A Latent Manifold Markovian Dynamics Gaussian Process

Abstract

In this paper, we propose a Gaussian process (GP) model for analysis of nonlinear time series. Formulation of our model is based on the consideration that the observed data are functions of latent variables, with the associated mapping between observations and latent representations modeled through GP priors. In addition, to capture the temporal dynamics in the modeled data, we assume that subsequent latent representations depend on each other on the basis of a hidden Markov prior imposed over them. Derivation of our model is performed by marginalizing out the model parameters in closed form using GP priors for observation mappings, and appropriate stick-breaking priors for the latent variable (Markovian) dynamics. This way, we eventually obtain a nonparametric Bayesian model for dynamical systems that accounts for uncertainty in the modeled data. We provide efficient inference algorithms for our model on the basis of a truncated variational Bayesian approximation. We demonstrate the efficacy of our approach considering a number of applications dealing with real-world data, and compare it with the related state-of-the-art approaches.

Leveraging Statistical Machine Learning to Address Failure Localization in Optical Networks

“…Overall, the results show that the accuracy of the proposed approach is insignificantly affected as the number of training data decreases. This is reasonable and expected, as it is known that GPs constitute an ideal modeling approach when dealing with sparse and/or limited training datasets [23,24].…”

Amortized Context Vector Inference for Sequence-to-Sequence Networks

“…Besides, our sampling strategy does not induce significant computational costs, since we adopt the reparameterization (24) for the most part of the model training algorithm. In the future, we aim to consider how ACVI can cope with power-law distributions [33,34]; such a capacity is of importance to real-world natural language generation.…”

Gaussian Processes Over Graphs

“…Given the training observations, Gaussian processes generate posterior probabilities of the target or output for new inputs or observations, as a function of the training data and the input kernel function [2]. Gaussian process models and its variants have been applied in a number of diverse fields such as model predictive control and system analysis [3]- [7], latent variable models [8]- [11], multi-task learning [10], [12], [13], image analysis and synthesis [14]- [17], speech processing [18]- [20], and magnetic resonance imaging (MRI) [21], [22]. Gaussian processes have also been extended to a non-stationary regression setting [23]- [25] and for regression over complex-valued data [26].…”