相关论文: Model Approximation Using Cascade of Tree Decompos…
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges…
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within…
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning…
Fractional cascading is one of the influential techniques in data structures, as it provides a general framework for solving the important iterative search problem. In the problem, the input is a graph $G$ with constant degree and a set of…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus…
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
In this article, an efficient numerical method for computing both the matrix exponential and a finite horizon controllability Gramian in Cholesky-factored form is proposed. The method is applicable to general dense matrices of moderate size…
Gaussian graphical models typically assume a homogeneous structure across all subjects, which is often restrictive in applications. In this article, we propose a weighted pseudo-likelihood approach for graphical modeling which allows…
For a family of graphs $\mathcal{F}$, Weighted $\mathcal{F}$-Deletion is the problem for which the input is a vertex weighted graph $G=(V,E)$ and the goal is to delete $S\subseteq V$ with minimum weight such that $G\setminus…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that…
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…
Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…
Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
We consider the problem of quantifying the quality of a model selection problem for a graphical model. We discuss this by formulating the problem as a detection problem. Model selection problems usually minimize a distance between the…
Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high…