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  1. Book ; Online: A Unified Characterization of Private Learnability via Graph Theory

    Alon, Noga / Moran, Shay / Schefler, Hilla / Yehudayoff, Amir

    2023  

    Abstract: We provide a unified framework for characterizing pure and approximate differentially private (DP) learnabiliity. The framework uses the language of graph theory: for a concept class $\mathcal{H}$, we define the contradiction graph $G$ of $\mathcal{H}$. ... ...

    Abstract We provide a unified framework for characterizing pure and approximate differentially private (DP) learnabiliity. The framework uses the language of graph theory: for a concept class $\mathcal{H}$, we define the contradiction graph $G$ of $\mathcal{H}$. It vertices are realizable datasets, and two datasets $S,S'$ are connected by an edge if they contradict each other (i.e., there is a point $x$ that is labeled differently in $S$ and $S'$). Our main finding is that the combinatorial structure of $G$ is deeply related to learning $\mathcal{H}$ under DP. Learning $\mathcal{H}$ under pure DP is captured by the fractional clique number of $G$. Learning $\mathcal{H}$ under approximate DP is captured by the clique number of $G$. Consequently, we identify graph-theoretic dimensions that characterize DP learnability: the clique dimension and fractional clique dimension. Along the way, we reveal properties of the contradiction graph which may be of independent interest. We also suggest several open questions and directions for future research.

    Comment: v1.2, acknowledgements
    Keywords Computer Science - Machine Learning
    Subject code 511
    Publishing date 2023-04-08
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Book ; Online: The Bayesian Stability Zoo

    Moran, Shay / Schefler, Hilla / Shafer, Jonathan

    2023  

    Abstract: We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian stability. ... ...

    Abstract We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian stability. Within each family, we establish equivalences between various definitions, encompassing approximate differential privacy, pure differential privacy, replicability, global stability, perfect generalization, TV stability, mutual information stability, KL-divergence stability, and R\'enyi-divergence stability. Along the way, we prove boosting results that enable the amplification of the stability of a learning rule. This work is a step towards a more systematic taxonomy of stability notions in learning theory, which can promote clarity and an improved understanding of an array of stability concepts that have emerged in recent years.

    Comment: v2, minor typo fix
    Keywords Computer Science - Machine Learning
    Publishing date 2023-10-27
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

    More links

    Kategorien

    Inter-library loan at ZB MED

    Your chosen title can be delivered directly to ZB MED Cologne location if you are registered as a user at ZB MED Cologne.

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