641 research outputs found
Inference of the sparse kinetic Ising model using the decimation method
In this paper we study the inference of the kinetic Ising model on sparse
graphs by the decimation method. The decimation method, which was first
proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising
problem, tries to recover the topology of the inferred system by setting the
weakest couplings to zero iteratively. During the decimation process the
likelihood function is maximized over the remaining couplings. Unlike the
-optimization based methods, the decimation method does not use the
Laplace distribution as a heuristic choice of prior to select a sparse
solution. In our case, the whole process can be done automatically without
fixing any parameters by hand. We show that in the dynamical inference problem,
where the task is to reconstruct the couplings of an Ising model given the
data, the decimation process can be applied naturally into a maximum-likelihood
optimization algorithm, as opposed to the static case where pseudo-likelihood
method needs to be adopted. We also use extensive numerical studies to validate
the accuracy of our methods in dynamical inference problems. Our results
illustrate that on various topologies and with different distribution of
couplings, the decimation method outperforms the widely-used -optimization based methods.Comment: 11 pages, 5 figure
Solving the inverse Ising problem by mean-field methods in a clustered phase space with many states
In this work we explain how to properly use mean-field methods to solve the
inverse Ising problem when the phase space is clustered, that is many states
are present. The clustering of the phase space can occur for many reasons, e.g.
when a system undergoes a phase transition. Mean-field methods for the inverse
Ising problem are typically used without taking into account the eventual
clustered structure of the input configurations and may led to very bad
inference (for instance in the low temperature phase of the Curie-Weiss model).
In the present work we explain how to modify mean-field approaches when the
phase space is clustered and we illustrate the effectiveness of the new method
on different clustered structures (low temperature phases of Curie-Weiss and
Hopfield models).Comment: 6 pages, 5 figure
Ensemble renormalization group for the random field hierarchical model
The Renormalization Group (RG) methods are still far from being completely
understood in quenched disordered systems. In order to gain insight into the
nature of the phase transition of these systems, it is common to investigate
simple models. In this work we study a real-space RG transformation on the
Dyson hierarchical lattice with a random field, which led to a reconstruction
of the RG flow and to an evaluation of the critical exponents of the model at T
= 0. We show that this method gives very accurate estimations of the critical
exponents, by comparing our results with the ones obtained by some of us using
an independent method
Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models
In this Letter we propose a new method to infer the topology of the
interaction network in pairwise models with Ising variables. By using the
pseudolikelihood method (PLM) at high temperature, it is generally possible to
distinguish between zero and nonzero couplings because a clear gap separate the
two groups. However at lower temperatures the PLM is much less effective and
the result depends on subjective choices, such as the value of the
regularizer and that of the threshold to separate nonzero couplings from null
ones. We introduce a decimation procedure based on the PLM that recursively
sets to zero the less significant couplings, until the variation of the
pseudolikelihood signals that relevant couplings are being removed. The new
method is fully automated and does not require any subjective choice by the
user. Numerical tests have been performed on a wide class of Ising models,
having different topologies (from random graphs to finite dimensional lattices)
and different couplings (both diluted ferromagnets in a field and spin
glasses). These numerical results show that the new algorithm performs better
than standard PLMComment: 5 pages, 4 figure
The Hierarchical Random Energy Model
We introduce a Random Energy Model on a hierarchical lattice where the
interaction strength between variables is a decreasing function of their mutual
hierarchical distance, making it a non-mean field model. Through small coupling
series expansion and a direct numerical solution of the model, we provide
evidence for a spin glass condensation transition similar to the one occuring
in the usual mean field Random Energy Model. At variance with mean field, the
high temperature branch of the free-energy is non-analytic at the transition
point
Unsupervised hierarchical clustering using the learning dynamics of RBMs
Datasets in the real world are often complex and to some degree hierarchical,
with groups and sub-groups of data sharing common characteristics at different
levels of abstraction. Understanding and uncovering the hidden structure of
these datasets is an important task that has many practical applications. To
address this challenge, we present a new and general method for building
relational data trees by exploiting the learning dynamics of the Restricted
Boltzmann Machine (RBM). Our method is based on the mean-field approach,
derived from the Plefka expansion, and developed in the context of disordered
systems. It is designed to be easily interpretable. We tested our method in an
artificially created hierarchical dataset and on three different real-world
datasets (images of digits, mutations in the human genome, and a homologous
family of proteins). The method is able to automatically identify the
hierarchical structure of the data. This could be useful in the study of
homologous protein sequences, where the relationships between proteins are
critical for understanding their function and evolution.Comment: Version accepted in Physical Review
Learning a local symmetry with neural networks
We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns: the gauge symmetry Z2. This symmetry is present in physical problems from topological transitions to quantum chromodynamics, and controls the computational hardness of instances of spin-glasses. Here, we show how to design a neural network, and a dataset, able to learn this symmetry and to find compressed latent representations of the gauge orbits. Our method pays special attention to system-wrapping loops, the so-called Polyakov loops, known to be particularly relevant for computational complexity
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