Related papers: Planar Graphical Models which are Easy

We consider the monomer-dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function,…

Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…

Inspired by some new advances on normal factor graphs (NFGs), we introduce NFGs as a simple and intuitive diagrammatic approach towards encoding some concepts from linear algebra. We illustrate with examples the workings of such an approach…

The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…

Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to…

Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely used in many applications, and the trade-off between the modeling capacity and the efficiency of learning and inference has been an important research problem. In…

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local Bosonic and Fermionic gauge…

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…

This paper defines, for each graph $G$, a flag vector $fG$. The flag vectors of the graphs on $n$ vertices span a space whose dimension is $p(n)$, the number of partitions on $n$. The analogy with convex polytopes indicates that the linear…

This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic combinatorics. On the one hand, a parallel with time and band…

Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…

Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…

We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We…

For any d-dimensional self-interacting fermionic model, all coefficients in the high-temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such…

We investigate the problem of estimating the structure of a weighted network from repeated measurements of a Gaussian Graphical Model (GGM) on the network. In this vein, we consider GGMs whose covariance structures align with the geometry…

Graph independence (also known as $\epsilon$-independence or $\lambda$-independence) is a mixture of classical independence and free independence corresponding to graph products or groups and operator algebras. Using conjugation by certain…

We consider multivariate centered Gaussian models for the random vector $(Z^1,\ldots, Z^p)$, whose conditional structure is described by a homogeneous graph and which is invariant under the action of a permutation subgroup. The following…

We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect…

This thesis focuses on data that has complex spatio-temporal structure and on probabilistic graphical models that learn the structure in an interpretable and scalable manner. We target two research areas of interest: Gaussian graphical…

Gaussian Boson Samplers aim to demonstrate quantum advantage by performing a sampling task believed to be classically hard. The probabilities of individual outcomes in the sampling experiment are determined by the Hafnian of an…