A multivariate von mises distribution with applications to bioinformatics

Mardia, Kanti V.; Hughes, G.; Taylor, Charles; Singh, Harshinder

doi:10.1002/cjs.5550360110

Cited by 127 publications

(134 citation statements)

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“…If we extend the von Mises as a multivariate distribution [3], we face the problem that no closed formulation is known for the normalization term when the number of variables is greater than two, and, therefore it cannot be easily fitted nor compared to other distributions. We introduce a computationally optimized version of the full pseudo-likelihood as well as a circular distance to address these problems.…”

Section: Introductionmentioning

confidence: 99%

Regularized Multivariate von Mises Distribution

Rodriguez-Lujan

Bielza

Larrañaga

2015

Advances in Artificial Intelligence

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Abstract. Regularization is necessary to avoid overfitting when the number of data samples is low compared to the number of parameters of the model. In this paper, we introduce a flexible L 1 regularization for the multivariate von Mises distribution. We also propose a circular distance that can be used to estimate the Kullback-Leibler divergence between two circular distributions by means of sampling, and also serves as goodness-of-fit measure. We compare the models on synthetic data and real morphological data from human neurons and show that the regularized model achieves better results than non regularized von Mises model.

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Section: Introductionmentioning

confidence: 99%

Regularized Multivariate von Mises Distribution

Rodriguez-Lujan

Bielza

Larrañaga

2015

Advances in Artificial Intelligence

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“…The non-truncated bivariate von Mises distribution was first proposed by Singh (2002) and extended and developed in Mardia et al (2008) and Mardia and Voss (2011). It is a unimodal/bi-modal function on the torus…”

Section: Bivariate Truncated Von Mises Distributionmentioning

confidence: 99%

Univariate and bivariate truncated von Mises distributions

2017

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In this article we study the univariate and bivariate truncated von Mises distribution, as a generalization of the von Mises distribution (Jupp and Mardia (1989)), (Mardia and Jupp (2000)). This implies the addition of two or four new truncation parameters in the univariate and, bivariate cases, respectively. The results include the definition, properties of the distribution and maximum likelihood estimators for the univariate and bivariate cases. Additionally, the analysis of the bivariate case shows how the conditional distribution is a truncated von Mises distribution, whereas the marginal distribution that generalizes the distribution introduced in Singh (2002). From the viewpoint of applications, we test the distribution with simulated data, as well as with data regarding leaf inclination angles (Bowyer and Danson. (2005)) and dihedral angles in protein chains (Murzin AG (1995)).This research aims to assert this probability distribution as a potential option for modelling or simulating any kind of phenomena where circular distributions are applicable.

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“…T he von Mises distribution [20] is the bestknown directional model and can be considered the directional analogue of the univariate normal distribution. Mardia [15,16] introduced a bivariate von Mises distribution and its extension to the multivariate case [17]. He showed that the conditional distributions are also von Mises distributions.…”

Section: Introductionmentioning

confidence: 99%