Signal Processing - January 2017 - 95
highly coordinated control of information. PP protocols allow the data owner
to control the fate of the data, instead
of chancing with the protection promised by the cloud severs. To this end,
the Defense Advanced Research Projects Agency (DARPA) has championed
a major Brandeis Program to develop
novel communication protocols so that
the uploaded data are useful only for the
intended utility but not easily repurposed
into privacy intrusion.
Utility Space
I(u;y)
Query (y)
Alice (x)
I(p;y)
Feature Space
Eve (p)
Privacy Space
Privacy communication paradigm
Note that, as depicted in Figure 2, both
Bob and Eve will receive the same data
(denoted by y), i.e., there is no key
required. Ideally, in this paradigm, the
query y should be useful to (friendly)
Bob but useless to (malicious) Eve.
More realistically, we would like to see
to it that the query may retain information as lossless as possible to Bob and,
at the same time, be as lossy as possible
against Eve.
In short, it should also be recognized
that the security protocols for data sharing are neither necessary nor sufficient
for data privacy protection. Therefore, it
is worth installing both the security and
privacy protocols for maximal protection of Internet data.
Differential privacy and
compressive privacy
Differential privacy
In the differential privacy (DP) theory
[1], a desensitizing function K is
said to provide e-DP of the data if
Pr [K (D) ! S] # e e Pr [K (Dl ) ! S ] for
all S ! Range (K) and all data sets D
and Dl differing by one entry. Note also
that the DP sensitization does not necessarily require the utility function to be
known in advance, and DP guarantees
that the distribution of the search result
should be indistinguishable (modulo a
factor of e e) with or without the missing
entry. Two types of "differential-log-likelihood" criteria, e-DP versus e-information privacy (a stronger privacy metric),
are analyzed and compared in the study
of the so-called privacy funnel in [2].
Due to the absence of systematical methods for the derivation of optimal que-
Bob (u)
Figure 2. Our study on privacy preservation involves joint optimization over three design spaces:
1) the feature space (Alice), 2) the utility space (Bob), and 3) the privacy space (Eve). Alice (the
data owner) wants to convey certain information relevant to Bob (the intended user/utilizer) while
preventing it from being eavesdropped by Eve (the intruder). In the CP paradigm, both Bob and Eve
will receive the same data (denoted by y), i.e., there is no key required. We propose a query encoding scheme which is 1) information preserving from the utility's perspective but 2) information lossy
from the perspective of privacy. Collectively, such a scheme is called CP. This article explores the
utility-privacy tradeoff analysis via comparing the I (u; y) and I (p; y).
ries, however, the DP approach remains
somewhat unwieldy for many real-world
applications. This prompts us to explore
other desensitizing methods for privacy
preservation.
Compressive privacy
The query, denoted by y, is represented
by y = f (x, f) where x denotes the feature vector representing the original data
and f is an independent random noise.
Unlike DP, the CP approach allows the
query to be tailor-designed according
to the known utility and privacy models. As depicted in Figure 2, we propose
a query encoding scheme that is 1)
information preserving from the utility's perspective but 2) information lossy
from the privacy's perspective. Collectively, such a scheme is called CP. This
article explores the tradeoff analysis
between the utility mutual information
(between y and Bob) and its privacy
counterpart (between y and Eve). This
is in a sharp contrast to most machinelearning problems, where the design
goal is exclusively focused only on the
utility information.
Scope and prerequisite of the article
This article explores the rich synergy
between information theory, estimation
theory, and machine learning and, ultimately, develops a PP methodology-CP.
IEEE Signal Processing Magazine
|
January 2017
|
While formal courses on information
theory, estimation theory, and machine
learning are highly recommended for
advanced and serious researchers, we
shall nevertheless review the basic materials for novice readers, hopefully making the article somewhat self-contained.
Information and estimation theory
Let the original data (owned by Alice)
be represented by a vector space containing M-dimensional random vectors
x = [x 1, x 2, f, x M] T .
To convey information concerning x,
the design of PP query y must be based
on joint consideration of both the utility
maximization (for Bob) and the privacy
protection (against Eve). Mathematically,
■■ Utility function: The utility function is denoted by u (x).
■■ Privacy function: The privacy function (i.e., cost function) is denoted by
p (x).
Prior work on non-Gaussian models
A natural formulation for the utility-privacy tradeoff analysis involves optimizing I (u; y) [respectively, I (p; y)] while
setting a bound on I (p; y) [respectively,
I (u; y)] . More specifically:
■■ Information bottleneck (IB) [4]. In
the IB scenarios, it is assumed that
95
Table of Contents for the Digital Edition of Signal Processing - January 2017
Signal Processing - January 2017 - Cover1
Signal Processing - January 2017 - Cover2
Signal Processing - January 2017 - 1
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Signal Processing - January 2017 - Cover3
Signal Processing - January 2017 - Cover4
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