In this paper, we study extensions to the Gaussian processes (GPs) continuous occupancy mapping problem. There are two classes of occupancy mapping problems that we particularly investigate. The first problem is related to mapping under pose uncertainty and how to propagate pose estimation uncertainty into the map inference. We develop expected kernel and expected submap notions to deal with uncertain inputs. In the second problem, we account for the complication of the robot's perception noise using warped Gaussian processes (WGPs). This approach allows for non-Gaussian noise in the observation space and captures the possible nonlinearity in that space better than standard GPs. The developed techniques can be applied separately or concurrently to a standard GP occupancy mapping problem. According to our experimental results, although taking into account pose uncertainty leads, as expected, to more uncertain maps, by modeling the nonlinearities present in the observation space WGPs improve the map quality.
Kernel methods in the form of Gaussian processes (GPs) framework @cite_34 are non-parametric regression and classification techniques that have been used to model spatial phenomena @cite_41 . The development of GPOM is discussed in @cite_14 @cite_23 . The incremental GP map building using the Bayesian Committee Machine (BCM) technique @cite_29 is developed in @cite_11 @cite_2 @cite_18 @cite_27 and for online applications in @cite_24 . @cite_12 , the Hilbert maps technique is proposed and is more scalable. However, it is an approximation for continuous occupancy mapping and produces maps with less accuracy than GPOM.
@cite_18 @cite_14 @cite_41 @cite_29 @cite_24 @cite_27 @cite_23 @cite_2 @cite_34 @cite_12 @cite_11
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We present a novel algorithm to produce descriptive online 3D occupancy maps using Gaussian processes (GPs). GP regression and classification have met with recent success in their application to robot mapping, as GPs are capable of expressing rich correlation among map cells and sensor data. However, the cubic computational complexity has limited its application to large-scale mapping and online use. In this paper we address this issue first by proposing test-data octrees, octrees within blocks of the map that prune away nodes of the same state, condensing the number of test data used in a regression, in addition to allowing fast data retrieval. We also propose a nested Bayesian committee machine which, after new sensor data is partitioned among several GP regressions, fuses the result and updates the map with greatly reduced complexity. Finally, by adjusting the range of influence of the training data and tuning a variance threshold implemented in our method's binary classification step, we are able to control the richness of inference achieved by GPs - and its tradeoff with classification accuracy. The performance of the proposed approach is evaluated with both simulated and real data, demonstrating that the method may serve both as an improved-accuracy classifier, and as a predictive tool to support autonomous navigation. We introduce the Gaussian Process Convolution Model (GPCM), a two-stage non-parametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametric-window moving average process and, conditionally, is itself a Gaussian process with a nonparametric kernel defined in a probabilistic fashion. The generative model can be equivalently considered in the frequency domain, where the power spectral density of the signal is specified using a Gaussian process. One of the main contributions of the paper is to develop a novel variational free-energy approach based on inter-domain inducing variables that efficiently learns the continuous-time linear filter and infers the driving white-noise process. In turn, this scheme provides closed-form probabilistic estimates of the covariance kernel and the noise-free signal both in denoising and prediction scenarios. Additionally, the variational inference procedure provides closed-form expressions for the approximate posterior of the spectral density given the observed data, leading to new Bayesian nonparametric approaches to spectrum estimation. The proposed GPCM is validated using synthetic and real-world signals. Gaussian processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous variational inferences, although have alleviated this issue by scaling up GPs to millions of samples, are still far from satisfactory for real-world large applications, where the data sizes are often orders of magnitudes larger, say, billions. To solve this problem, we propose ADVGP, the first Asynchronous Distributed Variational Gaussian Process inference for regression, on the recent large-scale machine learning platform, PARAMETERSERVER. ADVGP uses a novel, flexible variational framework based on a weight space augmentation, and implements the highly efficient, asynchronous proximal gradient optimization. While maintaining comparable or better predictive performance, ADVGP greatly improves upon the efficiency of the existing variational methods. With ADVGP, we effortlessly scale up GP regression to a real-world application with billions of samples and demonstrate an excellent, superior prediction accuracy to the popular linear models. We develop an approach for sparse representations of gaussian process (GP) models (which are Bayesian types of kernel machines) in order to overcome their limitations for large data sets. The method is based on a Combination of a Bayesian on-line algorithm, together with a sequential construction of a relevant subsample of the data that fully specifies the prediction of the GP model. By using an appealing parameterization and projection techniques in a reproducing kernel Hilbert space, recursions for the effective parameters and a sparse gaussian approximation of the posterior process are obtained. This allows for both a propagation of predictions and Bayesian error measures. The significance and robustness of our approach are demonstrated on a variety of experiments.