Sampling large hyperplane-truncated multivariate normal distributions

Hassan Maatouk (1, 2) , Didier Rullière (3, 4, 5, 6) , Xavier Bay (3, 4, 5, 6)

1 CY - CY Cergy Paris Université
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
3 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
4 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
5 FAYOL-ENSMSE - Institut Henri Fayol
6 FAYOL-ENSMSE - Département Génie mathématique et industriel

Generating multivariate normal distributions is widely used in various fields, including engineering, statistics, finance and machine learning. In this paper, simulating large multivariate normal distributions truncated on the intersection of a set of hyperplanes is investigated. Specifically, the proposed methodology focuses on cases where the prior multivariate normal is extracted from a stationary Gaussian process (GP). It is based on combining both Karhunen-Loève expansions (KLE) and Matheron’s update rules (MUR). The KLE requires the computation of the decomposition of the covariance matrix of the random variables, which can become expensive when the random vector is too large. To address this issue, the input domain is split in smallest subdomains where the eigendecomposition can be computed. Due to the stationary property, only the eigendecomposition of the first subdomain is required. Through this strategy, the computational complexity is drastically reduced. The mean-square truncation and block errors have been calculated. The efficiency of the proposed approach has been demonstrated through both synthetic and real data studies.

Domains: Methodology [stat.ME]; General Mathematics [math.GM]; Probability [math.PR]

Hassan Maatouk, Didier Rullière, Xavier Bay. Sampling large hyperplane-truncated multivariate normal distributions. Computational Statistics, 2023, ⟨10.1007/s00180-023-01416-7⟩. ⟨hal-03741860v2⟩