Gaussian process

About: Gaussian process is a research topic. Over the lifetime, 18944 publications have been published within this topic receiving 486645 citations. The topic is also known as: Gaussian stochastic process.

Mixtures of Gaussian Processes

Abstract: We introduce the mixture of Gaussian processes (MGP) model which is useful for applications in which the optimal bandwidth of a map is input dependent. The MGP is derived from the mixture of experts model and can also be used for modeling general conditional probability densities. We discuss how Gaussian processes - in particular in form of Gaussian process classification, the support vector machine and the MGP model--can be used for quantifying the dependencies in graphical models.

Efficient, generalized indoor WiFi GraphSLAM

Abstract: The widespread deployment of wireless networks presents an opportunity for localization and mapping using only signal-strength measurements. The current state of the art is to use Gaussian process latent variable models (GP-LVM). This method works well, but relies on a signature uniqueness assumption which limits its applicability to only signal-rich environments. Moreover, it does not scale computationally to large sets of data, requiring O (N3) operations per iteration. We present a GraphSLAM-like algorithm for signal strength SLAM. Our algorithm shares many of the benefits of Gaussian processes, yet is viable for a broader range of environments since it makes no signature uniqueness assumptions. It is also more tractable to larger map sizes, requiring O (N2) operations per iteration. We compare our algorithm to a laser-SLAM ground truth, showing it produces excellent results in practice.

Gaussian process occupancy maps

Abstract: We introduce a new statistical modelling technique for building occupancy maps. The problem of mapping is addressed as a classification task where the robot's environment is classified into regions of occupancy and free space. This is obtained by employing a modified Gaussian process as a non-parametric Bayesian learning technique to exploit the fact that real-world environments inherently possess structure. This structure introduces dependencies between points on the map which are not accounted for by many common mapping techniques such as occupancy grids. Our approach is an 'anytime' algorithm that is capable of generating accurate representations of large environments at arbitrary resolutions to suit many applications. It also provides inferences with associated variances into occluded regions and between sensor beams, even with relatively few observations. Crucially, the technique can handle noisy data, potentially from multiple sources, and fuse it into a robust common probabilistic representation of the robot's surroundings. We demonstrate the benefits of our approach on simulated datasets with known ground truth and in outdoor urban environments.

Asymptotic Properties for a Class of Partially Identified Models

Abstract: We propose inference procedures for partially identified population features for which the population identification region can be written as a transformation of the Aumann expectation of a properly defined set valued random variable (SVRV). An SVRV is a mapping that associates a set (rather than a real number) with each element of the sample space. Examples of population features in this class include sample means and best linear predictors with interval outcome data, and parameters of semiparametric binary models with interval regressor data. We extend the analogy principle to SVRVs, and show that the sample analog estimator of the population identificaiton region is given by a transformation of a Minkowski average SVRVs. Using the results of the mathematics literature on SVRVs, we show that this estimator converges in probability to the identificaiton region of the model with respect to the Hausdorff distance. We then show that the Hausdorff distance between the estimator and the population identification region, when properly normalized by square n, converges in distribution to the supremum of a Gaussian process whose covariance kernel depends on parameters of the population identificaiton region. We provide consistent bootstrap procedures to approximate this limiting distribution. Using similar arguments as those applied for vector valued random variables, we develop a methodology to test assumptions about the true identificaiton region and to calcuate the power of the test. We show that these results can be used to construct a confidence collection, that is a collection of sets that, when specified as null hypothesis for the true value of the population identification region, cannot be rejected by our test.