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Gaussian Processes for Regression
 Advances in Neural Information Processing Systems 8
, 1996
"... The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparame ..."
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Cited by 219 (18 self)
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The Bayesian analysis of neural networks is difficult because a simple prior over weights implies a complex prior distribution over functions. In this paper we investigate the use of Gaussian process priors over functions, which permit the predictive Bayesian analysis for fixed values of hyperparameters to be carried out exactly using matrix operations. Two methods, using optimization and averaging (via Hybrid Monte Carlo) over hyperparameters have been tested on a number of challenging problems and have produced excellent results.
Prediction With Gaussian Processes: From Linear Regression To Linear Prediction And Beyond
 Learning and Inference in Graphical Models
, 1997
"... The main aim of this paper is to provide a tutorial on regression with Gaussian processes. We start from Bayesian linear regression, and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions, rather than on priors over parameters. Th ..."
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Cited by 195 (4 self)
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The main aim of this paper is to provide a tutorial on regression with Gaussian processes. We start from Bayesian linear regression, and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions, rather than on priors over parameters. This leads in to a more general discussion of Gaussian processes in section 4. Section 5 deals with further issues, including hierarchical modelling and the setting of the parameters that control the Gaussian process, the covariance functions for neural network models and the use of Gaussian processes in classification problems. PREDICTION WITH GAUSSIAN PROCESSES: FROM LINEAR REGRESSION TO LINEAR PREDICTION AND BEYOND 2 1 Introduction In the last decade neural networks have been used to tackle regression and classification problems, with some notable successes. It has also been widely recognized that they form a part of a wide variety of nonlinear statistical techniques that can be used for...
The Bayesian image retrieval system, PicHunter: Theory, implementation, and psychophysical experiments
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2000
"... This paper presents the theory, design principles, implementation, and performance results of PicHunter, a prototype contentbased image retrieval (CBIR) system that has been developed over the past three years. In addition, this document presents the rationale, design, and results of psychophysica ..."
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Cited by 181 (2 self)
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This paper presents the theory, design principles, implementation, and performance results of PicHunter, a prototype contentbased image retrieval (CBIR) system that has been developed over the past three years. In addition, this document presents the rationale, design, and results of psychophysical experiments that were conducted to address some key issues that arose during PicHunter’s development. The PicHunter project makes four primary contributions to research on contentbased image retrieval. First, PicHunter represents a simple instance of a general Bayesian framework we describe for using relevance feedback to direct a search. With an explicit model of what users would do, given what target image they want, PicHunter uses Bayes’s rule to predict what is the target they want, given their actions. This is done via a probability distribution over possible image targets, rather than by refining a query. Second, an entropyminimizing display algorithm is described that attempts to maximize the information obtained from a user at each iteration of the search. Third, PicHunter makes use of hidden annotation rather than a possibly inaccurate/inconsistent annotation structure that the user must learn and make queries in. Finally, PicHunter introduces two experimental paradigms to quantitatively evaluate the performance of the system, and psychophysical experiments are presented that support the theoretical claims.
Nearoptimal sensor placements in gaussian processes
 In ICML
, 2005
"... When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. 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 t ..."
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Cited by 174 (27 self)
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When monitoring spatial phenomena, which can often be modeled as Gaussian processes (GPs), choosing sensor locations is a fundamental task. 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. In this paper, we tackle the combinatorial optimization problem of maximizing the mutual information between the chosen locations and the locations which are not selected. We prove that the problem of finding the configuration that maximizes mutual information is NPcomplete. To address this issue, we describe a polynomialtime approximation that is within (1 − 1/e) of the optimum by exploiting the submodularity of mutual information. We also show how submodularity can be used to obtain online bounds, and design branch and bound search procedures. We then extend our algorithm to exploit lazy evaluations and local structure in the GP, yielding significant speedups. We also extend our approach to find placements which are robust against node failures and uncertainties in the model. These extensions are again associated with rigorous theoretical approximation guarantees, exploiting the submodularity of the objective function. We demonstrate the advantages of our approach towards optimizing mutual information in a very extensive empirical study on two realworld data sets.
Random number generation
"... Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables dis ..."
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Cited by 136 (30 self)
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Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables distributed uniformly over the interval
Active learning literature survey
, 2010
"... The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., ..."
