Doubly stochastic variational inference for deep gaussian processes. Citeseerx citation query statistics for spatial data. In this section, we propose a novel variational posterior and demonstrate a method. Realtime optimal path planning and wind estimation using gaussian process. An introduction to gaussian processes for the kalman filter. This approach is based on a class of anisotropic covariance functions of gaussian processes introduced to model a broad range of spatiotemporal physical phenomena. Optimizing waypoints for monitoring spatiotemporal phenomena. Multitype sensor placements in gaussian spatial fields for.
A novel and efficient algorithm for sensor placements at in. Sensor placement strategies for swe estimation in the. Navigating the protein fitness landscape with gaussian processes. Adaptive sampling for learning gaussian processes using. Pdf nearoptimal sensor placements in gaussian processes. Nearoptimal sensor placements in gaussian processes learning. It a selects the best locations to observe, b calculates the cost and finds the best paths for each uav, and c estimates the measurement value within a given region using the gaussian process gp regression framework. The numbers within the spheres denote the sensors ids as given in table 4.
Near optimal sensor placements in gaussian processes. This algorithm is extended to exploit local structure in the gaussian process, significantly improving performance. Nearoptimal sensor placements cornell computer science. Sensor placement strategies for snow water equivalent swe estimation in the american river basin stephen c. The epub format uses ebook readers, which have several ease of reading features already built in. Current state of the art selects such a set so as to minimize the posterior variance of the gaussian process by exploiting submodularity. Gradient descent for gaussian processes variance reduction. Bayesian optimal design of experiments for inferring the. When monitoring spatial phenomena, which can often be modeled as gaussian processes gps, choosing sensor locations is a fundamental task. Optimal sensor placement and measurement of wind for water.
Proceedings of the 24th international conference on machine learning, pages 449456, 2007. A common strategy is to place sensors at the points of highest entropy variance in the gp model. Krause in electronic journal of statistics, the institute of mathematical statistics and the bernoulli society. Gaussian process 14,26 is a powerful formalism for predict the probability distributions over sensor values at uncovered locations. We propose a mutual information cri teria, and show that it. Theory, efficient algorithms and empirical studies february 2008 journal of machine learning research 9 1.
Deep gaussian processes dgps are multilayer generalizations of gps, but. Weak constraint gaussian processes for optimal sensor placement. Optimal sensor placement based on gaussian process regression. Nearoptimal sensor placements in gaussian processes 3. Near optimal sensor placements in gaussian processes by andreas krause, ajit singh, carlos guestrin, chris williams in icml, 2005 when monitoring spatial phenomena, which can often be modeled as gaussian processes gps, choosing sensor locations is a fundamental task. In this work, we study an optimal sensor placement scheme to measure the wind distribution over a large urban reservoir with a limited number of wind sensors. A good set of observations will provide a better model. Jan 21, 2012 gps actually arose out of an application. Roberts, journal2010 th international conference on information fusion, year2010, pages19 steven reece, stephen j. Emulating dynamic nonlinear simulators using gaussian processes. Nearoptimal sensor placements in gaussian processes core. To resolve this issue, we first exploit a structure common to sparse mogp models for deriving a novel active learning criterion. Nearoptimal active learning of multioutput gaussian processes. There are several common strategies to address this task, for example, geometry or disk models, placing sensors at the points of highest entropy variance in the gp model, and a, d, or eoptimal design.
Learning a spatial field with gaussian process regression in. Krause, a, singh, a, guestrin, c 2008 near optimal sensor placements in gaussian processes. A typical sensor placement technique is to greedily add sensors where uncertainty about the phenomena is highest, that is, the highest entropy location of the gp. Amarjeet singh, andreas krause, carlos guestrin, and william j kaiser. Nearoptimal sensor placements in gaussian processes 2005. Efficient and provably near optimal sensor placement in gaussian process models using the conditional entropy metric and greedy optimization is discussed in detail by ref. Comparison of probabilistic chain graphical modelbased and. In 12, the authors employed gaussian processes gps to build nonparametric probabilistic models using data from a pilot sensor work deployment, for monitoring spatial phenomena of interest. Bode is characterized by sequentially querying the function at specific designs selected by an infillsampling criterion. Optimal sensor placement based on gaussian process regression for shared office spaces under various ventilation conditions. Gaussian process models were then built from validation data points selected by the algorithm to evaluate the efficacy of each placement approach.
