Related papers: Inverse statistical problems: from the inverse Isi…
The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Over the last decade, many applications of the inverse Ising problem have arisen,…
The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
Our understanding of physical systems generally depends on our ability to match complex computational modelling with measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities,…
As a problem in data science the inverse Ising (or Potts) problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising (or Potts) model from samples drawn from that distribution. The algorithmic and computational…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the…
In this work we consider the problem of extracting a set of interaction parameters from an high-dimensional dataset describing T independent configurations of a complex system composed of N binary units. This problem is formulated in the…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
Correlations between two variables of a high-dimensional system can be indicative of an underlying interaction, but can also result from indirect effects. Inverse Ising inference is a method to distinguish one from the other. Essentially,…
Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
The inverse Ising problem and its generalizations to Potts and continuous spin models have recently attracted much attention thanks to their successful applications in the statistical modeling of biological data. In the standard setting,…
We introduce varying spin strengths to the Ising model, a central pillar of statistical physics. With inhomogeneous physical systems in mind, but also anticipating interdisciplinary applications, we present the model on network structures…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…