Results 1 - 10
of
43
Gaussian processes for global optimization
- in LION
, 2009
"... Abstract. We introduce a novel Bayesian approach to global optimization using Gaussian processes. We frame the optimization of both noisy and noiseless functions as sequential decision problems, and introduce myopic and non-myopic solutions to them. Here our solutions can be tailored to exactly the ..."
Abstract
-
Cited by 41 (7 self)
- Add to MetaCart
(Show Context)
Abstract. We introduce a novel Bayesian approach to global optimization using Gaussian processes. We frame the optimization of both noisy and noiseless functions as sequential decision problems, and introduce myopic and non-myopic solutions to them. Here our solutions can be tailored to exactly the degree of confidence we require of them. The use of Gaussian processes allows us to benefit from the incorporation of prior knowledge about our objective function, and also from any derivative observations. Using this latter fact, we introduce an innovative method to combat conditioning problems. Our algorithm demonstrates a significant improvement over its competitors in overall performance across a wide range of canonical test problems.
Decentralised Coordination of Mobile Sensors Using the Max-Sum Algorithm
, 2009
"... In this paper, we introduce an on-line, decentralised coordination algorithm for monitoring and predicting the state of spatial phenomena by a team of mobile sensors. These sensors have their application domain in disaster response, where strict time constraints prohibit path planning in advance. Th ..."
Abstract
-
Cited by 39 (10 self)
- Add to MetaCart
In this paper, we introduce an on-line, decentralised coordination algorithm for monitoring and predicting the state of spatial phenomena by a team of mobile sensors. These sensors have their application domain in disaster response, where strict time constraints prohibit path planning in advance. The algorithm enables sensors to coordinate their movements with their direct neighbours to maximise the collective information gain, while predicting measurements at unobserved locations using a Gaussian process. It builds upon the max-sum message passing algorithm for decentralised coordination, for which we present two new generic pruning techniques that result in speed-up of up to 92 % for 5 sensors. We empirically evaluate our algorithm against several on-line adaptive coordination mechanisms, and report a reduction in root mean squared error up to 50 % compared to a greedy strategy.
Kernels for Vector-Valued Functions: a Review
, 2011
"... Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kern ..."
Abstract
-
Cited by 32 (2 self)
- Add to MetaCart
(Show Context)
Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.
Bounded approximate decentralised coordination using the max-sum algorithm
- IN DISTRIBUTED CONSTRAINT REASONING WORKSHOP
, 2009
"... In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution qualit ..."
Abstract
-
Cited by 30 (9 self)
- Add to MetaCart
In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution quality. It uses the max-sum algorithm to optimally solve the resulting tree structured constraint network, providing a bounded approximation specific to the particular problem instance. We formally prove that our algorithm provides a bounded ap-proximation of the original problem and we present an empirical evaluation in a synthetic scenario. This shows that the approximate solutions that our algorithm provides are typically within 95 % of the optimum and the approximation ratio that our algorithm provides is typically 1.23.
Sparse convolved Gaussian processes for multi-output regression
- In Advances in Neural Information Processing Systems 21
, 2009
"... We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent func ..."
Abstract
-
Cited by 30 (5 self)
- Add to MetaCart
(Show Context)
We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network. 1
Computationally efficient convolved multiple output gaussian processes
- Journal of Machine Learning Research
"... Recently there has been an increasing interest in regression methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appr ..."
Abstract
-
Cited by 27 (2 self)
- Add to MetaCart
(Show Context)
Recently there has been an increasing interest in regression methods that deal with multiple outputs. This has been motivated partly by frameworks like multitask learning, multisensor networks or structured output data. From a Gaussian processes perspective, the problem reduces to specifying an appropriate covariance function that, whilst being positive semi-definite, captures the dependencies between all the data points and across all the outputs. One approach to account for non-trivial correlations between outputs employs convolution processes. Under a latent function interpretation of the convolution transform we establish dependencies between output variables. The main drawbacks of this approach are the associated computational and storage demands. In this paper we address these issues. We present different efficient approximations for dependent output Gaussian processes constructed through the convolution formalism. We exploit the conditional independencies present naturally in the model. This leads to a form of the covariance similar in spirit to the so called PITC and FITC approximations for a single output. We show experimental results with synthetic and real data, in particular, we show results in school exams score prediction, pollution prediction and gene expression data.
