The Power Spherical distribution
By Nicola De Cao, Wilker Aziz. 2020
42 citations recorded by the source corpus.
There is a growing interest in probabilistic models defined in hyper-spherical spaces, be it to accommodate observed data or latent structure. The von Mises-Fisher (vMF) distribution, often regarded as the Normal distribution on the hyper-sphere, is a standard modeling choice: it is an exponential family and thus enjoys important statistical results, for example, known Kullback-Leibler (KL) divergence from other vMF distributions. Sampling from a vMF distribution, however, requires a rejection sampling procedure which besides being slow poses difficulties in the context of stochastic backpropagation via the reparameterization trick. Moreover, this procedure is numerically unstable for certain vMFs, e.g., those with high concentration and/or in high dimensions. We propose a novel distribution, the Power Spherical distribution, which retains some of the important aspects of the vMF (e.g., support on the hyper-sphere, symmetry about its mean direction parameter, known KL from other vMF distributions) while addressing its main drawbacks (i.e., scalability and numerical stability). We demonstrate the stability of Power Spherical distributions with a numerical experiment and further apply it to a variational auto-encoder trained on MNIST. Code at: this https URL
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition
Citations in the corpus
- State-specific protein–ligand complex structure prediction with a multiscale deep generative model (2022, neutral): “[46] John Ingraham et al. “Illuminating protein space with a programmable generative model”. In: bioRxiv (2022). DOI: 10.1101/2022.12.01.518682. eprint: https://www.biorxiv.org/content/early/2022/12/ 02/2022.12.01.518682.full.pdf. URL: https://www.biorxiv.org/content/early/2022/ 12/02/2022.12.01.518”
- Dynamic-Backbone Protein-Ligand Structure Prediction with Multiscale Generative Diffusion Models (2022, unknown): “Each component the 3D distance-angle distribution q 3D is parameterized by where PowerSpherical is a power spherical distribution introduced in [62]; m iul .. = ( µ, σ, v ) iul , and whre 3DMixtureDensityHead is a 3-layer MLP.”