In order to predict the temperature at one of these locations from the other sensor readings,weneedthejointdistributionovertemperaturesatthe54locations. Bayesian optimal design of experiments bodes have been successful in acquiring information about a quantity of interest qoi which depends on a blackbox function. Optimizing sensor placements usually, we are limited to deploying a small number of sensors, and thus must carefully choose where to place them. A key issue in gaussian process modeling is to decide on the locations where measurements are going to be taken. The results in this setting, however, are not directly applicable. Though polynomial, the complexity of our basic algorithm is relatively highokn4 to select k out of n possible sensor locations. Gaussian processes gps both for the spatial phenomena of inter est and for.
Gaussian process landscapes can model various protein sequence. For gaussian process models, conditional entropy can be efficiently computed from the posterior covariance k t y of eq. Recursive path planning and wind field estimation for. Within each cluster, a quantitative sensor placement algorithm, based on maximizing the metric of mutual information, was implemented and compared to random placement. Optimal sensor placement we implement as well a greedy selection algorithm for near optimal sensor placement with gaussian processes. Nearoptimal sensor placements in gaussian processes. Unlike existing sensor placement solutions that assume gaussian process of target phenomena, this study measures the wind which inherently exhibits strong non gaussian yearly distribution. Using submodularity to analyze sequential experimental design in gaussian processes with uncertain kernel parameters. What are some applications of gaussian process models. In spatial statistics this is called sampling design. The epub format uses ebook readers, which have several ease of. Hence, it is estimated by the maximum a posteriori probability map estimator. Near optimal bayesian active learning with correlated and noisy tests y. Sensor placement strategies for snow water equivalent swe.
Rankbased clustering was compared to geographically based clustering subbasin delineation to determine the existence of stationary covariance structures within the overall swe dataset. Danie krige, is generally credited with the first use of a gplike model in the 1950s to model the distribution of ore content in south african mines from a small number of samples. Mar 14, 2018 this paper presents an systematic procedure for ipp and environmental mapping using multiple uav sensor platforms. Citeseerx nearoptimal sensor placements in gaussian processes. When monitoring spatial phenomena, which are often modeled as gaussian processes gps, choosing sensor locations is a fundamental task. Theory, efficient algorithms and empirical studies, the journal of. Theory, efficient algorithms and empirical studies a krause, a singh, c guestrin journal of machine learning research 9 feb, 235284, 2008.
Maximizing information while minimizing communication cost. Andreas krause, ajit singh, carlos guestrin, nearoptimal sensor placements in gaussian processes. Informative path planning and mapping with multiple uavs in. Optimal sensor placements when using a traditional gaussian process gp approach blue spheres or a weak constraint gaussian process wcgp approach red spheres in algorithm 4. Surface heat assessment for developed environments. Theory, efficient algorithms and empirical studies. Andreas krause, ajit paul singh, and carlos guestrin. Optimal nonmyopic value of information in graphical models efficient algorithms and theoretical limits. These models, based on gaussian processes, allow us to avoid strong assumptions previously made in the literature. Finally, we show that the sensor placements chosen by our algorithm can lead to significantly better predictions through extensive experimental validation on two realworld datasets. The intuition is that we want to pick a set of fixed size to maximize the mutual information between selected data points and nonselected data points. Gaussian process based iaq distribution mapping using an. The covariance function is assumed to be unknown a priori.
1497 149 499 384 626 418 1372 282 3 1067 845 227 289 81 355 1153 759 622 1312 107 1157 172 1514 1139 374 879 1070 193 57 349 705 363 240 732