A Survey on Sensor Networks from a Multi-Agent perspective
"... Sensor networks arise as one of the most promising technologies for the next decades. The recent emergence of small and inexpensive sensors based upon microelectromechanical system (MEMS) ease the development and proliferation of this kind of networks in a wide range of real-world applications. Mult ..."
Abstract
-
Cited by 26 (0 self)
- Add to MetaCart
(Show Context)
Sensor networks arise as one of the most promising technologies for the next decades. The recent emergence of small and inexpensive sensors based upon microelectromechanical system (MEMS) ease the development and proliferation of this kind of networks in a wide range of real-world applications. Multi-Agent systems (MAS) have been identified as one of the most suitable technologies to contribute to this domain due to their appropriateness for modeling autonomous self-aware sensors in a flexible way. Firstly, this survey summarizes the actual challenges and research areas concerning sensor networks while identifying the most relevant MAS contributions. Secondly, we propose a taxonomy for sensor networks that classifies them depending on their features (and the research problems they pose). Finally, we identify some open future research directions and opportunities for MAS research. 1.
Sequential Bayesian Prediction in the Presence of Changepoints
"... We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We ..."
Abstract
-
Cited by 19 (6 self)
- Add to MetaCart
(Show Context)
We introduce a new sequential algorithm for making robust predictions in the presence of changepoints. Unlike previous approaches, which focus on the problem of detecting and locating changepoints, our algorithm focuses on the problem of making predictions even when such changes might be present. We introduce nonstationary covariance functions to be used in Gaussian process prediction that model such changes, then proceed to demonstrate how to effectively manage the hyperparameters associated with those covariance functions. By using Bayesian quadrature, we can integrate out the hyperparameters, allowing us to calculate the marginal predictive distribution. Furthermore, if desired, the posterior distribution over putative changepoint locations can be calculated as a natural byproduct of our prediction algorithm. 1.
Bayesian optimization for sensor set selection
- In Proceedings of the 9th ACM/IEEE International Conference on Information Processing in Sensor Networks
, 2010
"... We consider the problem of selecting an optimal set of sensors, as determined, for example, by the predictive accuracy of the resulting sensor network. Given an underlying metric between pairs of set elements, we introduce a natural metric between sets of sensors for this task. Using this metric, we ..."
Abstract
-
Cited by 19 (0 self)
- Add to MetaCart
(Show Context)
We consider the problem of selecting an optimal set of sensors, as determined, for example, by the predictive accuracy of the resulting sensor network. Given an underlying metric between pairs of set elements, we introduce a natural metric between sets of sensors for this task. Using this metric, we can construct covariance functions over sets, and thereby perform Gaussian process inference over a function whose domain is a power set. If the function has additional inputs, our covariances can be readily extended to incorporate them—allowing us to consider, for example, functions over both sets and time. These functions can then be optimized using Gaussian process global optimization (GPGO). We use the root mean squared error (RMSE) of the predictions made using a set of sensors at a particular time as an example of such a function to be optimized; the optimal point specifies the best choice of sensor locations. We demonstrate the resulting method by dynamically selecting the best subset of a given set of weather sensors for the prediction of the air temperature across the United Kingdom.
Fast Sensor Placement Algorithms for Fusion-based Target Detection
"... Mission-critical target detection imposes stringent performance requirements for wireless sensor networks, such as high detection probabilities and low false alarm rates. Data fusion has been shown as an effective technique for improving system detection performance by enabling efficient collaborati ..."
Abstract
-
Cited by 15 (8 self)
- Add to MetaCart
Mission-critical target detection imposes stringent performance requirements for wireless sensor networks, such as high detection probabilities and low false alarm rates. Data fusion has been shown as an effective technique for improving system detection performance by enabling efficient collaboration among sensors with limited sensing capability. Due to the high cost of network deployment, it is desirable to place sensors at optimal locations to achieve maximum detection performance. However, for sensor networks employing data fusion, optimal sensor placement is a non-linear optimization problem with prohibitive computational complexity. In this paper, we present fast sensor placement algorithms based on a probabilistic data fusion model. Simulation results show that our algorithms can meet the desired detection performance with a small number of sensors while achieving up to 7-fold speedup over the optimal algorithm.
