Publication: Búsqueda de relaciones causales para aplicaciones en cardiología y psiquiatría
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2012-01
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2012-01-19
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Abstract
En esta tesis se presenta un estudio sobre la teoría de la causalidad y se desarrollan nuevas técnicas de inferencia causal en datos discretos y en señales continuas. Estos métodos se han utilizado para avanzar en el conocimiento de dos problemas médicos: uno en el campo de la psiquiatría y otro en cardiología. Los métodos clásicos para inferir relaciones causales a partir de muestras se basan en múltiples análisis de independencia estadística condicional. Estos métodos no dan buenos resultados cuando el número de variables aleatorias es elevado. Por el contrario, las técnicas de aprendizaje máquina son razonablemente robustas frente a problemas de alta dimensionalidad. Se han sustituido los test de independencia por una batería de clasificadores en el algoritmo de búsqueda causal propuesto. En la tesis se muestra cómo es posible identficar las relaciones causales en funci on del número de variables relevantes en una clasficaci on. Se ha ensayado con dos clasificadores, un k vecinos más próximos y una máquina de vectores soporte (SVM). Para aligerar la carga computacional impuesta por el gran número de clasificadores a entrenar, se ha recurrido a una permutación aleatoria para obtener la salida de problemas de menor dimensión a partir de máquinas entrenadas en dimensión superior. Se ha empleado la téccnica de remuestreo "bootstrap" para etapas intermedias de estos algoritmos. Para señales en tiempo continuo, el criterio de inferencia causal de Granger afirma que si una señal ayuda a la predicci on de otra, la primera tiene influencia causal en la segunda. El criterio se implementa comparando los residuos de modelos autorregresivos ARMA de las señales. La inferencia causal tipo Granger obtiene mejores resultados forzando dispersidad en los coeficientes del modelo. Con este objetivo, en la tesis se ha empleado una aproximación basada en SVM para el modelado autorregresivo (cSVARMA); adicionalmente, se ha desarrollado una versión multivariable del algoritmo cSVARMA, que supera las prestaciones del modelo unidimensional. La función de coste robusta de los algoritmos propuestos hace que se obtengan mejores resultados, especialmente en escenarios con ruido tipo impulsivo. Se presentan simulaciones con datos sintéticos comparando los métodos anteriores con los más relevantes en la literatura; los resultados validan el buen comportamiento de los algoritmos propuestos para identficar causalidad en datos discretos y en series temporales. La algoritmia desarrollada se ha aplicado a dos problemas médicos. En el problema psiquiátrico, se han estudiado los factores más relevantes relacionados con la repetición de intentos de suicidio. No existen modelos etiológicos de nidos para esta problemática. A partir de una base de datos de pacientes psiquiátricos, con información clíica y sociolóica, se han seleccionado las variables fuertemente relevantes y se ha generado su árbol causal. La interpretación del modelo permite generar nuevas hipótesis de trabajo. También se ha entrenado un clasificador con las variables causantes de la repetición de intentos de suicidio, que puede emplearse para valorar el riesgo de nuevos pacientes y prevenir otros intentos. En cardiología, se ha desarrollado una herramienta de representación de relaciones causales que permite identificar los mecanismos de generación y mantenimiento de fibrilaciones auriculares. Existen distintas hipótesis sobre esta patología, y cada una de ellas conlleva un tratamiento terapéutico distinto. Los métodos clásicos de análisis de estas señales, basados en las frecuencias dominantes de las ondas auriculares, presentan una importante limitación, pues usando únicamente la frecuencia no es posible identificar los focos y la manera de propagarse de los frentes de onda por el miocardio. Se ha recogido una base de datos de electrogramas de fibrilación auricular y se han aplicado a este problema los m étodos de inferencia causal desarrollados. Finalmente, se ha diseñado una herramienta de visualización de las interacciones causales, que puede servir de apoyo al médico en el estudio de estas arritmias. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
In this PhD thesis, an exposition of the theory of causation is presented, and new techniques of causal inference for discrete and continuous data are developed. These methods are used to advance in the knowledge of two medical problems within the fields of psychiatry and cardiology. The classical methods to infer causal relations from sample sets rest on multiple statistical independence tests. These methods operate bad in coping with high dimensional random variable spaces. On the contrary, machine learning techniques have shown good performance and robustness in these kind of problems. The proposal of the thesis is to substitute the independence tests with an ensemble of classifiers. In the thesis it is shown how the number of relevant features for a classification task is useful to identify causal relationships. Two classifiers have been used: a k nearest neighbour and a support vector machine. In order to improve the effectiveness of the method, in terms of processing time, a random permutation have been used to reduce the number of trainings. Some phases of the causal classifiers algorithm have been resolved with bootstrap techniques. In the field of continuous signals, the Granger criterion states that if a signal helps in the prediction of another, the former has a causal influence on the latter. The implementation of Granger causality rely on the comparison of the residuals of auto-regressive ARMA models of the signals. These causal relations can be improved if