Variational Approximated Restricted Maximum Likelihood Estimation for Spatial Data
TLDR
This paper introduces VREML, a scalable and efficient variational method for spatial data inference using Gaussian ICAR models, outperforming existing methods.
Key contributions
- Proposes Variational Restricted Maximum Likelihood (VREML) for scalable spatial data inference.
- Derives a computationally efficient coordinate-ascent algorithm for joint estimation.
- Theoretically establishes monotone ELBO convergence and exactness for Gaussian ICAR models.
- Empirically demonstrates VREML's superior performance over MLE and INLA.
Why it matters
This work addresses the computational bottleneck of classical REML for spatial data, making complex spatial models more accessible. By providing a scalable and accurate inference method, it enables broader application of ICAR models in various fields. The theoretical guarantees and empirical superiority highlight its practical importance.
Original Abstract
This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures. The classical estimation method, restricted maximum likelihood (REML), requires repeated inversion and factorization of large, sparse precision matrices, which makes this computation costly. To sort this problem out, we propose a variational restricted maximum likelihood (VREML) framework that approximates the intractable marginal likelihood using a Gaussian variational distribution. By constructing an evidence lower bound (ELBO) on the restricted likelihood, we derive a computationally efficient coordinate-ascent algorithm for jointly estimating the spatial random effects and variance components. In this article, we theoretically establish the monotone convergence of ELBO and mathematically exhibit that the variational family is exact under Gaussian ICAR settings, which is an indication of nullifying approximation error at the posterior level. We empirically establish the supremacy of our VREML over MLE and INLA.
📬 Weekly AI Paper Digest
Get the top 10 AI/ML arXiv papers from the week — summarized, scored, and delivered to your inbox every Monday.