal leakage is a $\tilde{f}$-mean of an elementary $α$-leakage for all $α\in [0,\infty)$, which generalizes the existing pointwise maximal leakage. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15202 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Cross Entropy Interpretation of R{é}nyi Entropy for $α$-leakage Ding, Ni Zarrabian, Mohammad Amin Sadeghi, Parastoo Information Theory This paper proposes an $α$-leakage measure for $α\in[0,\infty)$ by a cross entropy interpretation of R{é}nyi entropy. While Rényi entropy was originally defined as an $f$-mean for $f(t) = \exp((1-α)t)$, we reveal that it is also a $\tilde{f}$-mean cross entropy measure for $\tilde{f}(t) = \exp(\frac{1-α}αt)$. Minimizing this Rényi cross-entropy gives Rényi entropy, by which the prior and posterior uncertainty measures are defined corresponding to the adversary's knowledge gain on sensitive attribute before and after data release, respectively. The $α$-leakage is proposed as the difference between $\tilde{f}$-mean prior and posterior uncertainty measures, which is exactly the Arimoto mutual information. This not only extends the existing $α$-leakage from $α\in [1,\infty)$ to the overall R{é}nyi order range $α\in [0,\infty)$ in a well-founded way with $α=0$ referring to nonstochastic leakage, but also reveals that the existing maximal leakage is a $\tilde{f}$-mean of an elementary $α$-leakage for all $α\in [0,\infty)$, which generalizes the existing pointwise maximal leakage. |
| title | A Cross Entropy Interpretation of R{é}nyi Entropy for $α$-leakage |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.15202 |