Open AccessPosted Content
Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC
TLDR
This work presents a fully Bayesian approach to inference and learning in nonlinear nonparametric state-space models and places a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena.Abstract:
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.read more
Citations
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Proceedings ArticleDOI
Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks
TL;DR: A novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge of multivariate time series forecasting, using the Convolution Neural Network and the Recurrent Neural Network to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends.
Journal ArticleDOI
Survey Kernel methods in system identification, machine learning and function estimation: A survey
TL;DR: A survey of kernel-based regularization and its connections with reproducing kernel Hilbert spaces and Bayesian estimation of Gaussian processes to demonstrate that learning techniques tailored to the specific features of dynamic systems may outperform conventional parametric approaches for identification of stable linear systems.
Journal ArticleDOI
When Gaussian Process Meets Big Data: A Review of Scalable GPs
TL;DR: In this article, a review of state-of-the-art scalable Gaussian process regression (GPR) models is presented, focusing on global and local approximations for subspace learning.
Book
Applied Stochastic Differential Equations
Simo Särkkä,Arno Solin +1 more
TL;DR: The topic of this book is stochastic differential equations (SDEs), which are differential equations that produce a different “answer” or solution trajectory each time they are solved, and the emphasis is on applied rather than theoretical aspects of SDEs.
Posted Content
Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks
TL;DR: Long and Short-term Time-series Network (LSTNet) as mentioned in this paper uses CNN and RNN to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends.
References
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Journal ArticleDOI
Filtering via Simulation: Auxiliary Particle Filters
Michael K. Pitt,Neil Shephard +1 more
TL;DR: This article analyses the recently suggested particle approach to filtering time series and suggests that the algorithm is not robust to outliers for two reasons: the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution.
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A Unifying View of Sparse Approximate Gaussian Process Regression
TL;DR: A new unifying view, including all existing proper probabilistic sparse approximations for Gaussian process regression, relies on expressing the effective prior which the methods are using, and highlights the relationship between existing methods.
Book Chapter
A Tutorial on Particle Filtering and Smoothing: Fifteen years later
Arnaud Doucet,Adam M. Johansen +1 more
TL;DR: A complete, up-to-date survey of particle filtering methods as of 2008, including basic and advanced particle methods for filtering as well as smoothing.
Proceedings Article
Sparse Gaussian Processes using Pseudo-inputs
Edward Snelson,Zoubin Ghahramani +1 more
TL;DR: It is shown that this new Gaussian process (GP) regression model can match full GP performance with small M, i.e. very sparse solutions, and it significantly outperforms other approaches in this regime.
Journal ArticleDOI
Monte Carlo Strategies in Scientific Computing
TL;DR: The strength of this book is in bringing together advanced Monte Carlo methods developed in many disciplines, including the Ising model, molecular structure simulation, bioinformatics, target tracking, hypothesis testing for astronomical observations, Bayesian inference of multilevel models, missing-data problems.