The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform

Bernhard Sick - One of the best experts on this subject based on the ideXlab platform.

  • Toward optimal probabilistic active learning using a Bayesian approach
    Machine Learning, 2021
    Co-Authors: Daniel Kottke, Marek Herde, Christoph Sandrock, Denis Huseljic, Georg Krempl, Bernhard Sick
    Abstract:

    Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling resources. In this article, we propose a decision-theoretic selection strategy that (1) directly optimizes the gain in misclassification error, and (2) uses a Bayesian approach by introducing a Conjugate Prior Distribution to determine the class posterior to deal with uncertainties. By reformulating existing selection strategies within our proposed model, we can explain which aspects are not covered in current state-of-the-art and why this leads to the superior performance of our approach. Extensive experiments on a large variety of datasets and different kernels validate our claims.

Daniel A. Braun - One of the best experts on this subject based on the ideXlab platform.

  • NIPS - A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function
    2012
    Co-Authors: Pedro A. Ortega, Jordi Grau-moya, Tim Genewein, David Balduzzi, Daniel A. Braun
    Abstract:

    We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the Distribution over extrema. To this end, we devise a non-parametric Conjugate Prior based on a kernel regressor. The resulting posterior Distribution directly captures the uncertainty over the maximum of the unknown function. Given t observations of the function, the posterior can be evaluated efficiently in time O(t2) up to a multiplicative constant. Finally, we show how to apply our model to optimize a noisy, non-convex, high-dimensional objective function.

  • a nonparametric Conjugate Prior Distribution for the maximizing argument of a noisy function
    Neural Information Processing Systems, 2012
    Co-Authors: Pedro A. Ortega, Tim Genewein, David Balduzzi, Jordi Graumoya, Daniel A. Braun
    Abstract:

    We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the Distribution over extrema. To this end, we devise a non-parametric Conjugate Prior based on a kernel regressor. The resulting posterior Distribution directly captures the uncertainty over the maximum of the unknown function. Given t observations of the function, the posterior can be evaluated efficiently in time O(t2) up to a multiplicative constant. Finally, we show how to apply our model to optimize a noisy, non-convex, high-dimensional objective function.

  • A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function
    arXiv: Machine Learning, 2012
    Co-Authors: Pedro A. Ortega, Jordi Grau-moya, Tim Genewein, David Balduzzi, Daniel A. Braun
    Abstract:

    We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the Distribution over extrema. To this end, we devise a non-parametric Conjugate Prior based on a kernel regressor. The resulting posterior Distribution directly captures the uncertainty over the maximum of the unknown function. We illustrate the effectiveness of our model by optimizing a noisy, high-dimensional, non-convex objective function.

Daniel Kottke - One of the best experts on this subject based on the ideXlab platform.

  • Toward optimal probabilistic active learning using a Bayesian approach
    Machine Learning, 2021
    Co-Authors: Daniel Kottke, Marek Herde, Christoph Sandrock, Denis Huseljic, Georg Krempl, Bernhard Sick
    Abstract:

    Gathering labeled data to train well-performing machine learning models is one of the critical challenges in many applications. Active learning aims at reducing the labeling costs by an efficient and effective allocation of costly labeling resources. In this article, we propose a decision-theoretic selection strategy that (1) directly optimizes the gain in misclassification error, and (2) uses a Bayesian approach by introducing a Conjugate Prior Distribution to determine the class posterior to deal with uncertainties. By reformulating existing selection strategies within our proposed model, we can explain which aspects are not covered in current state-of-the-art and why this leads to the superior performance of our approach. Extensive experiments on a large variety of datasets and different kernels validate our claims.

Paul H Garthwaite - One of the best experts on this subject based on the ideXlab platform.

  • Eliciting Dirichlet and Connor–Mosimann Prior Distributions for multinomial models
    TEST, 2013
    Co-Authors: Fadlalla G. Elfadaly, Paul H Garthwaite
    Abstract:

    This paper addresses the task of eliciting an informative Prior Distribution for multinomial models. We first introduce a method of eliciting univariate beta Distributions for the probability of each category, conditional on the probabilities of other categories. Two different forms of multivariate Prior are derived from the elicited beta Distributions. First, we determine the hyperparameters of a Dirichlet Distribution by reconciling the assessed parameters of the univariate beta conditional Distributions. Although the Dirichlet Distribution is the standard Conjugate Prior Distribution for multinomial models, it is not flexible enough to represent a broad range of Prior information. Second, we use the beta Distributions to determine the parameters of a Connor–Mosimann Distribution, which is a generalization of a Dirichlet Distribution and is also a Conjugate Prior for multinomial models. It has a larger number of parameters than the standard Dirichlet Distribution and hence a more flexible structure. The elicitation methods are designed to be used with the aid of interactive graphical user-friendly software.

