A Continuous Gaussian Mixture Approach to Sample Multivariate Gaussians constrained by linear inequalities

We propose a new MCMC method to sample from truncated multivariate Gaussian (TMG) distributions under linear inequality constraints. Unlike existing approaches, our method is applicable even when the underlying, unconstrained Gaussian distribution is improper, and whatever the number of constraints. Our algorithm relies on continuous Gaussian mixture (CGM) decompositions of the target TMG distribution, derived from novel integral identities. Such decompositions are exact within the admissible domain, which allows us to get (asymptotically) exact samples from the TMG using blocked Gibbs updates followed by a rejection step to discard samples outside the admissible domain. Empirical results demonstrate that the proposed method outperforms state-of-the-art alternatives over a set of challenging settings.