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‣ Man-made structure segmentation using gaussian procesess and wavelet features.

Zhou, H.; Suter, D.
Fonte: IEEE; Online Publicador: IEEE; Online
Tipo: Conference paper
Publicado em //2007 Português
Relevância na Pesquisa
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We apply Gaussian process classification (GPC) to man-made structure segmentation, treated as a two class problem. GPC is a discriminative approach, and thus focuses on modelling the posterior directly. It relaxes the strong assumption of conditional independence of the observed data (generally used in a generative model). In addition, wavelet transform features, which are effective in describing directional textures, are incorporated in the feature vector. Satisfactory results have been obtained which show the effectiveness of our approach.; http://dx.doi.org/10.1109/ICIP.2007.4380026; Hang Zhou and David Suter

‣ Gaussian averages of interpolated bodies and applications to approximate reconstruction

Gordon, Y; Litvak, Alexander; Mendelson, Shahar; Pajor, Alain
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
563.59594%
We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of Bpn with ρ Bqn for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the intersection of Bp ∞n with ρ B2n for 0 < p ≤ 1 and ρ > 0. We present an ap

‣ Efficient High-Dimensional Gaussian Process Regression to calculate the Expected Value of Partial Perfect Information in Health Economic Evaluations

Heath, Anna; Manolopoulou, Ioanna; Baio, Gianluca
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/04/2015 Português
Relevância na Pesquisa
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The Expected Value of Perfect Partial Information (EVPPI) is a decision-theoretic measure of the "cost" of uncertainty in decision making used principally in health economic decision making. Despite having optimal properties in terms of quantifying the value of decision uncertainty, the EVPPI is rarely used in practise. This is due to the prohibitive computational time required to estimate the EVPPI via Monte Carlo simulations. However, a recent development has demonstrated that the EVPPI can be estimated by non parametric regression methods, which have significantly decreased the computation time required to approximate the EVPPI. Under certain circumstances, high-dimensional Gaussian Process regression is suggested, but this can still be prohibitively expensive. Applying fast computation methods developed in spatial statistics using Integrated Nested Laplace Approximations (INLA) and projecting from our high-dimensional input space allows us to decrease the computation time for fitting these high-dimensional Gaussian Processes from around 13 minutes to 10 seconds. We demonstrate that the EVPPI calculated using this new method for Gaussian Process regression is in line with the standard Gaussian Process regression method and that despite the methodological complexity of this new method...

‣ Gaussian Process-Based Bayesian Nonparametric Inference of Population Trajectories from Gene Genealogies

Palacios, Julia A.; Minin, Vladimir N.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
470.92363%
Changes in population size influence genetic diversity of the population and, as a result, leave a signature of these changes in individual genomes in the population. We are interested in the inverse problem of reconstructing past population dynamics from genomic data. We start with a standard framework based on the coalescent, a stochastic process that generates genealogies connecting randomly sampled individuals from the population of interest. These genealogies serve as a glue between the population demographic history and genomic sequences. It turns out that only the times of genealogical lineage coalescences contain information about population size dynamics. Viewing these coalescent times as a point process, estimating population size trajectories is equivalent to estimating a conditional intensity of this point process. Therefore, our inverse problem is similar to estimating an inhomogeneous Poisson process intensity function. We demonstrate how recent advances in Gaussian process-based nonparametric inference for Poisson processes can be extended to Bayesian nonparametric estimation of population size dynamics under the coalescent. We compare our Gaussian process (GP) approach to one of the state of the art Gaussian Markov random field (GMRF) methods for estimating population trajectories. Using simulated data...

‣ Optimal Bayesian estimation in random covariate design with a rescaled Gaussian process prior

Pati, Debdeep; Bhattacharya, Anirban; Cheng, Guang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
470.3261%
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a fixed design for covariates. The only random design result we are aware of (van der Vaart & van Zanten, 2011) assumes the assigned Gaussian process to be supported on the smoothness class specified by the true function with probability one. This is a fairly restrictive assumption as it essentially rules out the Gaussian process prior with a squared exponential kernel when modeling rougher functions. In this article, we show that an appropriate rescaling of the above Gaussian process leads to a rate-optimal posterior distribution even when the covariates are independently realized from a known density on a compact set. The proofs are based on deriving sharp concentration inequalities for frequentist kernel estimators; the results might be of independent interest.; Comment: To appear in the Journal of Machine Learning Research

