Efficient sampling from the Bingham distribution

by   Rong Ge, et al.

We give a algorithm for exact sampling from the Bingham distribution p(x)∝(x^⊤ A x) on the sphere 𝒮^d-1 with expected runtime of poly(d, λ_max(A)-λ_min(A)). The algorithm is based on rejection sampling, where the proposal distribution is a polynomial approximation of the pdf, and can be sampled from by explicitly evaluating integrals of polynomials over the sphere. Our algorithm gives exact samples, assuming exact computation of an inverse function of a polynomial. This is in contrast with Markov Chain Monte Carlo algorithms, which are not known to enjoy rapid mixing on this problem, and only give approximate samples. As a direct application, we use this to sample from the posterior distribution of a rank-1 matrix inference problem in polynomial time.


page 1

page 2

page 3

page 4


Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs

We present a polynomial-time Markov chain Monte Carlo algorithm for esti...

Polynomial Time Algorithms for Dual Volume Sampling

We study dual volume sampling, a method for selecting k columns from an ...

Approximating the Permanent by Sampling from Adaptive Partitions

Computing the permanent of a non-negative matrix is a core problem with ...

Notes on the runtime of A* sampling

The challenge of simulating random variables is a central problem in Sta...

Sampling from Discrete Energy-Based Models with Quality/Efficiency Trade-offs

Energy-Based Models (EBMs) allow for extremely flexible specifications o...

Geometric nested sampling: sampling from distributions defined on non-trivial geometries

Metropolis Hastings nested sampling evolves a Markov chain, accepting ne...

Machine Learning Trivializing Maps: A First Step Towards Understanding How Flow-Based Samplers Scale Up

A trivializing map is a field transformation whose Jacobian determinant ...