Results 1  10
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70
Principal Curves Revisited
 Statistics and Computing
, 1992
"... A principal curve (Hastie and Stuetzle, 1989) is a smooth curve passing through the "middle" of a distribution or data cloud, and is a generalization of linear principal components. We give an alternative definition of a principal curve, based on a mixture model. Estimation is carried out through an ..."
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Cited by 50 (0 self)
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A principal curve (Hastie and Stuetzle, 1989) is a smooth curve passing through the "middle" of a distribution or data cloud, and is a generalization of linear principal components. We give an alternative definition of a principal curve, based on a mixture model. Estimation is carried out through an EM algorithm. Some comparisons are made to the Hastie Stuetzle definition.
Efficient greedy learning of Gaussian mixture models
 Neural Computation
, 2003
"... This paper concerns the greedy learning of Gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one after the other. We propose a heuristic for searching for the optimal component to insert. In a randomized manner a set of candidate new components is generated. ..."
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Cited by 49 (7 self)
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This paper concerns the greedy learning of Gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one after the other. We propose a heuristic for searching for the optimal component to insert. In a randomized manner a set of candidate new components is generated. For each of these candidates we find the locally optimal new component. The best local optimum is then inserted into the existing mixture. The resulting algorithm resolves the sensitivity to initialization of stateoftheart methods, like EM, and has running time linear in the number of data points and quadratic in the (final) number of mixture components. Due to its greedy nature the algorithm can be particularly useful when the optimal number of mixture components is unknown. Experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided.
A greedy EM algorithm for Gaussian mixture learning
 Neural Processing Letters
, 2000
"... Learning a Gaussian mixture with a local algorithm like EM can be difficult because (i) the true number of mixing components is usually unknown, (ii) there is no generally accepted method for parameter initialization, and (iii) the algorithm can get stuck in one of the many local maxima of the likel ..."
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Cited by 37 (9 self)
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Learning a Gaussian mixture with a local algorithm like EM can be difficult because (i) the true number of mixing components is usually unknown, (ii) there is no generally accepted method for parameter initialization, and (iii) the algorithm can get stuck in one of the many local maxima of the likelihood function. In this paper we propose a greedy algorithm for learning a Gaussian mixture which tries to overcome these limitations. In particular, starting with a single component and adding components sequentially until a maximum number $k$, the algorithm is capable of achieving solutions superior to EM with $k$ components in terms of the likelihood of a test set. The algorithm is based on recent theoretical results on incremental mixture density estimation, and uses a combination of global and local search each time a new component is added to the mixture.
Managing uncertainty in call centers using Poisson mixtures
 Applied Stochastic Models in Business and Industry
, 2001
"... We model a call center as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call center. We compar ..."
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Cited by 29 (4 self)
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We model a call center as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call center. We compare it to the current practice of using a point estimate of the arrival rate (assumed constant) as forecast.
Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2001
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The support reduction algorithm for computing nonparametric function estimates in mixture models
, 2003
"... ABSTRACT. In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute nonparametric Mestimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the ‘Aspect problem ’ in quantum physic ..."
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Cited by 20 (6 self)
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ABSTRACT. In this paper, we study an algorithm (which we call the support reduction algorithm) that can be used to compute nonparametric Mestimators in mixture models. The algorithm is compared with natural competitors in the context of convex regression and the ‘Aspect problem ’ in quantum physics.
Semiparametric estimation of a twocomponent mixture model
 Annals of Statistics
, 2006
"... Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed distribution is symmetric, we obtain the identifiability of this ..."
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Cited by 15 (3 self)
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Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed distribution is symmetric, we obtain the identifiability of this model, which is then defined by four unknown parameters: the mixing proportion, two location parameters and the cumulative distribution function of the symmetric mixed distribution. We propose estimators for these four parameters when no training data is available. Our estimators are shown to be strongly consistent under mild regularity assumptions and their convergence rates are studied. Their finitesample properties are illustrated by a Monte Carlo study and our method is applied to real data.
Does unemployment compensation affect unemployment duration
 The Economic Journal
, 2003
"... We use a flexible hazard rate model with unrestricted spell duration and calendar time effects to analyse a dataset including all Norwegian unemployment spells during the 1990’s. The dataset provides a unique access to conditionally independent variation in unemployment compensation. We find that a ..."
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Cited by 15 (7 self)
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We use a flexible hazard rate model with unrestricted spell duration and calendar time effects to analyse a dataset including all Norwegian unemployment spells during the 1990’s. The dataset provides a unique access to conditionally independent variation in unemployment compensation. We find that a marginal increase in compensation reduces the escape rate from unemployment significantly, irrespective of business cycle conditions and spell duration. The escape rate rises sharply in the months just prior to benefit exhaustion. While men are more responsive than women with respect to marginal changes in compensation, women are most responsive with respect to benefit exhaustion.
Sensitivity of dynamical system to Banach space parameters
 J. Math. Analysis and Applications
, 2005
"... We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is prese ..."
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Cited by 10 (7 self)
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We consider general nonlinear dynamical systems in a Banach space with dependence on parameters in a second Banach space. An abstract theoretical framework for sensitivity equations is developed. An application to measure dependent delay differential systems arising in a class of HIV models is presented.