‣ Gaussian Process Regression with Heteroscedastic or Non-Gaussian Residuals

Wang, Chunyi; Neal, Radford M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/12/2012 Português
Relevância na Pesquisa
470.59773%
Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. In this paper, we propose a GP Regression model with a latent variable that serves as an additional unobserved covariate for the regression. This model (which we call GPLC) allows for heteroscedasticity since it allows the function to have a changing partial derivative with respect to this unobserved covariate. With a suitable covariance function, our GPLC model can handle (a) Gaussian residuals with input-dependent variance, or (b) non-Gaussian residuals with input-dependent variance, or (c) Gaussian residuals with constant variance. We compare our model, using synthetic datasets, with a model proposed by Goldberg, Williams and Bishop (1998), which we refer to as GPLV, which only deals with case (a), as well as a standard GP model which can handle only case (c). Markov Chain Monte Carlo methods are developed for both modelsl. Experiments show that when the data is heteroscedastic, both GPLC and GPLV give better results (smaller mean squared error and negative log-probability density) than standard GP regression. In addition...

‣ A Constrained Matrix-Variate Gaussian Process for Transposable Data

Koyejo, Oluwasanmi; Lee, Cheng; Ghosh, Joydeep
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/04/2014 Português
Relevância na Pesquisa
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Transposable data represents interactions among two sets of entities, and are typically represented as a matrix containing the known interaction values. Additional side information may consist of feature vectors specific to entities corresponding to the rows and/or columns of such a matrix. Further information may also be available in the form of interactions or hierarchies among entities along the same mode (axis). We propose a novel approach for modeling transposable data with missing interactions given additional side information. The interactions are modeled as noisy observations from a latent noise free matrix generated from a matrix-variate Gaussian process. The construction of row and column covariances using side information provides a flexible mechanism for specifying a-priori knowledge of the row and column correlations in the data. Further, the use of such a prior combined with the side information enables predictions for new rows and columns not observed in the training data. In this work, we combine the matrix-variate Gaussian process model with low rank constraints. The constrained Gaussian process approach is applied to the prediction of hidden associations between genes and diseases using a small set of observed associations as well as prior covariances induced by gene-gene interaction networks and disease ontologies. The proposed approach is also applied to recommender systems data which involves predicting the item ratings of users using known associations as well as prior covariances induced by social networks. We present experimental results that highlight the performance of constrained matrix-variate Gaussian process as compared to state of the art approaches in each domain.; Comment: 23 pages...

‣ On Some Asymptotic Properties and an Almost Sure Approximation of the Normalized Inverse-Gaussian Process

Labadi, Luai Al; Zarepour, Mahmoud
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/06/2012 Português
Relevância na Pesquisa
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In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem for the normalized inverse-Gaussian process and its corresponding quantile process. We also derive a finite sum-representation that converges almost surely to the Ferguson and Klass representation of the normalized inverse-Gaussian process. This almost sure approximation can be used to simulate efficiently the normalized inverse-Gaussian process.; Comment: 25

‣ Fractional Normal Inverse Gaussian Process

Kumar, Arun; Vellaisamy, P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/07/2009 Português
Relevância na Pesquisa
474.56934%
Normal inverse Gaussian (NIG) process was introduced by Barndorff-Nielsen (1997) by subordinating Brownian motion with drift to an inverse Gaussian process. Increments of NIG process are independent and stationary. In this paper, we introduce dependence between the increments of NIG process, by subordinating fractional Brownian motion to an inverse Gaussian process and call it fractional normal inverse Gaussian (FNIG) process. The basic properties of this process are discussed. Its marginal distributions are scale mixtures of normal laws, infinitely divisible for the Hurst parameter 1/2<=H< 1 and are heavy tailed. First order increments of the process are stationary and possess long-range dependence (LRD) property. It is shown that they have persistence of signs LRD property also. A generalization of the FNIG process called n-FNIG process is also discussed which allows Hurst parameter H in the interval (n-1, n). Possible applications to mathematical finance and hydraulics are also pointed out; Comment: 20 pages and 4 figures

‣ Mixture Gaussian Process Conditional Heteroscedasticity

Platanios, Emmanouil A.; Chatzis, Sotirios P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
470.2723%
Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a mixture Gaussian process conditional heteroscedasticity (MGPCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula- based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated MGPCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.; Comment: Technical Report...

