A novel ensemble Beta-scale invariant map algorithm

[Abstract]: This research presents a novel topology preserving map (TPM) called Weighted Voting Supervision -Beta-Scale Invariant Map (WeVoS-Beta-SIM), based on the application of the Weighted Voting Supervision (WeVoS) meta-algorithm to a novel family of learning rules called Beta-Scale Invariant Map (Beta-SIM). The aim of the novel TPM presented is to improve the original models (SIM and Beta-SIM) in terms of stability and topology preservation and at the same time to preserve their original features, especially in the case of radial datasets, where they all are designed to perform their best. These scale invariant TPM have been proved with very satisfactory results in previous researches. This is done by generating accurate topology maps in an effectively and efficiently way. WeVoS meta-algorithm is based on the training of an ensemble of networks and the combination of them to obtain a single one that includes the best features of each one of the networks in the ensemble. WeVoS-Beta-SIM is thoroughly analyzed and successfully demonstrated in this study over 14 diverse real benchmark datasets with diverse number of samples and features, using three different well-known quality measures. In order to present a complete study of its capabilities, results are compared with other topology preserving models such as Self Organizing Maps, Scale Invariant Map, Maximum Likelihood Hebbian Learning-SIM, Visualization Induced SOM, Growing Neural Gas and Beta- Scale Invariant Map. The results obtained confirm that the novel algorithm improves the quality of the single Beta-SIM algorithm in terms of topology preservation and stability without losing performance (where this algorithm has proved to overcome other well-known algorithms). This improvement is more remarkable when complexity of the datasets increases, in terms of number of features and samples and especially in the case of radial datasets improving the Topographic Error

Beta hebbian learning: definition and analysis of a new family of learning rules for exploratory projection pursuit

[EN] This thesis comprises an investigation into the derivation of learning rules in artificial neural networks from probabilistic criteria. •Beta Hebbian Learning (BHL). First of all, it is derived a new family of learning rules which are based on maximising the likelihood of the residual from a negative feedback network when such residual is deemed to come from the Beta Distribution, obtaining an algorithm called Beta Hebbian Learning, which outperforms current neural algorithms in Exploratory Projection Pursuit. • Beta-Scale Invariant Map (Beta-SIM). Secondly, Beta Hebbian Learning is applied to a well-known Topology Preserving Map algorithm called Scale Invariant Map (SIM) to design a new of its version called Beta-Scale Invariant Map (Beta-SIM). It is developed to facilitate the clustering and visualization of the internal structure of high dimensional complex datasets effectively and efficiently, specially those characterized by having internal radial distribution. The Beta-SIM behaviour is thoroughly analysed comparing its results, in terms performance quality measures with other well-known topology preserving models. • Weighted Voting Superposition Beta-Scale Invariant Map (WeVoS-Beta-SIM). Finally, the use of ensembles such as the Weighted Voting Superposition (WeVoS) is tested over the previous novel Beta-SIM algorithm, in order to improve its stability and to generate accurate topology maps when using complex datasets. Therefore, the WeVoS-Beta-Scale Invariant Map (WeVoS-Beta-SIM), is presented, analysed and compared with other well-known topology preserving models. All algorithms have been successfully tested using different artificial datasets to corroborate their properties and also with high-complex real datasets.[ES] Esta tesis abarca la investigación sobre la derivación de reglas de aprendizaje en redes neuronales artificiales a partir de criterios probabilísticos. • Beta Hebbian Learning (BHL). En primer lugar, se deriva una nueva familia de reglas de aprendizaje basadas en maximizar la probabilidad del residuo de una red con retroalimentación negativa cuando se considera que dicho residuo proviene de la Distribución Beta, obteniendo un algoritmo llamado Beta Hebbian Learning, que mejora a algoritmos neuronales actuales de búsqueda de proyecciones exploratorias. • Beta-Scale Invariant Map (Beta-SIM). En Segundo lugar, Beta Hebbian Learning se aplica a un conocido algoritmo de Mapa de Preservación de la Topología llamado Scale Invariant Map (SIM) para diseñar una nueva versión llamada Beta-Scale Invariant Map (Beta-SIM). Este nuevo algoritmo ha sido desarrollado para facilitar el agrupamiento y visualización de la estructura interna de conjuntos de datos complejos de alta dimensionalidad de manera eficaz y eficiente, especialmente aquellos caracterizados por tener una distribución radial interna. El comportamiento de Beta-SIM es analizado en profundidad comparando sus resultados, en términos de medidas de calidad de rendimiento con otros modelos bien conocidos de preservación de topología. • Weighted Voting Superposition Beta-Scale Invariant Map (WeVoS-Beta-SIM). Finalmente, el uso de ensembles como el Weighted Voting Superposition (WeVoS) sobre el algoritmo Beta-SIM es probado, con objeto de mejorar su estabilidad y generar mapas topológicos precisos cuando se utilizan conjuntos de datos complejos. Por lo tanto, se presenta, analiza y compara el WeVoS-Beta-Scale Invariant Map (WeVoS-Beta-SIM) con otros modelos bien conocidos de preservación de topología. Todos los algoritmos han sido probados con éxito sobre conjuntos de datos artificiales para corroborar sus propiedades, así como con conjuntos de datos reales de gran complejidad

