1. Some open questions: aggregation and privacy protection Coding, information theory and signal processing Du, Kargupta, Vora

2. Is this the question?
Allowed queries of form
Closureh({hi(x): minimum support of = })
Require responses of the form that enable accurate determination of
f(x): minimum support of = ’ typically >> 
While preventing determination of
g(x)  x or
g(x) if g(x) an outlier, i.e. x an outlier
Privacy should be representation-invariant
What is minimal information required for the “legitimate” activity?
5/4/2019
Poorvi Vora/CS/GWU

3. Privacy is related to data-representation Data representation questions
Modelling of data relationships
Entropy/mutual information (often used for discrete-valued data)
Number of principal components (often used for continuous-valued data)
Clustering into separate regimes in appropriate representations/codes: Fourier, Walsh, etc.
Consequent question: optimal source code
What is a good source code?
For example, jpeg is a decent compression, though lossy, of images
Walsh transform: similar band-limitedness notion in terms of decision tree lengths, data points used in a single query
5/4/2019
Poorvi Vora/CS/GWU

4. Adversary modelling What we know is if
the adversary is allowed any kind of adaptive query, and
the adversary wants error to go to zero
the minimum cost per bit is bounded below, tightly, if
both adversary and database are willing to participate in an unbounded number of queries. So
make it expensive to ask a question,
stop questioning (bound number of queries)
make it such that the capacity for allowed patterns is high, and capacity for private information is low How?
Can one limit the adversary in any other ways to obtain anything more interesting? (polynomial time is not enough of a limitation)
5/4/2019
Poorvi Vora/CS/GWU

5. Instead of uniform perturbation
Allow a total of np lies to n binary questions
What kinds of shapes can the ellipse be made to look like by computationally bounded Alice and Bob
What would be preserved? The “average” shape?
5/4/2019
Poorvi Vora/CS/GWU

6. Lying in a multiparty function evaluation
5/4/2019
Poorvi Vora/CS/GWU