Related papers: Faster solutions of the inverse pairwise Ising pro…
We propose the use of Monte Carlo histogram reweighting to extrapolate predictions of machine learning methods. In our approach, we treat the output from a convolutional neural network as an observable in a statistical system, enabling its…
Understanding the dependence structure between response variables is an important component in the analysis of correlated multivariate data. This article focuses on modeling dependence structures in multivariate binary data, motivated by a…
The estimation of model parameters with uncertainties from observed data is a ubiquitous inverse problem in science and engineering. In this paper, we suggest an inexpensive and easy to implement parameter estimation technique that uses a…
We completely describe by inequalities the set of boundary correlation matrices of planar Ising networks embedded in a disk. Specifically, we build on a recent result of M.~Lis to give a simple bijection between such correlation matrices…
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in…
We study analytically the performance of a recently proposed algorithm for learning the couplings of a random asymmetric kinetic Ising model from finite length trajectories of the spin dynamics. Our analysis shows the importance of the…
We construct neuron models from data by transferring information from an observed time series to the state variables and parameters of Hodgkin-Huxley models. When the learning period completes, the model will predict additional observations…
One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories and are described by polynomial terms in the action. The…
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for…
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…
We introduce a procedure to infer the interactions among a set of binary variables, based on their sampled frequencies and pairwise correlations. The algorithm builds the clusters of variables contributing most to the entropy of the…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Ising machines (IM) are physics-inspired alternatives to von Neumann architectures for solving hard optimization tasks. By mapping binary variables to coupled Ising spins, IMs can naturally solve unconstrained combinatorial optimization…
We revisit the problem of efficiently learning the underlying parameters of Ising models from data. Current algorithmic approaches achieve essentially optimal sample complexity when given i.i.d. samples from the stationary measure and the…
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
We demonstrate the capability of a convolutional deep neural network in predicting the nearest-neighbor energy of the 4x4 Ising model. Using its success at this task, we motivate the study of the larger 8x8 Ising model, showing that the…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
Many deep neural networks have been used to solve Ising models, including autoregressive neural networks, convolutional neural networks, recurrent neural networks, and graph neural networks. Learning a probability distribution of energy…
We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local…
To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging…