28,240 research outputs found
Bayesian Additive Regression Trees With Parametric Models of Heteroskedasticity
We incorporate heteroskedasticity into Bayesian Additive Regression Trees
(BART) by modeling the log of the error variance parameter as a linear function
of prespecified covariates. Under this scheme, the Gibbs sampling procedure for
the original sum-of- trees model is easily modified, and the parameters for the
variance model are updated via a Metropolis-Hastings step. We demonstrate the
promise of our approach by providing more appropriate posterior predictive
intervals than homoskedastic BART in heteroskedastic settings and demonstrating
the model's resistance to overfitting. Our implementation will be offered in an
upcoming release of the R package bartMachine.Comment: 20 pages, 5 figure
Incremental Sparse GP Regression for Continuous-time Trajectory Estimation & Mapping
Recent work on simultaneous trajectory estimation and mapping (STEAM) for
mobile robots has found success by representing the trajectory as a Gaussian
process. Gaussian processes can represent a continuous-time trajectory,
elegantly handle asynchronous and sparse measurements, and allow the robot to
query the trajectory to recover its estimated position at any time of interest.
A major drawback of this approach is that STEAM is formulated as a batch
estimation problem. In this paper we provide the critical extensions necessary
to transform the existing batch algorithm into an extremely efficient
incremental algorithm. In particular, we are able to vastly speed up the
solution time through efficient variable reordering and incremental sparse
updates, which we believe will greatly increase the practicality of Gaussian
process methods for robot mapping and localization. Finally, we demonstrate the
approach and its advantages on both synthetic and real datasets.Comment: 10 pages, 10 figure
A Comparison of Machine-Learning Methods to Select Socioeconomic Indicators in Cultural Landscapes
Cultural landscapes are regarded to be complex socioecological systems that originated as a result of the interaction between humanity and nature across time. Cultural landscapes present complex-system properties, including nonlinear dynamics among their components. There is a close relationship between socioeconomy and landscape in cultural landscapes, so that changes in the socioeconomic dynamic have an effect on the structure and functionality of the landscape. Several numerical analyses have been carried out to study this relationship, with linear regression models being widely used. However, cultural landscapes comprise a considerable amount of elements and processes, whose interactions might not be properly captured by a linear model. In recent years, machine-learning techniques have increasingly been applied to the field of ecology to solve regression tasks. These techniques provide sound methods and algorithms for dealing with complex systems under uncertainty. The term ‘machine learning’ includes a wide variety of methods to learn models from data. In this paper, we study the relationship between socioeconomy and cultural landscape (in Andalusia, Spain) at two different spatial scales aiming at comparing different regression models from a predictive-accuracy point of view, including model trees and neural or Bayesian networks
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