Learning with Sparse Temporal and Spatial Data

• Activity Number: 174
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Reza Hosseini*+ and Akimichi Takemura and Kiros Berhane
• Companies: IBM Research and University of Tokyo and University of Southern California
• Keywords: Lipschitz Bound ; Sparse Data ; Spatial-temporal data ; Interpolation ; Fitting

Abstract

In this talk we develop a framework to learning functions when the data are sparse but slow-moving patterns allow for a useful fit. This is done by investigating the properties of Lipschitz functions and extending the concept to wiggly functions by allowing a deviation. Deterministic bounds are found for the approximation error of various methods in terms of the Lipschitz constant and the deviation. Moreover we present an optimal method which outperforms other methods such as nearest neighbor and linear interpolation. The developed methods can also use the extra assumption of periodicity to obtain better prediction error bounds.