no code implementations • 7 Mar 2018 • Jonathan Jonker, Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto, Sarah Webster
We therefore suggest that the proposed approach be the {\it default choice} for estimating state space models outside of the Gaussian context, regardless of whether the error covariances are singular or not.
no code implementations • 4 Mar 2017 • James V. Burke, Yuan Gao, Tim Hoheisel
Generalized matrix-fractional (GMF) functions are a class of matrix support functions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix optimization problems associated with inverse problems, regularization and learning.
1 code implementation • 30 Sep 2013 • Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto
This paper extends linear system identification to a wide class of nonsmooth stable spline estimators, where regularization functionals and data misfits can be selected from a rich set of piecewise linear-quadratic (PLQ) penalties.
no code implementations • 22 Jan 2013 • Aleksandr Y. Aravkin, Bradley M. Bell, James V. Burke, Gianluigi Pillonetto
Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS).
no code implementations • 19 Jan 2013 • Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto
We introduce a class of quadratic support (QS) functions, many of which play a crucial role in a variety of applications, including machine learning, robust statistical inference, sparsity promotion, and Kalman smoothing.
no code implementations • 19 Nov 2012 • Aleksandr Y. Aravkin, James V. Burke
One of the basic assumptions required to apply the Kalman smoothing framework is that error covariance matrices are known and given.