arXiv subjects

F. Herrera

Publications and source records attributed to F. Herrera.

8 recordsLinked to original sources

arXiv2026

Data-Driven Energy-Based Learning via Gibbs Measures on Hierarchical Structures

We introduce a data-driven probabilistic framework for learning systems based on Gibbs measures on hierarchical structures. Unlike standard empirical risk minimization, where a dataset is used to identify a single optimal parameter, our approach transforms the empirical loss function into an interaction potential defining an energy-based model. The resulting Gibbs distribution describes a family of equilibrium learning states generated by the data. We formulate the consistency conditions of the associated finite-volume distributions and derive nonlinear integral fixed-point equations whose solutions characterize the admissible learning states. These equations provide a rigorous connection between empirical loss landscapes and probabilistic inference on trees. For translation-invariant solutions, the problem reduces to the analysis of positive compact operators induced by data-dependent kernels, allowing us to establish existence and uniqueness conditions in the one-dimensional setting. Furthermore, we show that hierarchical learning systems may exhibit phase-transition phenomena: for certain empirical kernels on Cayley trees, multiple Gibbs measures emerge beyond a critical inverse temperature, corresponding to distinct equilibrium prediction regimes. Numerical experiments with non-separable kernels illustrate the appearance of multiple solution branches and demonstrate the coexistence of several data-induced learning states. Our results provide a new perspective on energy-based learning, where data do not merely determine an optimal model through minimization but define an entire probabilistic landscape of possible inference states.

cs.LG↗

arXiv2025

Ising Models with Hidden Markov Structure: Applications to Probabilistic Inference in Machine Learning

In this paper, we investigate tree-indexed Markov chains (Gibbs measures) defined by a Hamiltonian that couples two Ising layers: hidden spins $s(x) \in \{\pm 1\}$ and observed spins $\sigma(x) \in \{\pm 1\}$ on a Cayley tree. The Hamiltonian incorporates Ising interactions within each layer and site-wise emission couplings between layers, extending hidden Markov models to a bilayer Markov random field. Specifically, we explore translation-invariant Gibbs measures (TIGM) of this Hamiltonian on Cayley trees. Under certain explicit conditions on the model's parameters, we demonstrate that there can be up to three distinct TIGMs. Each of these measures represents an equilibrium state of the spin system. These measures provide a structured approach to inference on hierarchical data in machine learning. They have practical applications in tasks such as denoising, weakly supervised learning, and anomaly detection. The Cayley tree structure is particularly advantageous for exact inference due to its tractability.

cs.LG↗

arXiv2020

COVIDGR dataset and COVID-SDNet methodology for predicting COVID-19 based on Chest X-Ray images

Currently, Coronavirus disease (COVID-19), one of the most infectious diseases in the 21st century, is diagnosed using RT-PCR testing, CT scans and/or Chest X-Ray (CXR) images. CT (Computed Tomography) scanners and RT-PCR testing are not available in most medical centers and hence in many cases CXR images become the most time/cost effective tool for assisting clinicians in making decisions. Deep learning neural networks have a great potential for building COVID-19 triage systems and detecting COVID-19 patients, especially patients with low severity. Unfortunately, current databases do not allow building such systems as they are highly heterogeneous and biased towards severe cases. This paper is three-fold: (i) we demystify the high sensitivities achieved by most recent COVID-19 classification models, (ii) under a close collaboration with Hospital Universitario Clínico San Cecilio, Granada, Spain, we built COVIDGR-1.0, a homogeneous and balanced database that includes all levels of severity, from normal with Positive RT-PCR, Mild, Moderate to Severe. COVIDGR-1.0 contains 426 positive and 426 negative PA (PosteroAnterior) CXR views and (iii) we propose COVID Smart Data based Network (COVID-SDNet) methodology for improving the generalization capacity of COVID-classification models. Our approach reaches good and stable results with an accuracy of $97.72\% \pm 0.95 \%$, $86.90\% \pm 3.20\%$, $61.80\% \pm 5.49\%$ in severe, moderate and mild COVID-19 severity levels (Paper accepted for publication in Journal of Biomedical and Health Informatics). Our approach could help in the early detection of COVID-19. COVIDGR-1.0 along with the severity level labels are available to the scientific community through this link https://dasci.es/es/transferencia/open-data/covidgr/.

eess.IV↗

arXiv2020

MNIST-NET10: A heterogeneous deep networks fusion based on the degree of certainty to reach 0.1 error rate. Ensembles overview and proposal

