Alarm tree analysis using statistical techniques

This work presents a systematic method for the generation and treatment of the alarms' graphs, being its final object to find the Alarm Root Cause of the Massive Alarms that are produced in the dispatching centers. Although many works about this matter have been already developed, the problem about the alarm management in the industry is still completely unsolved. In this paper, a simple statistic analysis of the historical data base is conducted. The results obtained by the acquisition alarm systems, are used to generate a directed graph from which the more significant alarms are extracted, previously analyzing any possible case in which a great quantity of alarms are produced.

Regularization for sparsity in statistical analysis and machine learning

Pragmatism is the leading motivation of regularization. We can understand regularization as a modification of the maximum-likelihood estimator so that a reasonable answer could be given in an unstable or ill-posed situation. To mention some typical examples, this happens when fitting parametric or non-parametric models with more parameters than data or when estimating large covariance matrices. Regularization is usually used, in addition, to improve the bias-variance tradeoff of an estimation. Then, the definition of regularization is quite general, and, although the introduction of a penalty is probably the most popular type, it is just one out of multiple forms of regularization. In this dissertation, we focus on the applications of regularization for obtaining sparse or parsimonious representations, where only a subset of the inputs is used. A particular form of regularization, L1-regularization, plays a key role for reaching sparsity. Most of the contributions presented here revolve around L1-regularization, although other forms of regularization are explored (also pursuing sparsity in some sense). In addition to present a compact review of L1-regularization and its applications in statistical and machine learning, we devise methodology for regression, supervised classification and structure induction of graphical models. Within the regression paradigm, we focus on kernel smoothing learning, proposing techniques for kernel design that are suitable for high dimensional settings and sparse regression functions. We also present an application of regularized regression techniques for modeling the response of biological neurons. Supervised classification advances deal, on the one hand, with the application of regularization for obtaining a na¨ıve Bayes classifier and, on the other hand, with a novel algorithm for brain-computer interface design that uses group regularization in an efficient manner. Finally, we present a heuristic for inducing structures of Gaussian Bayesian networks using L1-regularization as a filter. El pragmatismo es la principal motivación de la regularización. Podemos entender la regularización como una modificación del estimador de máxima verosimilitud, de tal manera que se pueda dar una respuesta cuando la configuración del problema es inestable. A modo de ejemplo, podemos mencionar el ajuste de modelos paramétricos o no paramétricos cuando hay más parámetros que casos en el conjunto de datos, o la estimación de grandes matrices de covarianzas. Se suele recurrir a la regularización, además, para mejorar el compromiso sesgo-varianza en una estimación. Por tanto, la definición de regularización es muy general y, aunque la introducción de una función de penalización es probablemente el método más popular, éste es sólo uno de entre varias posibilidades. En esta tesis se ha trabajado en aplicaciones de regularización para obtener representaciones dispersas, donde sólo se usa un subconjunto de las entradas. En particular, la regularización L1 juega un papel clave en la búsqueda de dicha dispersión. La mayor parte de las contribuciones presentadas en la tesis giran alrededor de la regularización L1, aunque también se exploran otras formas de regularización (que igualmente persiguen un modelo disperso). Además de presentar una revisión de la regularización L1 y sus aplicaciones en estadística y aprendizaje de máquina, se ha desarrollado metodología para regresión, clasificación supervisada y aprendizaje de estructura en modelos gráficos. Dentro de la regresión, se ha trabajado principalmente en métodos de regresión local, proponiendo técnicas de diseño del kernel que sean adecuadas a configuraciones de alta dimensionalidad y funciones de regresión dispersas. También se presenta una aplicación de las técnicas de regresión regularizada para modelar la respuesta de neuronas reales. Los avances en clasificación supervisada tratan, por una parte, con el uso de regularización para obtener un clasificador naive Bayes y, por otra parte, con el desarrollo de un algoritmo que usa regularización por grupos de una manera eficiente y que se ha aplicado al diseño de interfaces cerebromáquina. Finalmente, se presenta una heurística para inducir la estructura de redes Bayesianas Gaussianas usando regularización L1 a modo de filtro.

Analysis of spontaneous MEG activity in mild cognitive impairment and Alzheimer's disease using spectral entropies and statistical complexity measures

Alzheimer's disease (AD) is the most common cause of dementia. Over the last few years, a considerable effort has been devoted to exploring new biomarkers. Nevertheless, a better understanding of brain dynamics is still required to optimize therapeutic strategies. In this regard, the characterization of mild cognitive impairment (MCI) is crucial, due to the high conversion rate from MCI to AD. However, only a few studies have focused on the analysis of magnetoencephalographic (MEG) rhythms to characterize AD and MCI. In this study, we assess the ability of several parameters derived from information theory to describe spontaneous MEG activity from 36 AD patients, 18 MCI subjects and 26 controls. Three entropies (Shannon, Tsallis and Rényi entropies), one disequilibrium measure (based on Euclidean distance ED) and three statistical complexities (based on Lopez Ruiz–Mancini–Calbet complexity LMC) were used to estimate the irregularity and statistical complexity of MEG activity. Statistically significant differences between AD patients and controls were obtained with all parameters (p < 0.01). In addition, statistically significant differences between MCI subjects and controls were achieved by ED and LMC (p < 0.05). In order to assess the diagnostic ability of the parameters, a linear discriminant analysis with a leave-one-out cross-validation procedure was applied. The accuracies reached 83.9% and 65.9% to discriminate AD and MCI subjects from controls, respectively. Our findings suggest that MCI subjects exhibit an intermediate pattern of abnormalities between normal aging and AD. Furthermore, the proposed parameters provide a new description of brain dynamics in AD and MCI.

Operational modal analisys using joint statistical analysis of multiple records

In Operational Modal Analysis (OMA) of a structure, the data acquisition process may be repeated many times. In these cases, the analyst has several similar records for the modal analysis of the structure that have been obtained at di�erent time instants (multiple records). The solution obtained varies from one record to another, sometimes considerably. The differences are due to several reasons: statistical errors of estimation, changes in the external forces (unmeasured forces) that modify the output spectra, appearance of spurious modes, etc. Combining the results of the di�erent individual analysis is not straightforward. To solve the problem, we propose to make the joint estimation of the parameters using all the records. This can be done in a very simple way using state space models and computing the estimates by maximum-likelihood. The method provides a single result for the modal parameters that combines optimally all the records.