Computer Generation of Distributions on the M‐Sphere

By Gary Ulrich. 1984

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Nicola De Cao
2. Weiyang Liu
3. L. Yu
4. Zhen Liu
5. Wilker Aziz
6. Ta-Chu Kao
7. Tim R. Davidson
8. Adrian Weller

Citations in the corpus

• Continual Learning by Modeling Intra-Class Variation (2022, methodology): “The sampling of the vMF distribution follows the procedure of Ulrich (1984); Davidson et al. (2018) and the detailed algorithm is given in Appendix A. 4.3 Model-based MOCA x old f y h g x old f yh g+ fΔSampling x old f yh g+ fΔ xnew Dropout(h) x old f yh g+ fΔ x old xnew or h(x )-h(x)new variation…”
• Manifold GPLVMs for discovering non-Euclidean latent structure in neural data (2020, background): “5 because (i) there are well-known algorithms for sampling from the distribution using rejection-sampling (Ulrich, 1984) and (ii) both the entropy term H ( q θ ) and its gradient can be derived analytically (Davidson et al., 2018).”
• A Bayesian Analysis of Directional Data Using the von Mises–Fisher Distribution (2005, methodology): “In higher dimensions p > 3 , one can use Wood’s method (Wood, 1994) which is based on the VM algorithm of Ulrich (1984).”
• Bayesian Inference of General Linear Restrictions on the Cointegration Space (2007, unknown): “Ulrich (1984) describes an e¢ cient algorithm for generating variates from the von Mises distribution.”
• The Power Spherical distribution (2020, background): “Thus, rejection sampling is normally used to draw samples from it (Ulrich, 1984).”
• SIMULATING BESSEL RANDOM VARIABLES (2002, background): “Note however that for a ≥ 1/2, a beta (a, 1/2) random variate can be obtained in one line of code as 1 − 1 − U 2 2a−1 1 cos 2 (2πU 2 ) where U 1 , U 2 are independent uniform [0] [1] random variables (Devroye, 1996, based in part upon a formula of Ulrich, 1984).”
• Hyperspherical Variational Auto-Encoders (2018, methodology): “To sample from the vMF we follow the procedure of Ulrich (1984), outlined in Algorithm 1.”
• BAYESIAN ESTIMATION IN SINGLE-INDEX MODELS (2004, methodology): “The proposal distribution is taken as Fisher–von Mises, which is sampled using an algorithm of Ulrich (1984).”