sparsity in the coeficients of the ARMA model is imposed. To this end, an ARMA model based in support vector machines (SVM) has been implemented and applied to causal inference (cSVARMA). A multivariate version of the algorithm has been derived, which improves the performance of the unidimensional model. The robust cost function of SVM based ARMA models makes them soundness, specially in contexts with impulsive noise. Some toy problems with synthetic data are provided to prove the good performance of the algorithms compared with the state-of-the-art methods; the results show the validity of the proposed algorithms, both in discrete and continuous data. The causal inference methods presented in the thesis have been applied to a pair of medical problems. In psychiatry there are few etiological models for the factors that impels for the repetition of suicide attempts. A data base of sociodemographic and clinical variables has been used to select the strongly relevant features, and their causal graph has been generated. The interpretation of the findings in the causal models permits to provide new hypothesis to be proved. A classifier trained with the identfied causes of suicidal behaviour is provided, that can be used to prevent new attempts and evaluate their risk. In cardiology, the physiological mechanisms responsible for the onset and maintenance of the atrial brillation are not completely known. There are several hypothesis of this phenomenon, which lead to different therapeutic strategies. The typical analysis procedures, related with the detection of the brillation dominant frequency, present a serious limitation, because the information of the frequency is not enough to allow the identification of the triggering area of the arrhythmia. A data base of brillation electrograms has been recollected. Causal methodology for signals in continuous time have been applied to this problem, and the causal relationships found in the electrograms have been shown thanks to the design of a visualization tool. The methodology presented can be used to identify the propagation patterns of signals in the heart atria.
In this PhD thesis, an exposition of the theory of causation is presented, and new techniques of causal inference for discrete and continuous data are developed. These methods are used to advance in the knowledge of two medical problems within the fields of psychiatry and cardiology. The classical methods to infer causal relations from sample sets rest on multiple statistical independence tests. These methods operate bad in coping with high dimensional random variable spaces. On the contrary, machine learning techniques have shown good performance and robustness in these kind of problems. The proposal of the thesis is to substitute the independence tests with an ensemble of classifiers. In the thesis it is shown how the number of relevant features for a classification task is useful to identify causal relationships. Two classifiers have been used: a k nearest neighbour and a support vector machine. In order to improve the effectiveness of the method, in terms of processing time, a random permutation have been used to reduce the number of trainings. Some phases of the causal classifiers algorithm have been resolved with bootstrap techniques. In the field of continuous signals, the Granger criterion states that if a signal helps in the prediction of another, the former has a causal influence on the latter. The implementation of Granger causality rely on the comparison of the residuals of auto-regressive ARMA models of the signals. These causal relations can be improved if sparsity in the coeficients of the ARMA model is imposed. To this end, an ARMA model based in support vector machines (SVM) has been implemented and applied to causal inference (cSVARMA). A multivariate version of the algorithm has been derived, which improves the performance of the unidimensional model. The robust cost function of SVM based ARMA models makes them soundness, specially in contexts with impulsive noise. Some toy problems with synthetic data are provided to prove the good performance of the algorithms compared with the state-of-the-art methods; the results show the validity of the proposed algorithms, both in discrete and continuous data. The causal inference methods presented in the thesis have been applied to a pair of medical problems. In psychiatry there are few etiological models for the factors that impels for the repetition of suicide attempts. A data base of sociodemographic and clinical variables has been used to select the strongly relevant features, and their causal graph has been generated. The interpretation of the findings in the causal models permits to provide new hypothesis to be proved. A classifier trained with the identfied causes of suicidal behaviour is provided, that can be used to prevent new attempts and evaluate their risk. In cardiology, the physiological mechanisms responsible for the onset and maintenance of the atrial brillation are not completely known. There are several hypothesis of this phenomenon, which lead to different therapeutic strategies. The typical analysis procedures, related with the detection of the brillation dominant frequency, present a serious limitation, because the information of the frequency is not enough to allow the identification of the triggering area of the arrhythmia. A data base of brillation electrograms has been recollected. Causal methodology for signals in continuous time have been applied to this problem, and the causal relationships found in the electrograms have been shown thanks to the design of a visualization tool. The methodology presented can be used to identify the propagation patterns of signals in the heart atria.
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Keywords
Teoría de la causalidad, Inferencia causal, Datos discretos, Señales continuas, Psiquiatría, Cardiología