  Preserving privacy of continuous and/or high-dimensional data such as images,
videos and audios, can be challenging with syntactic anonymization methods
which are designed for discrete attributes. Differential privacy, which
provides a more formal definition of privacy, has shown more success in
sanitizing continuous data. However, both syntactic and differential privacy
are susceptible to inference attacks, i.e., an adversary can accurately infer
sensitive attributes from sanitized data. The paper proposes a novel
filter-based mechanism which preserves privacy of continuous and
high-dimensional attributes against inference attacks. Finding the optimal
utility-privacy tradeoff is formulated as a min-diff-max optimization problem.
The paper provides an ERM-like analysis of the generalization error and also a
practical algorithm to perform the optimization. In addition, the paper
proposes an extension that combines minimax filter and differentially-private
noisy mechanism. Advantages of the method over purely noisy mechanisms is
explained and demonstrated with examples. Experiments with several real-world
tasks including facial expression classification, speech emotion
classification, and activity classification from motion, show that the minimax
filter can simultaneously achieve similar or better target task accuracy and
lower inference accuracy, often significantly lower than previous methods.
