Frobenius Norm Regularization for the Multivariate Von Mises Distribution

Abstract

Penalizing the model complexity is necessary to avoid overfitting when the number of data samples is low with respect to the number of model parameters. In this paper, we introduce a penalization term that places an independent prior distribution for each parameter of the multivariate von Mises distribution. We also propose a circular distance that can be used to estimate the Kullback–Leibler divergence between any two circular distributions as goodness‐of‐fit measure. We compare the resulting regularized von Mises models on synthetic data and real neuroanatomical data to show that the distribution fitted using the penalized estimator generally achieves better results than nonpenalized multivariate von Mises estimator.