The von Mises Graphical Model : Structure Learning

The von Mises distribution is a continuous probability distribution on the circle used in directional statistics. In this paper, we introduce the undirected von Mises Graphical model and present an algorithm for structure learning using L1 regularization. We show that the learning algorithm is both consistent and efficient. We also introduce a simple inference algorithm based on Gibbs sampling. We compare and contrast the von Mises Graphical Model (VGM) with a Gaussian Graphical Model (GGM) on both synthetic data and on data from protein structures and demonstrate that the VGM achieves higher accuracy than the GGM.

[1]  Kanti V. Mardia,et al.  Statistics of Directional Data , 1972 .

[2]  Mark W. Schmidt,et al.  Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches , 2007, ECML.

[3]  B. Schölkopf,et al.  High-Dimensional Graphical Model Selection Using ℓ1-Regularized Logistic Regression , 2007 .

[4]  Richard S. Zemel,et al.  Lending direction to neural networks , 1995, Neural Networks.

[5]  Robert Tibshirani,et al.  Estimation of Sparse Binary Pairwise Markov Networks using Pseudo-likelihoods , 2009, J. Mach. Learn. Res..

[6]  Guy Lebanon,et al.  Statistical and Computational Tradeoffs in Stochastic Composite Likelihood , 2009, AISTATS.

[7]  S. R. Jammalamadaka,et al.  Directional Statistics, I , 2011 .

[8]  Wouter Boomsma,et al.  Beyond rotamers: a generative, probabilistic model of side chains in proteins , 2010, BMC Bioinformatics.

[9]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[10]  Daphne Koller,et al.  Efficient Structure Learning of Markov Networks using L1-Regularization , 2006, NIPS.

[11]  Thomas Hofmann,et al.  Efficient Structure Learning of Markov Networks using L1-Regularization , 2007 .

[12]  Richard S. Zemel,et al.  Directional-Unit Boltzmann Machines , 1992, NIPS.

[13]  Joel A. Tropp,et al.  Just relax: convex programming methods for identifying sparse signals in noise , 2006, IEEE Transactions on Information Theory.

[14]  Mark W. Schmidt,et al.  Structure learning in random fields for heart motion abnormality detection , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Nicholas I. Fisher,et al.  Statistical Analysis of Circular Data , 1993 .