B.Sc., Department of Mathematics and Informatics, Vilnius University, Lithuania, 1996; D.E.A., Laboratoire de Probabilites et Modeles Aleatoires, University of Paris 6, France, 1997; Ph.D., Department of Mathematics and Statistics, Boston University, 2002
Modeling high-dimensional, multivariate, time series and spatial fields; Extremal behavior of dynamical systems modeling physical phenomena; Sampling and streaming algorithms in connection to “big data;” Modeling scaling and self-similar phenomena
Modeling High-Dimensional, Multivariate, Time Series and Spatial Fields
The topics of interest include: sparse modeling with regularization, lasso and variants, dimension reduction with factor models, change points, non-linear models, classification and clustering, and others. The data for which the methods are explored and developed come from Economics and Finance, Psychology, Neuroscience, Environmental Sciences, Geophysics. Current collaborators in this area include: R. Davis, Columbia, K. Gates, UNC, Psychology and Neuroscience, R. Lund, Clemson, and former Ph.D. students C. Baek, Sungkyunkwan University, Korea, and S. Kechagias, SAS Institute.
Extremal Behavior of Dynamical Systems Modeling Physical Phenomena
This research direction has been pursued in collaboration with researchers in US Navy, and more specifically the NSWC Carderock Division, NSWCCD, Maryland, where I spent ten weeks as a senior fellow of the ONR summer faculty program each of the past six years. One basic problem of interest in this area concerns understanding extreme motions of a ship, which we have studied from various angles, including statistics, stochastic dynamics and differential equations, naval architecture and others.
Sampling and Streaming Algorithms in Connection to "Big Data"
My previous work in this area focused on understanding how various methods to sample packets in Internet traffic can be used to infer characteristics of the underlying original traffic, more specifically, the so-called flow size and duration distributions.
My current projects involve developing streaming algorithms for estimating flow duration distribution, as well as contributing to estimation of various quantities of interest, for example, frequency moments, when dealing with streaming data objects. I am also looking into problems on sampling and streaming large graphs, networks. Data of interest in these applications come from Internet traffic, and social, www and other networks. My collaborators include N. Antunes, Algarve, Portugal, D. Veitch, University of Technology Sydney, and S. Bhamidi, UNC.
Modeling Scaling and Self-Similar Phenomena
This theme was the main driver of my research efforts since receiving my Ph.D. and joining the department in 2002. These efforts have concluded with a comprehensive monograph on the subject and another smaller specialized textbook.