64,125 research outputs found
Infinite Mixtures of Multivariate Gaussian Processes
This paper presents a new model called infinite mixtures of multivariate
Gaussian processes, which can be used to learn vector-valued functions and
applied to multitask learning. As an extension of the single multivariate
Gaussian process, the mixture model has the advantages of modeling multimodal
data and alleviating the computationally cubic complexity of the multivariate
Gaussian process. A Dirichlet process prior is adopted to allow the (possibly
infinite) number of mixture components to be automatically inferred from
training data, and Markov chain Monte Carlo sampling techniques are used for
parameter and latent variable inference. Preliminary experimental results on
multivariate regression show the feasibility of the proposed model.Comment: Proceedings of the International Conference on Machine Learning and
Cybernetics, 2013, pages 1011-101
Mixtures of controlled Gaussian processes for dynamical modeling of deformable objects
Control and manipulation of objects is a highly relevant topic in Robotics research. Although significant advances have been made over the manipulation of rigid bodies, the manipulation of non-rigid objects is still challenging and an open problem. Due to the uncertainty of the outcome when applying physical actions to non-rigid objects, using prior knowledge on objects’ dynamics can greatly improve the control performance. However, fitting such models is a challenging task for materials such as clothing, where the state is represented by points in a mesh, resulting in very large dimensionality that makes models difficult to learn, process and predict based on measured data. In this paper, we expand previous work on Controlled Gaussian Process Dynamical Models (CGPDM), a method that uses a non-linear projection of the state space onto a much smaller dimensional latent space, and learns the object dynamics in the latent space. We take advantage of the variability in training data by employing Mixture of Experts (MoE), and we devise theory and experimental validations that demonstrate significant improvements in training and prediction times, plus robustness and error stability when predicting deformable objects exposed to disparate movement ranges.This work was partially developed in the context of the project CLOTHILDE (”CLOTH manIpulation Learning from DEmonstrations”), which has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Advanced Grant agreement No 741930). We would like to thank the members of the HCRL Lab and the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin for their feedback during the development of this work.Peer ReviewedPostprint (published version
Approximating multivariate posterior distribution functions from Monte Carlo samples for sequential Bayesian inference
An important feature of Bayesian statistics is the opportunity to do
sequential inference: the posterior distribution obtained after seeing a
dataset can be used as prior for a second inference. However, when Monte Carlo
sampling methods are used for inference, we only have a set of samples from the
posterior distribution. To do sequential inference, we then either have to
evaluate the second posterior at only these locations and reweight the samples
accordingly, or we can estimate a functional description of the posterior
probability distribution from the samples and use that as prior for the second
inference. Here, we investigated to what extent we can obtain an accurate joint
posterior from two datasets if the inference is done sequentially rather than
jointly, under the condition that each inference step is done using Monte Carlo
sampling. To test this, we evaluated the accuracy of kernel density estimates,
Gaussian mixtures, vine copulas and Gaussian processes in approximating
posterior distributions, and then tested whether these approximations can be
used in sequential inference. In low dimensionality, Gaussian processes are
more accurate, whereas in higher dimensionality Gaussian mixtures or vine
copulas perform better. In our test cases, posterior approximations are
preferable over direct sample reweighting, although joint inference is still
preferable over sequential inference. Since the performance is case-specific,
we provide an R package mvdens with a unified interface for the density
approximation methods
Clustering based on Mixtures of Sparse Gaussian Processes
Creating low dimensional representations of a high dimensional data set is an
important component in many machine learning applications. How to cluster data
using their low dimensional embedded space is still a challenging problem in
machine learning. In this article, we focus on proposing a joint formulation
for both clustering and dimensionality reduction. When a probabilistic model is
desired, one possible solution is to use the mixture models in which both
cluster indicator and low dimensional space are learned. Our algorithm is based
on a mixture of sparse Gaussian processes, which is called Sparse Gaussian
Process Mixture Clustering (SGP-MIC). The main advantages to our approach over
existing methods are that the probabilistic nature of this model provides more
advantages over existing deterministic methods, it is straightforward to
construct non-linear generalizations of the model, and applying a sparse model
and an efficient variational EM approximation help to speed up the algorithm
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