Forecasting high-dimensional dynamics exploiting suboptimal embeddings

High Dimensional Yield Curves: Models and Forecasting

Functional Signal plus Noise (FSN) models are proposed for analysing the dynamics of a large cross-section of yields or asset prices in which contemporaneous observations are functionally related. The FSN models are used to forecast high dimensional yield curves for US Treasury bonds at the one month ahead horizon. The models achieve large reductions in mean square forecast errors relative to a...

High-dimensional Classification and Attribute-based Forecasting

Better Algorithms for High-dimensional Proximity Problems via Asymmetri Embeddings

High-Dimensional Geometry of Sliding Window Embeddings of Periodic Videos

We explore the high dimensional geometry of sliding windows of periodic videos. Under a reasonable model for periodic videos, we show that the sliding window is necessary to disambiguate all states within a period, and we show that a video embedding with a sliding window of an appropriate dimension lies on a topological loop along a hypertorus. This hypertorus has an independent ellipse for eac...

Exploration of high dimensional biomedical datasets with low-distortion embeddings

Different physical phenomena contribute to the dynamical changes in the functional magnetic resonance imaging (fMRI) signal: task-related hemodynamic response, nontask-related physiological rhythms, machine and motion artifacts, etc. The contribution of this work is a novel method to chart functional maps, that are build globally based on the geometry of the fMRI time series. This method relies...