4 citations · 9 across the 11 of their papers we have counts for
15 papers
Accelerated Random-Sweep Gibbs Sampling for Gaussian Graphical Models via Dual Normal Factor Graphs
Borna Khodabandeh, Mehdi Molkaraie
We study the convergence properties of the random-sweep Gibbs sampler for Gaussian graphical models with a thin-membrane prior. We demonstrate that the convergence rate of the Gibb…
On the Equivalence of Gaussian Graphical Models Defined on Complete Bipartite Graphs
Mehdi Molkaraie
This paper introduces two Gaussian graphical models defined on complete bipartite graphs. We show that the determinants of the precision matrices associated with the models are equ…
The Exact Determinant of a Specific Class of Sparse Positive Definite Matrices
Mehdi Molkaraie
For a specific class of sparse Gaussian graphical models, we provide a closed-form solution for the determinant of the covariance matrix. In our framework, the graphical interactio…
Mappings for Marginal Probabilities with Applications to Models in Statistical Physics
Mehdi Molkaraie
We present local mappings that relate the marginal probabilities of a global probability mass function represented by its primal normal factor graph to the corresponding marginal p…
Duality for Continuous Graphical Models
Mehdi Molkaraie
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph dual…
Marginal Densities, Factor Graph Duality, and High-Temperature Series Expansions
Mehdi Molkaraie
We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph…
The Primal versus the Dual Ising Model
Mehdi Molkaraie
We represent the Ising model of statistical physics by normal factor graphs in the primal and in the dual domains. By analogy with Kirchhoff's voltage and current laws, we show tha…
An Importance Sampling Scheme for Models in a Strong External Field
Mehdi Molkaraie
We propose Monte Carlo methods to estimate the partition function of the two-dimensional Ising model in the presence of an external magnetic field. The estimation is done in the du…
Monte Carlo Methods for the Ferromagnetic Potts Model Using Factor Graph Duality
Mehdi Molkaraie, Vicenc Gomez
Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models. Specifically, we consider the problem of estimating the partition function of t…
An Importance Sampling Algorithm for the Ising Model with Strong Couplings
Mehdi Molkaraie
We consider the problem of estimating the partition function of the ferromagnetic Ising model in a consistent external magnetic field. The estimation is done via importance samplin…
An Importance Sampling Scheme on Dual Factor Graphs. I. Models in a Strong External Field
Mehdi Molkaraie
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic -state Potts m…
Partition Function of the Ising Model via Factor Graph Duality
Mehdi Molkaraie, Hans-Andrea Loeliger
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this res…
Extending Monte Carlo Methods to Factor Graphs with Negative and Complex Factors
Mehdi Molkaraie, Hans-Andrea Loeliger
The partition function of a factor graph can sometimes be accurately estimated by Monte Carlo methods. In this paper, such methods are extended to factor graphs with negative and c…
Monte Carlo Algorithms for the Partition Function and Information Rates of Two-Dimensional Channels
Mehdi Molkaraie, Hans-Andrea Loeliger
The paper proposes Monte Carlo algorithms for the computation of the information rate of two-dimensional source/channel models. The focus of the paper is on binary-input channels w…
On Properties of the Minimum Entropy Sub-tree to Compute Lower Bounds on the Partition Function
Mehdi Molkaraie, Payam Pakzad
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we pres…