FOUNDS Seminar Series Talk 05 - Copulas and Compression

Talk Abstract: A key property of Gaussian models is the exponential decay of the probability density function. In many applications, large values occur with much higher probabilities, leading to heavy-tailed probability distributions. In this talk, we consider the family of regularly varying distributions, which captures many popular heavy-tailed models such as alpha-stable and student-t distributions. This family also includes shot noise models which can arise as interference models in wireless communications. By exploiting copula models of statistical dependence, we study (distributed) compression of such non-Gaussian data, highlighting the role of extremal dependence measures and their connection to information measures.