‣ Varying-coefficient models with isotropic Gaussian process priors

Bussas, Matthias; Sawade, Christoph; Scheffer, Tobias; Landwehr, Niels
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
471.5189%
We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this conditional. Varying-coefficient models subsume hierarchical Bayesian multitask models, but also generalizations in which the conditional varies continuously, for instance, in time or space. However, Bayesian inference in varying-coefficient models is generally intractable. We show that inference for varying-coefficient models with isotropic Gaussian process priors resolves to standard inference for a Gaussian process that can be solved efficiently. MAP inference in this model resolves to multitask learning using task and instance kernels, and inference for hierarchical Bayesian multitask models can be carried out efficiently using graph-Laplacian kernels. We report on experiments for geospatial prediction.; Comment: 17 pages, 4 Figures, minor revision

‣ Gaussian Process Kernels for Pattern Discovery and Extrapolation

Wilson, Andrew Gordon; Adams, Ryan Prescott
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
472.99977%
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density -- the Fourier transform of a kernel -- with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. We also show that we can reconstruct standard covariances within our framework.; Comment: 10 pages, 5 figures, 1 table. Minor edits and titled changed from "Gaussian Process Covariance Kernels for Pattern Discovery and Extrapolation" to "Gaussian Process Kernels for Pattern Discovery and Extrapolation". Appears at the International Conference on Machine Learning (ICML), JMLR W&CP 28(3):1067-1075, 2013

‣ A Gaussian Process Emulator Approach for Rapid Contaminant Characterization with an Integrated Multizone-CFD Model

Tagade, Piyush M.; Jeong, Byeong-Min; Choi, Han-Lim
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
473.90285%
This paper explores a Gaussian process emulator based approach for rapid Bayesian inference of contaminant source location and characteristics in an indoor environment. In the pre-event detection stage, the proposed approach represents transient contaminant fate and transport as a random function with multivariate Gaussian process prior. Hyper-parameters of the Gaussian process prior are inferred using a set of contaminant fate and transport simulation runs obtained at predefined source locations and characteristics. This paper uses an integrated multizone-CFD model to simulate contaminant fate and transport. Mean of the Gaussian process, conditional on the inferred hyper-parameters, is used as an computationally efficient statistical emulator of the multizone-CFD simulator. In the post event-detection stage, the Bayesian framework is used to infer the source location and characteristics using the contaminant concentration data obtained through a sensor network. The Gaussian process emulator of the contaminant fate and transport is used for Markov Chain Monte Carlo sampling to efficiently explore the posterior distribution of source location and characteristics. Efficacy of the proposed method is demonstrated for a hypothetical contaminant release through multiple sources in a single storey seven room building. The method is found to infer location and characteristics of the multiple sources accurately. The posterior distribution obtained using the proposed method is found to agree closely with the posterior distribution obtained by directly coupling the multizone-CFD simulator with the Markov Chain Monte Carlo sampling.; Comment: The paper is submitted to the journal "Building and Environment" for possible publication

‣ Automatically Grading Learners? English Using a Gaussian Process

van Dalen, Rogier C.; Knill, Kate M.; Gales, Mark J. F.
Fonte: ISCA Publicador: ISCA
Tipo: Article; accepted version
Português
Relevância na Pesquisa
668.21805%
This is the author accepted manuscript. The final version is available from ISCA via http://www.isca-speech.org/archive/slate_2015/sl15_007.html; There is a high demand around the world for the learning of English as a second language. Correspondingly, there is a need to assess the proficiency level of learners both during their studies and for formal qualifications. A number of automatic methods have been proposed to help meet this demand with varying degrees of success. This paper considers the automatic assessment of spoken English proficiency, which is still a challenging problem. In this scenario, the grader should be able to accurately assess the learner?s ability level from spontaneous, prompted, speech, independent of L1 language and the quality of the audio recording. Automatic graders are potentially more consistent than humans. However, the validity of the predicted grade varies. This paper proposes an automatic grader based on a Gaussian process. The advantage of using a Gaussian process is that as well as predicting a grade, it provides a measure of the uncertainty of its prediction. The uncertainty measure is sufficiently accurate to decide which automatic grades should be re-graded by humans. It can also be used to determine which candidates are hard to grade for humans and therefore need expert grading. Performance of the automatic grader is shown to be close to human graders on real candidate entries. Interpolation of human and GP grades further boosts performance.; This work was supported by Cambridge English...

‣ Gaussian processes for state space models and change point detection

Turner, Ryan Darby
Fonte: University of Cambridge; Department of Engineering Publicador: University of Cambridge; Department of Engineering
Tipo: Thesis; doctoral; PhD
Português
Relevância na Pesquisa
480.0321%
This thesis details several applications of Gaussian processes (GPs) for enhanced time series modeling. We first cover different approaches for using Gaussian processes in time series problems. These are extended to the state space approach to time series in two different problems. We also combine Gaussian processes and Bayesian online change point detection (BOCPD) to increase the generality of the Gaussian process time series methods. These methodologies are evaluated on predictive performance on six real world data sets, which include three environmental data sets, one financial, one biological, and one from industrial well drilling. Gaussian processes are capable of generalizing standard linear time series models. We cover two approaches: the Gaussian process time series model (GPTS) and the autoregressive Gaussian process (ARGP). We cover a variety of methods that greatly reduce the computational and memory complexity of Gaussian process approaches, which are generally cubic in computational complexity. Two different improvements to state space based approaches are covered. First, Gaussian process inference and learning (GPIL) generalizes linear dynamical systems (LDS), for which the Kalman filter is based, to general nonlinear systems for nonparametric system identification. Second...

