Related papers: A Near-Linear Time Sampler for the Ising Model wit…
Contrary to the actual nonlinear Glauber model (NLGM), the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition…
We present novel results for fast mixing of Glauber dynamics using the newly introduced and powerful Spectral Independence method from [Anari, Liu, Oveis-Gharan: FOCS 2020]. In our results, the parameters of the Gibbs distribution are…
The dynamics of non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The…
It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the…
We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-field…
Motivated by the community detection problem in Bayesian inference, as well as the recent explosion of interest in spin glasses from statistical physics, we study the classical Glauber dynamics for sampling from Ising models with sparse…
Over the last decade, a large variety of clustering algorithms have been developed to detect coregulatory relationships among genes from microarray gene expression data. Model based clustering approaches have emerged as statistically well…
In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approximation to this covariance by repeatedly sampling from the…
We present a numerical study based on Monte Carlo algorithm of the magnetic properties of a mixed Ising ferrimagnetic model on a cubic lattice where spins $\sigma =\pm 1/2$ and spins $S=0,\pm 1$ are in alternating sites on the lattice. We…
We present here two novel algorithms for simulated tempering simulations, which break detailed balance condition (DBC) but satisfy the skewed detailed balance to ensure invariance of the target distribution. The irreversible methods we…
In this paper, we study the problem of sampling from a graphical model when the model itself is changing dynamically with time. This problem derives its interest from a variety of inference, learning, and sampling settings in machine…
We study sampling algorithms for $\beta$-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a…
In some applied scenarios, the availability of complete data is restricted, often due to privacy concerns; only aggregated, robust and inefficient statistics derived from the data are made accessible. These robust statistics are not…
Large interacting systems in biology often exhibit emergent dynamics, such as coexistence of multiple time scales, manifested by fat tails in the distribution of waiting times. While existing tools in statistical inference, such as maximum…
We present a near-optimal reduction from approximately counting the cardinality of a discrete set to approximately sampling elements of the set. An important application of our work is to approximating the partition function $Z$ of a…
We consider the phase ordering problem for the low-temperature Ising dynamics initialized from a biased and disordered initialization. Work of Fontes, Schonmann, Sidoravicius (2002) showed that at zero-temperature, Ising Glauber dynamics on…
The Ising model doesn't have a strictly defined dynamics, only a spectrum. There are different ways to equip it with a time dependence e.g. the Glauber or the Kawasaki dynamics, which are both stochastic, but it means there is a master…
We study the d-dimensional random Ising model using a Bethe-Peierls approximation in the framework of the replica method. We take into account the correct interaction only inside replicated clusters of spins. Our ansatz is that the…
A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential…
In this note we consider the Glauber dynamics for the mean-field Ising model, when all couplings are equal and the external field is uniform. It is proved that the relaxation time of the dynamics is monotonically decreasing in temperature.