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Cited by 132 (1 self)
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The key idea behind active learning is that a machine learning algorithm can achieve greater accuracy with fewer labeled training instances if it is allowed to choose the data from which is learns. An active learner may ask queries in the form of unlabeled instances to be labeled by an oracle (e.g., a human annotator). Active learning is wellmotivated in many modern machine learning problems, where unlabeled data may be abundant but labels are difficult, timeconsuming, or expensive to obtain. This report provides a general introduction to active learning and a survey of the literature. This includes a discussion of the scenarios in which queries can be formulated, and an overview of the query strategy frameworks proposed in the literature to date. An analysis of the empirical and theoretical evidence for active learning, a summary of several problem setting variants, and a discussion
Bayesian Classification with Gaussian Processes
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... We consider the problem of assigning an input vector x to one of m classes by predicting P (cjx) for c = 1; : : : ; m. For a twoclass problem, the probability of class 1 given x is estimated by oe(y(x)), where oe(y) = 1=(1 + e ). A Gaussian process prior is placed on y(x), and is combined wi ..."
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Cited by 130 (1 self)
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We consider the problem of assigning an input vector x to one of m classes by predicting P (cjx) for c = 1; : : : ; m. For a twoclass problem, the probability of class 1 given x is estimated by oe(y(x)), where oe(y) = 1=(1 + e ). A Gaussian process prior is placed on y(x), and is combined with the training data to obtain predictions for new x points.
Social Interactions, Local Spillovers and Unemployment
 Review of Economic Studies
, 2001
"... I analyse a model that explicitly incorporates local interactions and allows agents to exchange information about job openings within their social networks. Agents are more likely to be employed if their social contacts are also employed. The model generates a stationary distribution of unemployment ..."
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Cited by 116 (6 self)
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I analyse a model that explicitly incorporates local interactions and allows agents to exchange information about job openings within their social networks. Agents are more likely to be employed if their social contacts are also employed. The model generates a stationary distribution of unemployment that exhibits positive spatial correlations. I estimate the model via an indirect inference procedure, using Census Tract data for Chicago. I find a significantly positive amount of social interactions across neighbouring tracts. The local spillovers are stronger for areas with less educated workers and higher fractions of minorities. Furthermore, they are shaped by ethnic dividing lines and neighbourhood boundaries. 1.
SeRLoc: Secure RangeIndependent Localization for Wireless Sensor Networks
 in Proceedings of WiSe
, 2004
"... In many applications of wireless sensor networks (WSN), sensors are deployed untethered in hostile environments. For locationaware WSN applications, it is essential to ensure that sensors can determine their location, even in the presence of malicious adversaries. In this paper we address the probl ..."
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Cited by 104 (3 self)
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In many applications of wireless sensor networks (WSN), sensors are deployed untethered in hostile environments. For locationaware WSN applications, it is essential to ensure that sensors can determine their location, even in the presence of malicious adversaries. In this paper we address the problem of enabling sensors of WSN to determine their location in an untrusted environment. Since localization schemes based on distance estimation are expensive for the resource constrained sensors, we propose a rangeindependent localization algorithm called SeRLoc. SeRLoc is distributed algorithm and does not require any communication among sensors. In addition, we show that SeRLoc is robust against severe WSN attacks, such as the wormhole attack, the sybil attack and compromised sensors. To the best of our knowledge, ours is the first work that provides a securityaware rangeindependent localization scheme for WSN. We present a threat analysis and comparison of the performance of SeRLoc with stateoftheart rangeindependent localization schemes.
Modelbased Geostatistics
 Applied Statistics
, 1998
"... Conventional geostatistical methodology solves the problem of predicting the realised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i ) + Z i at sampling locations x i , where the Z i are mutually independent, zeromean Gaussian random v ..."
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Cited by 96 (4 self)
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Conventional geostatistical methodology solves the problem of predicting the realised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i ) + Z i at sampling locations x i , where the Z i are mutually independent, zeromean Gaussian random variables. We describe two spatial applications for which Gaussian distributional assumptions are clearly inappropriate. The first concerns the assessment of residual contamination from nuclear weapons testing on a South Pacific island, in which the sampling method generates spatially indexed Poisson counts conditional on an unobserved spatially varying intensity of radioactivity; we conclude that a coventional geostatistical analysis oversmooths the data and underestimates the spatial extremes of the intensity. The second application provides a description of spatial variation in the risk of campylobacter infections relative to other enteric infections in part of North Lancashire and South C...