Abstract: Given a random sequence of length n from some discrete but unknown distribution, can we estimate, for each k, the mass placed by the distribution on elements occurring k times? Can we produce a region in which the (n+ 1)-th point must lie with some prescribed confidence? Flavors of these questions have been tackled by an extensive body of literature spanning statistics, information theory and computer science; the former question of functional estimation is addressed by various estimators of the “unseen”, and the latter question of predictive inference is addressed by, e.g., conformal prediction methods. Such methods are known to possess desirable properties when the data is i.i.d.; however, they are no longer reliable in modern settings spanning genomics and language, where the data can be temporally dependent. In this talk, I will present alternative families of methods for functional estimation and predictive inference when the data can exhibit dependence. These methods are based on a framework for estimation and inference based on “leaving-a-window-out”, as well as some new analysis tools for temporally dependent data that may be of independent interest.
About the Speaker: Ashwin Pananjady is an Assistant Professor at Georgia Tech with a joint appointment between the H. Milton Stewart School of Industrial and Systems Engineering and the School of Electrical and Computer Engineering. His research interests lie broadly in statistics, optimization, and information theory, as well as their applications in data science, machine learning, and signal processing. He is particularly interested in statistical and computational problems arising from high-dimensional data with geometric structure.
