Related papers: Trek separation for Gaussian graphical models
In this short note, we give a very simple but useful generalization of a result of Vershynin (Theorem 5.39 of [1]) for a random matrix with independent sub-Gaussian rows. We also explain with an example where our generalization is useful.
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
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…
We explore the concept of separating systems of vertex sets of graphs. A separating system of a set $X$ is a collection of subsets of $X$ such that for any pair of distinct elements in $X$, there exists a set in the separating system that…
Baker devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Within the framework of Gaussian graphical models, a prior distribution for the underlying graph is introduced to induce a block structure in the adjacency matrix of the graph and learning relationships between fixed groups of variables. A…
Pearl's d-separation is a foundational notion to study conditional independence between random variables. We define the topological conditional separation and we show that it is equivalent to the d-separation, extended beyond acyclic…
We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…
Let $G$ be a nontrivial connected graph with vertex set $V(G)$. A set of vertices $D\subseteq V(G)$ is called a total outer-independent dominating set of $G$ if every vertex of $G$ is adjacent to at least one vertex in $D$, and…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
The vertices of a $k$-token graph of a graph $G$ correspond to $k$ indistinguishable tokens placed on $k$ different vertices of $G$. Changing some conditions on both the nature of the tokens and the number of tokens allowed in each vertex…
A seminal technique of theoretical physics called Wick's theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by…
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…
A k-ranking of a graph G is a labeling of the vertices of G with values from {1,...,k} such that any path joining two vertices with the same label contains a vertex having a higher label. The tree-depth of G is the smallest value of k for…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…