Anindya Roy

University of Maryland Baltimore County

Estimation of Vector Autoregressive Moving Average Under Causality and Invertibility Constraints

We present a reparameterization of vector autoregressive moving average (VARMA) models that allows estimation of parameters under the constraints of causality and invertibility. The parameter constraints associated with a causal invertible VARMA model are highly complex. An m-variate VARMA(p; q) process contains (p+q)m2 + m(m+1)/2 parameters, which must be constrained to a complicated subset of the Euclidean space in order to guarantee causality, invertibility. The main result of the paper is a bijection from the constrained set to the entire Euclidean space.

Thursday, October 22, 2015 - 3:30pm

Jun Liu

Harvard University

Detecting Nonlinear Relationships via Slicing

I will discuss a few recent results from my group aiming to the detection of non-linear dependence and interactive effects of several random variables. These approaches were all developed by taking a Bayesian viewpoint on the inverse-slicing idea first proposed by Ker-Chau Li. We will also show how these methods are applied to bioinformatics problems such as gene-set enrichment analysis, transcriptional regulation analysis, etc.

Friday, April 22, 2016 - 3:30pm

David Banks

Duke University

Mining Text Networks

The last decade has seen substantial progress in topic modeling, and considerable progress in the study of dynamic networks.  This research combines these threads, so that the network structure informs topic discovery and the identified topics predict network behavior.  The data consist of text and links from all U.S. political blogs curated by Technorati during the calendar year 2012.  A particular advantage of the model used in this research is that it naturally enforces cluster structure in the topics, through a block model for the bloggers.

Thursday, October 1, 2015 - 3:30pm

David Ruppert

Cornell University

A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework.

Thursday, April 7, 2016 - 3:30pm

Yingnian Wu

University of California, Los Angeles

Inducing Wavelets into Random Fields via Generative Boosting

We propose a learning algorithm for a class of random field models of natural image patterns, where the energy functions of the random fields are in the form of linear combinations of rectified filter responses from subsets of wavelets selected from a given over-complete dictionary. The algorithm consists of the following two components. (1) We propose to induce the wavelets into the random field model by a generative version of the epsilon-boosting algorithm.

Thursday, September 24, 2015 - 3:30pm

Bo Li

University of Illinois at Urbana-Champaign

Statistics in Paleoclimate Reconstruction

Understanding the complex dynamics of Earth's climate system is a grand scientific challenge. Projecting climate for 50 or 100 years into the future is, however, complicated by the fact that the behavior of the Earth system over such time scales is not well characterized over the modern instrumental interval, which only stretches back about 100-150 years with global extent.

Thursday, December 3, 2015 - 3:30pm

Debashis Paul

University of CA at Davis

Nonparametric estimation of dynamics of monotone trajectories

We propose a nonparametric estimator of the dynamics of monotonically increasing or decreasing trajectories defined on a finite time interval. Such trajectories can be described as solutions of autonomous ODEs. Under suitable regularity conditions, we derive the optimal rate of convergence for the proposed estimator and show that it is the same as that for estimating the derivative of a trajectory. We also show that commonly used two-stage estimation schemes are typically inefficient.

Thursday, September 17, 2015 - 3:30pm

Bing Li

Penn State University

Nonlinear sufficient dimension reduction for functional data

We propose a general theory and the estimation procedures for nonlinear sufficient dimension reduction where the predictor or the response, or both, are random functions. The relation between the response and predictor can be arbitrary and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads naturally to consideration of two levels of functional spaces: the first space consisting of functions of time; the second space consisting of functions defined on the first space.

Thursday, October 15, 2015 - 3:30pm


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