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The Ising model is a celebrated example of a Markov random field, introduced in statistical physics to model ferromagnetism. This is a discrete exponential family with binary outcomes, where the sufficient statistic involves a quadratic…
The Ising model is famous model for magnetic substances in Statistical Physics, and has been greatly studied in many forms. It was solved in one-dimension by Ernst Ising in 1925 and in two-dimensions without an external magnetic field by…
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…
Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and…
We investigate the Ising model on a spherical surface, utilizing a Fibonacci lattice to approximate uniform coverage. This setup poses challenges in achieving consistent lattice distribution across the sphere for comparison with planar…
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…
Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models, however they fail for frustrated spin systems. Recently a generalized cluster algorithm was introduced that works extremely well for…
Analyzing classification model performance is a crucial task for machine learning practitioners. While practitioners often use count-based metrics derived from confusion matrices, like accuracy, many applications, such as weather…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
Disordered lattice spin systems are crucial in both theoretical and applied physics. However, understanding their properties poses significant challenges for Monte Carlo simulations. In this work, we investigate the two-dimensional…
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…
Using the techniques of Neural Networks (NN), we study the three-dimensional (3D) 5-state ferromagnetic Potts model on the cubic lattice as well as the two-dimensional (2D) 3-state antiferromagnetic Potts model on the square lattice. Unlike…
A Monte Carlo algorithm is proposed to simulate ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes…
Latent force models are a class of hybrid models for dynamic systems, combining simple mechanistic models with flexible Gaussian process (GP) perturbations. An extension of this framework to include multiplicative interactions between the…
Topic models provide a useful text-mining tool for learning, extracting, and discovering latent structures in large text corpora. Although a plethora of methods have been proposed for topic modeling, lacking in the literature is a formal…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by physical systems, such as the liquid-vapor transition. Its…