164 research outputs found
Parallelizable sparse inverse formulation Gaussian processes (SpInGP)
We propose a parallelizable sparse inverse formulation Gaussian process
(SpInGP) for temporal models. It uses a sparse precision GP formulation and
sparse matrix routines to speed up the computations. Due to the state-space
formulation used in the algorithm, the time complexity of the basic SpInGP is
linear, and because all the computations are parallelizable, the parallel form
of the algorithm is sublinear in the number of data points. We provide example
algorithms to implement the sparse matrix routines and experimentally test the
method using both simulated and real data.Comment: Presented at Machine Learning in Signal Processing (MLSP2017
Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes
In this paper, we propose a class of efficient, accurate, and general methods
for solving state-estimation problems with equality and inequality constraints.
The methods are based on recent developments in variable splitting and
partially observed Markov processes. We first present the generalized framework
based on variable splitting, then develop efficient methods to solve the
state-estimation subproblems arising in the framework. The solutions to these
subproblems can be made efficient by leveraging the Markovian structure of the
model as is classically done in so-called Bayesian filtering and smoothing
methods. The numerical experiments demonstrate that our methods outperform
conventional optimization methods in computation cost as well as the estimation
performance.Comment: 3 figure
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