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 $\ell_1$-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 $\ell _1$-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

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 $\ell_1$ 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

Apprentissage par renforcement pour l'improvisation musicale automatique

National audienceThe DYCI2 ANR project aims to explore interactions between humans and artificial agents in the field of music improvisation. Interactive learning, one of the main's project research area, proposes models able to detect musical structures. All of these research are based on the OMax paradigm, an automatic music improvisation system. Unfortunately, such a system still creates false notes. Is it possible to have the system learned not to do those mistakes again ?To answer that question, we propose a melodic classification into two classes : the ones which has at least one wrong note, and the others which have no ones. This classification allows us to enhance the system by using an reinforcement learning algorithm. After introducing some musical words and explaining what are LSTMs, we present our neural network model which is going to classify melodies. We also propose a musical encoding scheme. We use Deep Q-Learning as reinforcement learning algorithm to improve the current system. We evaluate our neural network model with classical criteria. The final enhancement will be evaluate by listening to the melodies. At last, we discuss about our strategies.Le projet ANR DYCI2 vise à explorer les interactions entre l'homme et des agents artificiels dans le domaine de l'improvisation musicale. L'apprentissage interactif, l'un des domaines de recherche du projet, veut mettre en avant des modèles capables de capturer les structures musicales. Toutes les recherches se basent sur le paradigme OMax, un système automatique d'improvisation. Malheureusement, ce système génère encore des fausses notes. Est-il possible d'apprendre au système à ne plus commettre de telles erreurs ? Pour répondre à cette problématique, ce mémoire propose une méthode pour classifier les mélodies en deux catégories : celles qui ont au moins une fausse note et celles qui n'en ont aucune. Une telle classification devra permettre d'améliorer le système actuel à l'aide de l'apprentissage par renforcement. Après avoir défini quelques notions musicales et expliqué ce que sont les LSTMs, nous proposons un modèle de réseau de neurones pour la classification. Nous proposons également un procédé pour encoder les notes musicales. Nous utilisons le Deep Q-Learning en tant qu'algorithme d'apprentissage par renforcement. L'évaluation du réseau neuronal repose sur les critères classiques. L'évaluation de l'amélioration du système est basée sur l'écoute des mélodies générées. Enfin, nous discutons des méthodes utilisées