[Busec] Seminar today: Local Differential Privacy for Physical Sensor Data and Sparse Recovery

Yilei Chen chenyl at bu.edu
Wed Oct 4 00:24:07 EDT 2017

Local Differential Privacy for Physical Sensor Data and Sparse Recovery
Audra McMillan, University of Michigan
Wednesday October 4, 2017, ** 9:45 am - 10:45 am **
BU Computer Science, ** Room MCS 148 **
111 Cummington St, Boston MA 02215


In recent years, wireless technology has allowed the power of lightweight
(thermal, light, motion, etc.) sensors to be explored. This data offers
important benefits to society. For example, thermal sensor data now plays
an important role in controlling HVAC systems and minimising energy
consumption in smart buildings. Simultaneously, we have begun to understand
the extent to which our privacy is compromised by this level of data
collection. In particular, allowing sensors into the home has resulted in
considerable privacy concerns. Differential privacy has been developed to
help alleviate these privacy concerns.

In this talk we will exploit the ill-posedness of the inverse heat equation
to design a locally differentially private algorithm for releasing thermal
sensor measurements. Intuitively, ill-posedness should mean that we do not
have to perturb the sensor data very much to achieve privacy. It turns out
that while partially true, the definition of differential privacy is too
strong for this to be true for general ill-conditioned inverse problems. We
discuss the connections between the property of being ill-conditioned and
how much noise we need to add to make measurements private.

To verify the utility of the private data, we will discuss how l_1
minimisation can be used to recover the general “geographic vicinity” of
the heat sources from the private thermal data when the initial heat source
vector is sparse. It is well-known that recovery in traditional norms like
l_1 and l_2 is impossible under the presence of even a small amount of
noise. However, we find that the recovered vector is satisfactorily close
(for reasonable parameter settings) to the true source vector in the Earth
Mover Distance. Our work is a generalisation of Li, Other and Tsai [Inverse
Problems and Imaging, 1(1), 2014] to heat source vectors with more than one

Joint work with Anna C. Gilbert.
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