high-dimensional data

Monday, September 16, 2019 - 10:30am - 11:30am
Dennis Cook (University of Minnesota, Twin Cities)
Essentially a form of targeted dimension reduction, an envelope is a construct for increasing efficiency of multivariate methods without altering traditional goals, sometimes producing gains equivalent to increasing the sample size many times over. Recognizing that the data may contain unanticipated variation that is effectively immaterial to estimation, an envelope is a subspace that envelops the material variation and thereby reduces estimative and predictive error.
Wednesday, December 5, 2018 - 1:30pm - 2:30pm
Mike Wei (University at Buffalo (SUNY))
We propose a minimax concave penalized multi-armed bandit algorithm under generalized linear model (G-MCP-Bandit) for a decision-maker facing high-dimensional data in an online learning and decision-making process. We demonstrate that the G-MCP-Bandit algorithm asymptotically achieves the optimal cumulative regret in the sample size dimension T, O(log T), and further attains a tight bound in the covariates dimension d, O(log d).
Thursday, April 26, 2018 - 3:30pm - 4:00pm
Singdhansu (Ansu) Chatterjee (University of Minnesota, Twin Cities)
We present a scheme of studying the geometry of high-dimensional data to discover patterns in it, using minimal parametric distributional assumptions. Our approach is to define multivariate quantiles and extremes, and develop a method of center-outward partial ordering of observations. We formulate methods for quantifying relationships among observed variables, thus generalizing the notions of regression and principal components. We devise geometric algorithms for detection of outliers in high dimensions, classification and supervised learning.
Thursday, February 22, 2018 - 1:30pm - 2:10pm
Katherine Ensor (Rice University)
High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with statistical error. We consider high-dimensional vector autoregressive processes with spatial structure, a simple and common form of additional structure. We propose novel high-dimensional methods that take advantage of such structure without making model assumptions about how distance affects dependence.
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