Related papers: An Importance Sampling Algorithm for the Ising Mod…
The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers.…
This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in…
Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…
The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically-driven circuits of stochastic binary resistors with memory. A key feature of our…
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 probabilities in its dual normal factor graph. The mapping is…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
In this paper, we show analytically that the duality of normal factor graphs (NFG) can facilitate stochastic estimation of partition functions. In particular, our analysis suggests that for the $q-$ary two-dimensional nearest-neighbor Potts…
In this paper we compute exactly the ground state energy and entropy of the dilute ferromagnetic Ising model. The two thermodynamic quantities are also computed when a magnetic field with random locations is present. The result is reached…
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the…
We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the…
We consider the ferromagnetic Ising model on a sequence of graphs $G_n$ converging locally weakly to a rooted random tree. Generalizing [Montanari, Mossel, Sly '11], under an appropriate "continuity" property, we show that the Ising…
The $q$-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model…
The two-dimensional Ising model of a ferromagnet allows for many ways of computing its partition function and other properties. Each way reveals surprising features of what we might call Ising Matter. Moreover, the various ways would appear…
The Ising model is important in statistical modeling and inference in many applications, however its normalizing constant, mean number of active vertices and mean spin interaction -- quantities needed in inference -- are computationally…
An introduction to the Propp-Wilson method of coupling-from-the-past for the Ising model is presented. It enables one to obtain exact samples from the equilibrium spin distribution for ferromagnetic interactions. Both uniform and random…
Shapley values have seen widespread use in machine learning as a way to explain model predictions and estimate the importance of covariates. Accurately explaining models is critical in real-world models to both aid in decision making and to…
In this paper we analytically study the recurrence equations of an Ising model with three competing interactions on a Cayley tree of order three. We exactly describe paramagnetic and ferromagnetic phases of the Ising model. We obtain some…
Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become…
The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most…
Importance sampling is a popular method for efficient computation of various properties of a distribution such as probabilities, expectations, quantiles etc. The output of an importance sampling algorithm can be represented as a weighted…