Formalizing class dynamic software updating
First we introduce a new multivariate distribution over circular variables, called the multivariate Generalised von Mises (m Gv M) distribution.
This distribution can be constructed by restricting and renormalising a general multivariate Gaussian distribution to the unit hyper-torus.
We test our method on the cartpole swing-up task, which involves nonlinear dynamics and requires nonlinear control. The first is using the well-known unit quaternion as state (q-IEKF) while the other is using orientation deviation which we call IMEKF.
The third method is based on nonlinear least squares (NLS) estimation of the angular velocity which is used to parametrise the orientation.
[ GPs | Clustering | Graphical Models | MCMC | Semi-Supervised | Non-Parametric | Approximations | Bioinformatics | Information Retreival | RL and Control | Time Series | Network Modelling | Active Learning | Neuroscience | Signal Processing | Machine Vision | Machine Hearing | NLP | Deep Learning | Review ] [ Balog | Bauer | Bui | Dziugaite | Ge | Ghahramani | Gu | Hernández-Lobato | Kilbertus | Kok | Li | Lomeli | Matthews | Navarro | Peharz | Rasmussen | Rojas-Carulla | Rowland | Ścibior | Shah | Steinrücken | Rich Turner | Weller ] [ Borgwardt | Bratières | Calliess | Chen | Cunningham | Davies | Deisenroth | Duvenaud | Eaton | Frellsen | Frigola | Van Gael | Gal | Heaukulani | Heller | Hoffman | Houlsby | Huszár | Knowles | Lacoste-Julien | Lloyd | Lopez-Paz | Mc Allister | Mc Hutchon | Mohamed | Orbanz | Ortega | Palla | Quadrianto | Roy | Saatçi | Tobar | Ryan Turner | Snelson | van der Wilk | Williamson | Wilson ] Gaussian processes are non-parametric distributions useful for doing Bayesian inference and learning on unknown functions.
They can be used for non-linear regression, time-series modelling, classification, and many other problems., volume 31, Long Beach, California, USA, December 2017.
In this way all of the approximation is performed at `inference time' rather than at `modelling time', resolving awkward philosophical and empirical questions that trouble previous approaches. Inertial sensor measurements are obtained at high sampling rates and can be integrated to obtain position and orientation information.
Crucially, we demonstrate that the new framework includes new pseudo-point approximation methods that outperform current approaches on regression and classification tasks. These estimates are accurate on a short time scale, but suffer from integration drift over longer time scales.
covariance functions and methods for automatic relevance determination). Although elegant, the application of GPs is limited by computational and analytical intractabilities that arise when data are sufficiently numerous or when employing non-Gaussian models.In this paper we develop a new pseudo-point approximation framework using Power Expectation Propagation (Power EP) that unifies a large number of these pseudo-point approximations.Unlike much of the previous venerable work in this area, the new framework is built on standard methods for approximate inference (variational free-energy, EP and Power EP methods) rather than employing approximations to the probabilistic generative model itself. Using inertial sensors for position and orientation estimation. Abstract: In recent years, MEMS inertial sensors (3D accelerometers and 3D gyroscopes) have become widely available due to their small size and low cost.The small number of existing approaches either use suboptimal hand-crafted heuristics for hyperparameter learning, or suffer from catastrophic forgetting or slow updating when new data arrive.This paper develops a new principled framework for deploying Gaussian process probabilistic models in the streaming setting, providing principled methods for learning hyperparameters and optimising pseudo-input locations.
Krzysztof Choromanski, Mark Rowland, and Adrian Weller.