Communication, Control and Signal Processing Seminar 

Abstracts of talks

Spring 2011

02/24 Arya Mazumdar (UMD), Constructions of matrices  with restricted isometry property for compressive sampling

ABSTRACT: Compressive sampling is a technique of recovering sparse N-dimensional signals from low-dimensional sketches, i.e., their linear images in R^m, m << N.  The main question associated with this technique is construction of linear operators that allow faithful recovery of the signal from its sketch.  The most frequently used sufficient condition for robust recovery is the near-isometry property (RIP) of the operator when restricted to k-sparse signals.

The talk will begin with a brief overview of the main problem of Compressive Sampling and known results. Our emphasis will be on the construction of binary m x N matrices that satisfy the restricted isometry property of order k for almost all k-sparse signals (statistical k-RIP).  Previous results were concerned with specific constructions of matrices obtained from DFT-like arrays.  Here we discuss a general method of constructing sampling matrices for which a statistical version of k-RIP holds, enabling one to recover almost all k-sparse signals from sketches much shorter than those in previous works. Our constructions are practical and cover a large set of parameters.

We also show that k-RIP matrices that recover all (rather than almost all) sparse signals can be found constructively with time complexity polynomial (in N), while the number of samples is close to the smallest possible dimension. The construction involves derandomizing the construction of generator matrices of Gilbert-Varshamov codes. Joint work with Alexander Barg

03/03 No seminar, instead:
Marilyn Wolf (Georgia Tech) Control and Computing in Cyber-Physical Systems

03/07 (MONDAY, 11am, AVW1146) Pascal Vontobel (HP Labs) Should We Believe in Numbers Computed by Loopy Belief Propagation?

ABSTRACT: Loopy belief propagation (LBP) has been very popular in the last fifteen years in the area of coded data transmission (and beyond) because of its low implementation complexity and its outstanding performance. In this talk, we discuss an analysis technique that allows one to obtain a better understanding of why LBP works so well for some problems, yet also has some limitations.
Although this LBP analysis technique is broadly applicable, to be concrete, we present it in a specific context. Namely, we focus on the use of LBP for estimating the sum of so-called perfect matchings in a weighted complete bipartite graph, a setup that subsumes many interesting counting problems.
Common wisdom would suggest that LBP does not work well in this context because the underlying graph is dense and has many short cycles. However, it turns out that LBP gives a very valuable estimate for this counting problem, and the above-mentioned analysis technique allows us to see why this is so by providing a combinatorial characterization of the LBP-based estimate: on the one hand, this combinatorial characterization gives insights why the LBP-based estimate is useful, on the other hand, it shows why the LBP-based estimate differs in general from the correct value.
At the end, we will contemplate the use of the above LBP-based estimates for the analysis of pseudo-codewords and for kernel-based techniques in machine learning.

03/10 Armand Makowsky (UMD) Some remarks on random graphs

04/07 Isaak Mayergoyz (UMD), Landau-Lifshitz Magnetization Dynamics Driven by a Jump-Noise Process

Abstract: In this self-contained talk, the basic mathematical and physical facts related to the Landau-Lifshitz equation will be reviewed first along with relevant technological applications. Then, stochastic Landau-Lifshitz dynamics driven by a jump-noise process will be discussed and some new results in this area will be presented.

04/14 Benjamin Kedem (UMD) Integration of information from multiple sources

ABSTRACT: A great deal of the statistical literature deals with a single sample coming from a distribution, univariate or multivariate, and the problem
is to identify the distribution or parts thereof by an array of estimation and testing procedures. As such, this practice neglects to bring in
information from other sources which could improve the desired inference. An approach which fuses information from many sources will be
presented and applied in various statistical problems, including time series forecasting. The basic idea: Finding relationships between
probability distributions using many data sources.

04/21 Abram Kagan (UMD) Semiparametric Estimation for Kernel Families


04/22 Tsachy Weissmann (Stanford) Mutual Information, Relative Entropy, and the Costs of Causality and of Mismatch in Estimation

ABSTRACT: I will start with a brief tour through some of the literature - ranging from the 1950s to the 2010s - on relations between information
and estimation in the Gaussian channel. A remarkably parallel set of relations will then be seen to hold for the Poissonian channel. As I
will illustrate with a few examples, beyond their elegance, these relations give insight into and a quantitative understanding of the
costs of causality and of mismatch in estimation, and allow to transfer both theoretical tools and algorithmic know-how from one
field to the other. I will end by mentioning some future research directions and speculating about how some of these results carry over
to other channels. The parts of the talk presenting new results are based on joint work with Rami Atar.

05/05 Himanshu Tyagi (UMD) Relationships Between Certain Quantities of Information Theory and Statistics

ABSTRACT: In this talk, we will first present the de Bruijn's identity which relates differential entropy
and Fisher information. Then we will present the work of Guo-Shamai-Verdu which relates Shannon's mutual information to the minimum mean square error for a Gaussian channel. The equivalence of the two results will be established and the de Bruijn's identity will be applied to prove the entropy-power inequality [Stam '59].

Raef Bassily (UMD) Cryptographic Security and Public key Encryption

ABSTRACT: In this talk, the notion of cryptographic security of public key encryption schemes will be defined. We will then introduce the factoring problem, the RSA (Rivest-Shamir-Adleman) problem, the Discrete Logarithm problem, and the DH (Deffie-Hellman) problem.
Based on the hardness assumption of the RSA problem, the RSA public key encryption scheme will be presented. We will also present El Gamal scheme that is based on the DH key exchange protocol and prove its security (in the cryptographic sense) under the Chosen Ciphertext Attack based on the hardness of a stronger version the DH problem, namely, the Decisional DH problem.
If time permits, the notion of Trapdoor Permutations (TDPs) and hardcore predicates will be introduced and a method of constructing cryptographic secure public key encryption schemes based on TDPs will be introduced.