‣ Automatic model construction with Gaussian processes

Duvenaud, David
Fonte: University of Cambridge; Department of Engineering Publicador: University of Cambridge; Department of Engineering
Tipo: Thesis; doctoral; PhD
Português
Relevância na Pesquisa
472.8641%
This thesis develops a method for automatically constructing, visualizing and describing a large class of models, useful for forecasting and finding structure in domains such as time series, geological formations, and physical dynamics. These models, based on Gaussian processes, can capture many types of statistical structure, such as periodicity, changepoints, additivity, and symmetries. Such structure can be encoded through kernels, which have historically been hand-chosen by experts. We show how to automate this task, creating a system that explores an open-ended space of models and reports the structures discovered. To automatically construct Gaussian process models, we search over sums and products of kernels, maximizing the approximate marginal likelihood. We show how any model in this class can be automatically decomposed into qualitatively different parts, and how each component can be visualized and described through text. We combine these results into a procedure that, given a dataset, automatically constructs a model along with a detailed report containing plots and generated text that illustrate the structure discovered in the data. The introductory chapters contain a tutorial showing how to express many types of structure through kernels...

‣ Bayesian Modeling Using Latent Structures

Wang, Xiaojing
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2012 Português
Relevância na Pesquisa
471.23895%

This dissertation is devoted to modeling complex data from the

Bayesian perspective via constructing priors with latent structures.

There are three major contexts in which this is done -- strategies for

the analysis of dynamic longitudinal data, estimating

shape-constrained functions, and identifying subgroups. The

methodology is illustrated in three different

interdisciplinary contexts: (1) adaptive measurement testing in

education; (2) emulation of computer models for vehicle crashworthiness; and (3) subgroup analyses based on biomarkers.

Chapter 1 presents an overview of the utilized latent structured

priors and an overview of the remainder of the thesis. Chapter 2 is

motivated by the problem of analyzing dichotomous longitudinal data

observed at variable and irregular time points for adaptive

measurement testing in education. One of its main contributions lies

in developing a new class of Dynamic Item Response (DIR) models via

specifying a novel dynamic structure on the prior of the latent

trait. The Bayesian inference for DIR models is undertaken, which

permits borrowing strength from different individuals, allows the

retrospective analysis of an individual's changing ability...

‣ Multivariate Spatial Process Gradients with Environmental Applications

Terres, Maria Antonia
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2014 Português
Relevância na Pesquisa
566.45723%

Previous papers have elaborated formal gradient analysis for spatial processes, focusing on the distribution theory for directional derivatives associated with a response variable assumed to follow a Gaussian process model. In the current work, these ideas are extended to additionally accommodate one or more continuous covariate(s) whose directional derivatives are of interest and to relate the behavior of the directional derivatives of the response surface to those of the covariate surface(s). It is of interest to assess whether, in some sense, the gradients of the response follow those of the explanatory variable(s), thereby gaining insight into the local relationships between the variables. The joint Gaussian structure of the spatial random effects and associated directional derivatives allows for explicit distribution theory and, hence, kriging across the spatial region using multivariate normal theory. The gradient analysis is illustrated for bivariate and multivariate spatial models, non-Gaussian responses such as presence-absence and point patterns, and outlined for several additional spatial modeling frameworks that commonly arise in the literature. Working within a hierarchical modeling framework, posterior samples enable all gradient analyses to occur as post model fitting procedures.

; Dissertation

‣ Heteroscedastic gaussian process regression

Le, Quoc; Smola, Alexander; Canu, Stephane
Fonte: OmniPress Publicador: OmniPress
Tipo: Conference paper
Português
Relevância na Pesquisa
666.4572%
This paper presents an algorithm to estimate simultaneously both mean and variance of a non parametric regression problem. The key point is that we are able to estimate variance locally unlike standard Gaussian Process regression or SVMs. This means that

‣ Accelerating evolutionary algorithms with Gaussian process fitness function models

Buche, Dirk; Schraudolph, Nicol; Koumoutsakos, Petros
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
671.5189%
We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between evolution control and the surrogate approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration versus exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian process optimization procedure clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: The optimization of stationary gas turbine compressor profiles.