Communication, Control and Signal Processing Seminar
Abstracts of talks
02/08 Ajaykrishnan Nageswaran (UMD), Data Privacy for a $\rho$-Recoverable Function
ABSTRACT: A user's data is represented by a finite-valued random variable. A querier seeks to compute
a given function of the data based on a query response provided by the user. Under the requirement
that the querier must recover the function value from the query response with at least a prescribed
probability, we analyze single and multiple independent query responses that provide maximum data
privacy to the user by inflicting a maximum probability of data-estimation error on the querier.
Explicit achievability schemes for randomization in query responses are given and their privacy
compared with converse upper bounds.
This is joint work with Prof. Prakash Narayan.
02/15 Abram Kagan (UMD), Efficiency Requires Innovation
02/22 Yi-Peng Wei (UMD), Cache-Aided Private Information Retrieval with Unknown and Uncoded Prefetching
Private information retrieval (PIR) is a canonical problem to investigate the privacy of the contents
downloaded from public databases. In the classical form of the problem, a user requests to download a
message from $K$ messages from $N$ non-communicating databases such that no database can distinguish
individually which message has been retrieved. A naive though inefficient PIR scheme is to download all
of the $K$ messages from a database. Consequently, the aim of the PIR problem is to retrieve the desired
message correctly by downloading as few bits as possible from the $N$ databases under the privacy constraint.
In this talk, we consider PIR from $N$ non-colluding and replicated databases when the user is equipped with a cache that holds an uncoded fraction $r$ from each of the $K$ stored messages in the databases. We assume that the databases are unaware of the cache content. We investigate $D^*(r)$, the optimal download cost normalized with the message size as a function of $K$, $N$, $r$.
Joint work with Karim Banawan and Prof. Sennur Ulukus.
03/08 Radu Balan (UMD), Low-rank Matrix Estimation and Rank-one Matrix Decompositions: When Nonlinear Analysis meets Statistics
In this talk, we present two points of view to broad classes of inverse problems: Lipschitz inversion and Cramer-Rao Lower (CRL) bounds. Given a nonlinear transformation of some data (e.g. incomplete observations of a low-rank matrix, or measurements of magnitudes of a linear transform) one is presented with the problem of stable inversion of this transformation. In this talk, we are interested in finding fundamental lower bounds of any algorithm. We shall discuss the concept of Lipschitz retract and a universal class of signal estimators (Whitney-McShaun-Kirszbraun). Then we formulate the same problem from a frequentist statistical estimation perspective and discuss the associated CRL bound.
If time permits we discuss also a special matrix decomposition problem inspired by expansions of integral operators on modulation spaces. Here we seek a decomposition of the covariance matrix into a sum of rank-one matrices that minimize an l1-type penalty.