Compressed Sensing for Privacy-Preserving Data Processing

Abstract

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Sketching Data Sets for Large-Scale Learning: Keeping only what you need

“…Here, > 0 plays the role of a privacy level: smaller implies a stronger privacy guarantee. In words, (49) says that, when is small, the densities of s(X ) and s(X ) are almost indistinguishable, as depicted in Figure 14.…”

“…where we find it helpful to explicitly denote the dependence of the dataset X . We will assume that the realization Φ(•) of the random feature map is fixed and publicly known, in contrast to other approaches like [49,50] that use linear mixing matrices as encryption keys to ensure privacy preservation. As a result, when we treat s(X ) as random, this is due to the randomness in v, not the randomness in Φ(•) or X .…”

“…Thus, when (49) holds with small , it is fundamentally difficult for an adversary to determine whether x j or x j was present in the sketch. Even if the adversary had non-trivial prior knowledge of the true hypothesis (as in so-called "linkage attacks," which make use of a second public dataset to which the target user contributed), (49) implies that-for any method-the probability of recovering the true hypothesis from the sketch is only slightly higher than that which is achievable without observing the sketch.…”

Compressive learning with privacy guarantees

“…The adversary is non-interactive, in that they have full access to the sketch of the dataset, or to sketches of disjoint subsets of the dataset if the latter is distributed across multiple devices (Figure 2), but cannot query the curator(s) for more data. Whereas there exist some approaches that use random projection matrices as encryption keys [51], we here assume that the feature map and the matrix of frequencies Ω are publicly known (similarly to, e.g., [32]). This is essential for analysts, who need to know the feature map in order to learn from the sketch.…”

Method of Lagrange Multipliers for Normalized Zero Norm Minimization

“…e decomposition of the coefficient vector can be seen as a superposition of dictionary elements with a remaining term [2]. Compressed sensing was an emerging field that spans many applications in science and engineering, e.g., imaging and vision [3], photonic mixer device [4], electronic defense [5], security and cryptosystem [6], radar [7,8], earth observation [9], wireless networks [10,11], biometric watermarking [12], and healthcare [13].…”