50 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
La macchina di Boltzmann: quando il modello di Ising incontra il Machine Learning
International audienceMachine Learning is becoming more and more important in research and in daily life, yet the learning process remains largely misunderstood and many important questions are still unresolved. Statistical physicists, in a long tradition of looking for universal behavior and simple mechanisms to understand complex collective phenomena, have taken their turn in trying to understand these models with their own language. It is therefore natural that the Boltzmann Machine - or the inverse Ising problem- enters at the crossroad of statistical physics and machine learningIl machine learning sta diventando sempre più importante nella ricerca e nella vita quotidiana, tuttavia il processo dell’apprendimento rimane in gran parte oscuro e molte questioni importanti sono ancora irrisolte. I meccanici statistici, in una lunga tradizione di ricerca di comportamenti universali e meccanismi semplici per comprendere fenomeni collettivi complessi, hanno provato a comprendere questi modelli con il loro linguaggio. È quindi naturale che la macchina di Boltzmann - o il problema inverso di Ising- si inserisca nell’intersezione tra meccanica statistica e machine learning
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
Fast and Functional Structured Data Generators Rooted in Out-of-Equilibrium Physics
In this study, we address the challenge of using energy-based models to
produce high-quality, label-specific data in complex structured datasets, such
as population genetics, RNA or protein sequences data. Traditional training
methods encounter difficulties due to inefficient Markov chain Monte Carlo
mixing, which affects the diversity of synthetic data and increases generation
times. To address these issues, we use a novel training algorithm that exploits
non-equilibrium effects. This approach, applied on the Restricted Boltzmann
Machine, improves the model's ability to correctly classify samples and
generate high-quality synthetic data in only a few sampling steps. The
effectiveness of this method is demonstrated by its successful application to
four different types of data: handwritten digits, mutations of human genomes
classified by continental origin, functionally characterized sequences of an
enzyme protein family, and homologous RNA sequences from specific taxonomies.Comment: 15 page
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