Kernelized Hashcode Representations for Relation Extraction

Kernel methods have produced state-of-the-art results for a number of NLP tasks such as relation extraction, but suffer from poor scalability due to the high cost of computing kernel similarities between natural language structures. A recently proposed technique, kernelized locality-sensitive hashing (KLSH), can significantly reduce the computational cost, but is only applicable to classifiers operating on kNN graphs. Here we propose to use random subspaces of KLSH codes for efficiently constructing an explicit representation of NLP structures suitable for general classification methods. Further, we propose an approach for optimizing the KLSH model for classification problems by maximizing an approximation of mutual information between the KLSH codes (feature vectors) and the class labels. We evaluate the proposed approach on biomedical relation extraction datasets, and observe significant and robust improvements in accuracy w.r.t. state-of-the-art classifiers, along with drastic (orders-of-magnitude) speedup compared to conventional kernel methods.Comment: To appear in the proceedings of conference, AAAI-1

Phase Structure of Lattice N=4 Super Yang-Mills

We make a first study of the phase diagram of four-dimensional N=4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consistent with the existence of a single deconfined phase at all observed values of the bare coupling.Comment: 29 pages, 11 figures. References added, minor edits to tex

A Nonparametric Bayesian Approach to Uncovering Rat Hippocampal Population Codes During Spatial Navigation

Rodent hippocampal population codes represent important spatial information about the environment during navigation. Several computational methods have been developed to uncover the neural representation of spatial topology embedded in rodent hippocampal ensemble spike activity. Here we extend our previous work and propose a nonparametric Bayesian approach to infer rat hippocampal population codes during spatial navigation. To tackle the model selection problem, we leverage a nonparametric Bayesian model. Specifically, to analyze rat hippocampal ensemble spiking activity, we apply a hierarchical Dirichlet process-hidden Markov model (HDP-HMM) using two Bayesian inference methods, one based on Markov chain Monte Carlo (MCMC) and the other based on variational Bayes (VB). We demonstrate the effectiveness of our Bayesian approaches on recordings from a freely-behaving rat navigating in an open field environment. We find that MCMC-based inference with Hamiltonian Monte Carlo (HMC) hyperparameter sampling is flexible and efficient, and outperforms VB and MCMC approaches with hyperparameters set by empirical Bayes

Learning Representations from EEG with Deep Recurrent-Convolutional Neural Networks

One of the challenges in modeling cognitive events from electroencephalogram (EEG) data is finding representations that are invariant to inter- and intra-subject differences, as well as to inherent noise associated with such data. Herein, we propose a novel approach for learning such representations from multi-channel EEG time-series, and demonstrate its advantages in the context of mental load classification task. First, we transform EEG activities into a sequence of topology-preserving multi-spectral images, as opposed to standard EEG analysis techniques that ignore such spatial information. Next, we train a deep recurrent-convolutional network inspired by state-of-the-art video classification to learn robust representations from the sequence of images. The proposed approach is designed to preserve the spatial, spectral, and temporal structure of EEG which leads to finding features that are less sensitive to variations and distortions within each dimension. Empirical evaluation on the cognitive load classification task demonstrated significant improvements in classification accuracy over current state-of-the-art approaches in this field.Comment: To be published as a conference paper at ICLR 201

Bayesian inference on the sphere beyond statistical isotropy

We present a general method for Bayesian inference of the underlying covariance structure of random fields on a sphere. We employ the Bipolar Spherical Harmonic (BipoSH) representation of general covariance structure on the sphere. We illustrate the efficacy of the method as a principled approach to assess violation of statistical isotropy (SI) in the sky maps of Cosmic Microwave Background (CMB) fluctuations. SI violation in observed CMB maps arise due to known physical effects such as Doppler boost and weak lensing; yet unknown theoretical possibilities like cosmic topology and subtle violations of the cosmological principle, as well as, expected observational artefacts of scanning the sky with a non-circular beam, masking, foreground residuals, anisotropic noise, etc. We explicitly demonstrate the recovery of the input SI violation signals with their full statistics in simulated CMB maps. Our formalism easily adapts to exploring parametric physical models with non-SI covariance, as we illustrate for the inference of the parameters of a Doppler boosted sky map. Our approach promises to provide a robust quantitative evaluation of the evidence for SI violation related anomalies in the CMB sky by estimating the BipoSH spectra along with their complete posterior.Comment: 16 pages, 6 figure

A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability

Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter $\theta$, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on $\theta$ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.Comment: 29 pages, 23 figures, references adde