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# Dalhousie-AARMS AAMP Seminar: Alex Barnett (Flatiron Institute, NYC)

## January 27, 2023 @ 4:00 pm - 5:00 pm

Title: Equispaced Fourier representations for efficient Gaussian process regression from a billion data pointsAbstract: Gaussian process regression is widely used in geostatistics, time-series analysis, and machine learning. It infers an unknown continuous function in a principled fashion from noisy measurements at $N$ scattered data points.  The prior on the function is Gaussian, with covariance given by some user-chosen translationally invariantkernel.  Yet $N$ has been limited to about $10^6$, even with modern low-rank methods.  Focusing on low spatial dimension (1–3), we present a GP regression method using kernel approximation by an equispaced quadrature grid in the Fourier domain.  This enables the iterative solution of a smaller Toeplitz linear system, exploiting both the FFT and the nonuniform FFT to give ${\mathcal O}(N)$ cost. The result is often one to two orders of magnitude faster than state of the art methods, and enables cheap massive-scale regressions. For example, for a 2D Mat\’ern-3/2 kernel and $N = 10^9$ points, the posterior mean function is found to 3-digit accuracy in two minutes on a desktop.Joint work with Philip Greengard (Columbia) and Manas Rachh (Flatiron Institute)

The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker.  If you would like to attend, please email the organizers for connection details.

## Details

Date:
January 27, 2023
Time:
4:00 pm - 5:00 pm
Event Category:
Website:
https://sureshes.wordpress.com/dalhousie-analysis-seminar/

## Venue

Dalhousie University