Ensemble methods have been widely used for improving the results of the best single classificationmodel. A large body of works have achieved better performance mainly by applying one specific ensemble method. However, very few works have explored complex fusion schemes using het-erogeneous ensembles with new aggregation strategies. This paper is three-fold: 1) It provides an overview of the most popular ensemble methods, 2) analyzes several fusion schemes using MNIST as guiding thread and 3) introduces MNIST-NET10, a complex heterogeneous fusion architecture based on a degree of certainty aggregation approach; it combines two heterogeneous schemes from the perspective of data, model and fusion strategy. MNIST-NET10 reaches a new record in MNISTwith only 10 misclassified images. Our analysis shows that such complex heterogeneous fusionarchitectures based on the degree of certainty can be considered as a way of taking benefit fromdiversity.

cs.LG↗

arXiv2020

Recent Trends in the Use of Statistical Tests for Comparing Swarm and Evolutionary Computing Algorithms: Practical Guidelines and a Critical Review

A key aspect of the design of evolutionary and swarm intelligence algorithms is studying their performance. Statistical comparisons are also a crucial part which allows for reliable conclusions to be drawn. In the present paper we gather and examine the approaches taken from different perspectives to summarise the assumptions made by these statistical tests, the conclusions reached and the steps followed to perform them correctly. In this paper, we conduct a survey on the current trends of the proposals of statistical analyses for the comparison of algorithms of computational intelligence and include a description of the statistical background of these tests. We illustrate the use of the most common tests in the context of the Competition on single-objective real parameter optimisation of the IEEE Congress on Evolutionary Computation (CEC) 2017 and describe the main advantages and drawbacks of the use of each kind of test and put forward some recommendations concerning their use.

cs.NE↗

arXiv2015

Synchronization of Interacting Quantum Dipoles

Macroscopic ensembles of radiating dipoles are ubiquitous in the physical and natural sciences. In the classical limit the dipoles can be described as damped-driven oscillators, which are able to spontaneously synchronize and collectively lock their phases. Here we investigate the correspond- ing phenomenon in the quantum regime with arrays of quantized two-level systems coupled via long-range and anisotropic dipolar interactions. Our calculations demonstrate that the dipoles may overcome the decoherence induced by quantum fluctuations and inhomogeneous couplings and evolve to a synchronized steady-state. This steady-state bears much similarity to that observed in classical systems, and yet also exhibits genuine quantum properties such as quantum correlations and quan- tum phase diffusion (reminiscent of lasing). Our predictions could be relevant for the development of better atomic clocks and a variety of noise tolerant quantum devices.

quant-ph↗

arXiv2015

JavaNPST: Nonparametric Statistical Tests in Java

Nonparametric statistical tests are useful procedures that can be applied in a wide range of situations, such as testing randomness or goodness of fit, one-sample, two-sample and multiple-sample analysis, association between bivariate samples or count data analysis. Their use is often preferred to parametric tests due to the fact that they require less restrictive assumptions about the population sampled. In this work, JavaNPST, an open source Java library implementing 40 nonparametric statistical tests, is presented. It can be helpful for programmers and practitioners interested in performing nonparametric statistical analyses, providing a quick and easy way of running these tests directly within any Java code. Some examples of use are also shown, highlighting some of the more remarkable capabilities of the library.

stat.CO↗

arXiv2014

Collective Effects in Linear Spectroscopy of Dipole-Coupled Molecular Arrays

We present a consistent analysis of linear spectroscopy for arrays of nearest neighbor dipole-coupled two-level molecules that reveals distinct signatures of weak and strong coupling regimes separated for infinite size arrays by a quantum critical point. In the weak coupling regime, the ground state of the molecular array is disordered, but in the strong coupling regime it has (anti)ferroelectric ordering. We show that multiple molecular excitations (odd/even in weak/strong coupling regime) can be accessed directly from the ground state. We analyze the scaling of absorption and emission with system size and find that the oscillator strengths show enhanced superradiant behavior in both ordered and disordered phases. As the coupling increases, the single excitation oscillator strength rapidly exceeds the well known Heitler-London value. In the strong coupling regime we show the existence of a unique spectral transition with excitation energy that can be tuned by varying the system size and that asymptotically approaches zero for large systems. The oscillator strength for this transition scales quadratically with system size, showing an anomalous one-photon superradiance. For systems of infinite size, we find a novel, singular spectroscopic signature of the quantum phase transition between disordered and ordered ground states. We outline how arrays of ultra cold dipolar molecules trapped in an optical lattice can be used to access the strong coupling regime and observe the anomalous superradiant effects associated with this regime.

quant-ph↗