Autoregressive Identification of Kronecker Graphical Models

Empirical Bayesian Learning in AR Graphical Models

We address the problem of learning graphical models which correspond to high dimensional autoregressive stationary stochastic processes. A graphical model describes the conditional dependence relations among the components of a stochastic process and represents an important tool in many fields. We propose an empirical Bayes estimator of sparse autoregressive graphical models and latent-variable autoregressive graphical models. Numerical experiments show the benefit to take this Bayesian perspective for learning these types of graphical models.

Learning Quasi-Kronecker Product Graphical Models

We consider the problem of learning graphical models where the support of the concentration matrix can be decomposed as a Kronecker product. We propose a method that uses the Bayesian hierarchical learning modeling approach. Thanks to the particular structure of the graph, we use a the number of hyperparameters which is small compared to the number of nodes in the graphical model. In this way, we avoid overfitting in the estimation of the hyperparameters. Finally, we test the effectiveness of the proposed method by a numerical example.

Graphical Normalizing Flows

Normalizing flows model complex probability distributions by combining a base distribution with a series of bijective neural networks. State-of-the-art architectures rely on coupling and autoregressive transformations to lift up invertible functions from scalars to vectors. In this work, we revisit these transformations as probabilistic graphical models, showing they reduce to Bayesian networks with a pre-defined topology and a learnable density at each node. From this new perspective, we propose the graphical normalizing flow, a new invertible transformation with either a prescribed or a lear…

动态潜变量图自回归模型的稀疏加低秩辨识

Sparse plus low-rank identification for dynamical latent-variable graphical AR models

针对带动态潜变量的图自回归模型辨识问题，结合观测变量稀疏交互与潜变量模型低秩特性，构建稀疏加低秩优化问题并通过迹近似等方法求解，再恢复潜变量动态，仿真验证了方法有效性。

Bayesian inference for general Gaussian graphical models with application to multivariate lattice data

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis of spatial data. These models embed a great deal of flexibility in estimating both the correlation structure across outcom…

Gaussian graphical models with graph constraints for magnetic moment interaction in high entropy alloys

This article is motivated by studying the interaction of magnetic moments in high entropy alloys (HEAs), which plays an important role in guiding HEA designs in materials science. While first principles simulations can capture magnetic moments of individual atoms, explicit models are required to analyze their interactions. This is essentially an inverse covariance matrix estimation problem. Unlike most of the literature on graphical models, the inverse covariance matrix possesses inherent structural constraints encompassing node types, topological distance of nodes, and partially specified con…