Inferring effective couplings with Restricted Boltzmann Machines

Generative models offer a direct way to model complex data. Among them, energy-based models provide us with a neural network model that aims to accurately reproduce all statistical correlations observed in the data at the level of the Boltzmann weight of the model. However, one challenge is to understand the physical interpretation of such models. In this study, we propose a simple solution by implementing a direct mapping between the energy function of the Restricted Boltzmann Machine and an effective Ising spin Hamiltonian that includes high-order interactions between spins. This mapping includes interactions of all possible orders, going beyond the conventional pairwise interactions typically considered in the inverse Ising approach, and allowing the description of complex datasets. Earlier work attempted to achieve this goal, but the proposed mappings did not do properly treat the complexity of the problem or did not contain direct prescriptions for practical application. To validate our method, we perform several controlled numerical experiments where the training samples are equilibrium samples of predefined models containing local external fields, two-body and three-body interactions in various low-dimensional topologies. The results demonstrate the effectiveness of our proposed approach in learning the correct interaction network and pave the way for its application in modeling interesting datasets. We also evaluate the quality of the inferred model based on different training methods.Comment: 16 figures, 22 page

Inferring effective couplings with Restricted Boltzmann Machines

15 figures, 31 pagesGenerative models offer a direct way to model complex data. Among them, energy-based models provide us with a neural network model that aims to accurately reproduce all statistical correlations observed in the data at the level of the Boltzmann weight of the model. However, one challenge is to understand the physical interpretation of such models. In this study, we propose a simple solution by implementing a direct mapping between the energy function of the Restricted Boltzmann Machine and an effective Ising spin Hamiltonian that includes high-order interactions between spins. This mapping includes interactions of all possible orders, going beyond the conventional pairwise interactions typically considered in the inverse Ising approach, and allowing the description of complex datasets. Earlier works attempted to achieve this goal, but the proposed mappings did not do properly treat the complexity of the problem or did not contain direct prescriptions for practical application. To validate our method, we performed several controlled numerical experiments where we trained the RBMs using equilibrium samples of predefined models containing local external fields, two-body and three-body interactions in various low-dimensional topologies. The results demonstrate the effectiveness of our proposed approach in learning the correct interaction network and pave the way for its application in modeling interesting datasets. We also evaluate the quality of the inferred model based on different training methods

Inferring effective couplings with Restricted Boltzmann Machines

15 figures, 31 pagesGenerative models offer a direct way to model complex data. Among them, energy-based models provide us with a neural network model that aims to accurately reproduce all statistical correlations observed in the data at the level of the Boltzmann weight of the model. However, one challenge is to understand the physical interpretation of such models. In this study, we propose a simple solution by implementing a direct mapping between the energy function of the Restricted Boltzmann Machine and an effective Ising spin Hamiltonian that includes high-order interactions between spins. This mapping includes interactions of all possible orders, going beyond the conventional pairwise interactions typically considered in the inverse Ising approach, and allowing the description of complex datasets. Earlier works attempted to achieve this goal, but the proposed mappings did not do properly treat the complexity of the problem or did not contain direct prescriptions for practical application. To validate our method, we performed several controlled numerical experiments where we trained the RBMs using equilibrium samples of predefined models containing local external fields, two-body and three-body interactions in various low-dimensional topologies. The results demonstrate the effectiveness of our proposed approach in learning the correct interaction network and pave the way for its application in modeling interesting datasets. We also evaluate the quality of the inferred model based on different training methods

Patients awaiting surgery for neurosurgical diseases during the first wave of the COVID-19 pandemic in Spain: a multicentre cohort study.

The large number of infected patients requiring mechanical ventilation has led to the postponement of scheduled neurosurgical procedures during the first wave of the COVID-19 pandemic. The aims of this study were to investigate the factors that influence the decision to postpone scheduled neurosurgical procedures and to evaluate the effect of the restriction in scheduled surgery adopted to deal with the first outbreak of the COVID-19 pandemic in Spain on the outcome of patients awaiting surgery. This was an observational retrospective study. A tertiary-level multicentre study of neurosurgery activity between 1 March and 30 June 2020. A total of 680 patients awaiting any scheduled neurosurgical procedure were enrolled. 470 patients (69.1%) were awaiting surgery because of spine degenerative disease, 86 patients (12.6%) due to functional disorders, 58 patients (8.5%) due to brain or spine tumours, 25 patients (3.7%) due to cerebrospinal fluid (CSF) disorders and 17 patients (2.5%) due to cerebrovascular disease. The primary outcome was mortality due to any reason and any deterioration of the specific neurosurgical condition. Second, we analysed the rate of confirmed SARS-CoV-2 infection. More than one-quarter of patients experienced clinical or radiological deterioration. The rate of worsening was higher among patients with functional (39.5%) or CSF disorders (40%). Two patients died (0.4%) during the waiting period, both because of a concurrent disease. We performed a multivariate logistic regression analysis to determine independent covariates associated with maintaining the surgical indication. We found that community SARS-CoV-2 incidence (OR=1.011, p Patients awaiting neurosurgery experienced significant collateral damage even when they were considered for scheduled procedures