This paper considers the problem of differentially private semi-supervised
transfer learning. The notion of membership-mapping is developed using measure
theory basis to learn data representation via a fuzzy membership function. An
alternative conception of deep autoencoder, referred to as Conditionally Deep
Membership-Mapping Autoencoder (CDMMA) (that consists of a nested compositions
of membership-mappings), is considered. Under practice-oriented settings, an
analytical solution for the learning of CDMFA can be derived by means of
variational optimization. The paper proposes a transfer learning approach that
combines CDMMA with a tailored noise adding mechanism to achieve a given level
of privacy-loss bound with the minimum perturbation of the data. Numerous
experiments were carried out using MNIST, USPS, Office, and Caltech256 datasets
to verify the competitive robust performance of the proposed methodology.

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