  • non Conjugate Prior Distribution assessment for multivariate normal sampling
    Journal of The Royal Statistical Society Series B-statistical Methodology, 2001
    Co-Authors: Paul H Garthwaite, Shafeeqah A Alawadhi
    Abstract:

    Elicitation methods are proposed for quantifying expert opinion about a multivariate normal sampling model. The natural Conjugate Prior family imposes a relationship between the mean vector and the covariance matrix that can portray an expert's opinion poorly. Instead we assume that opinions about the mean and the covariance are independent and suggest innovative forms of question which enable the expert to quantify separately his or her opinion about each of these parameters. Prior opinion about the mean vector is modelled by a multivariate normal Distribution and about the covariance matrix by both an inverse Wishart Distribution and a generalized inverse-Wishart (GIW) Distribution. To construct the latter, results are developed that give insight into the GIW parameters and their interrelationships. Certain of the elicitation methods exploit unconditional assessments as fully as possible, since these can reflect an expert's beliefs more accurately than conditional assessments. Methods are illustrated through an example.

  • Prior Distribution assessment for a multivariate normal Distribution an experimental study
    Journal of Applied Statistics, 2001
    Co-Authors: Shafeeqah A Alawadhi, Paul H Garthwaite
    Abstract:

    A variety of methods of eliciting a Prior Distribution for a multivariate normal (MVN) Distribution have recently been proposed. This paper reports an experiment in which 16 meteorologists used the methods to quantify their opinions about climatology variables. Our results compare Prior models and show, in particular, that it can be better to assume the mean and variance of an MVN Distribution are independent a Priori, rather than to model opinion by the Conjugate Prior Distribution. Using a proper scoring rule, different forms of assessment task are examined and alternative ways of estimating parameters are compared. To quantify opinion about means, it proved preferable to ask directly about the means rather than individual observations while, to quantify opinion about the variance matrix, it was best to ask about deviations from the mean. Further results include recommendations for the way parameters of the Prior Distribution are estimated.

  • Assessment of Prior Distributions for regression models: an experimental study
    Communications in Statistics - Simulation and Computation, 1994
    Co-Authors: Paul H Garthwaite
    Abstract:

    Kadane et ah (1980) describe a method of eliciting a subjective Conjugate Prior Distribution for a linear regression model with the usual normal error structure. Here we describe an experiment in which assessors used a modified form of the method to quantify their opinions about four linear models. The accuracy of assessed Prior Distributions is measured by a scoring rule and different ways of implementing the method are considered and the effect on scores examined. The empirical results provide guidance for using the method in practice. In addition, the information contained in assessed Prior Distributions is quantified in terms of equivalent sample sizes, using methods developed here. The question of whether assessed Distributions are useful rather than misleading is also addressed

  • An elicitation method for multiple linear regression models
    Journal of Behavioral Decision Making, 1991
    Co-Authors: Paul H Garthwaite, James M. Dickey
    Abstract:

    This paper describes a method of quantifying subjective opinion about a normal linear regression model. Opinion about the regression coefficients and experimental error is elicited and modeled by a multivariate probability Distribution (a Bayesian Conjugate Prior Distribution). The Distribution model is richly parameterized and various assessment tasks are used to estimate its parameters. These tasks include the revision of opinion in the light of hypothetical data, the assessment of credible intervals, and a task commonly performed in cue-weighting experiments. A new assessment task is also introduced. In addition, implementation of the method in an interactive computer program is described and the method is illustrated with a practical example.

Pedro A. Ortega - One of the best experts on this subject based on the ideXlab platform.

  • NIPS - A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function
    2012
    Co-Authors: Pedro A. Ortega, Jordi Grau-moya, Tim Genewein, David Balduzzi, Daniel A. Braun
    Abstract:

    We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the Distribution over extrema. To this end, we devise a non-parametric Conjugate Prior based on a kernel regressor. The resulting posterior Distribution directly captures the uncertainty over the maximum of the unknown function. Given t observations of the function, the posterior can be evaluated efficiently in time O(t2) up to a multiplicative constant. Finally, we show how to apply our model to optimize a noisy, non-convex, high-dimensional objective function.

  • a nonparametric Conjugate Prior Distribution for the maximizing argument of a noisy function
    Neural Information Processing Systems, 2012
    Co-Authors: Pedro A. Ortega, Tim Genewein, David Balduzzi, Jordi Graumoya, Daniel A. Braun
    Abstract:

    We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the Distribution over extrema. To this end, we devise a non-parametric Conjugate Prior based on a kernel regressor. The resulting posterior Distribution directly captures the uncertainty over the maximum of the unknown function. Given t observations of the function, the posterior can be evaluated efficiently in time O(t2) up to a multiplicative constant. Finally, we show how to apply our model to optimize a noisy, non-convex, high-dimensional objective function.

  • A Nonparametric Conjugate Prior Distribution for the Maximizing Argument of a Noisy Function
    arXiv: Machine Learning, 2012
    Co-Authors: Pedro A. Ortega, Jordi Grau-moya, Tim Genewein, David Balduzzi, Daniel A. Braun
    Abstract:

    We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the Distribution over extrema. To this end, we devise a non-parametric Conjugate Prior based on a kernel regressor. The resulting posterior Distribution directly captures the uncertainty over the maximum of the unknown function. We illustrate the effectiveness of our model by optimizing a noisy, high-dimensional, non-convex objective function.