Modelos híbridos de aprendizaje basados en instancias y reglas para Clasificación Monotónica

En los problemas de clasificación supervisada, el atributo respuesta depende de determinados atributos de entrada explicativos. En muchos problemas reales el atributo respuesta está representado por valores ordinales que deberían incrementarse cuando algunos de los atributos explicativos de entrada también lo hacen. Estos son los llamados problemas de clasificación con restricciones monotónicas. En esta Tesis, hemos revisado los clasificadores monotónicos propuestos en la literatura y hemos formalizado la teoría del aprendizaje basado en ejemplos anidados generalizados para abordar la clasificación monotónica. Propusimos dos algoritmos, un primer algoritmos voraz, que require de datos monotónicos y otro basado en algoritmos evolutivos, que es capaz de abordar datos imperfectos que presentan violaciones monotónicas entre las instancias. Ambos mejoran el acierto, el índice de no-monotonicidad de las predicciones y la simplicidad de los modelos sobre el estado-del-arte.In supervised prediction problems, the response attribute depends on certain explanatory attributes. Some real problems require the response attribute to represent ordinal values that should increase with some of the explaining attributes. They are called classification problems with monotonicity constraints. In this thesis, we have reviewed the monotonic classifiers proposed in the literature and we have formalized the nested generalized exemplar learning theory to tackle monotonic classification. Two algorithms were proposed, a first greedy one, which require monotonic data and an evolutionary based algorithm, which is able to address imperfect data with monotonic violations present among the instances. Both improve the accuracy, the non-monotinic index of predictions and the simplicity of models over the state-of-the-art.Tesis Univ. Jaén. Departamento INFORMÁTIC

Robustness Verification of k-Nearest Neighbor Classifiers by Abstract Interpretation

openAbstract interpretation is an established mathematical framework introduced by Cousot and Cousot in 1977 and ubiquitously used in static program analysis. In recent years, many noteworthy works have shown how abstract interpretation can be successfully applied to formally verify robustness properties of some major machine learning techniques like (deep) neural networks, decision trees and support vector machines. This research work aims to pursue this line of research by proposing a novel abstract interpretation-based framework for designing a sound abstract version of the k-Nearest Neighbors (kNN) algorithm, a well-known non-parametric supervised learning method widely used for classification and regression tasks, which is then instantiated to the standard interval domain approximating the range of numerical features, to verify its robustness and stability properties. This verification approach has been fully implemented and evaluated on several datasets, including standard benchmark datasets for individual fairness verification, and then compared with some related works finding adversarial examples on kNNs. The experimental results turned out to be very promising and showed high percentages of provable robustness and stability in most of the reference datasets, thus making a step forward in the current state-of-the-art of formal verification of machine learning models.Abstract interpretation is an established mathematical framework introduced by Cousot and Cousot in 1977 and ubiquitously used in static program analysis. In recent years, many noteworthy works have shown how abstract interpretation can be successfully applied to formally verify robustness properties of some major machine learning techniques like (deep) neural networks, decision trees and support vector machines. This research work aims to pursue this line of research by proposing a novel abstract interpretation-based framework for designing a sound abstract version of the k-Nearest Neighbors (kNN) algorithm, a well-known non-parametric supervised learning method widely used for classification and regression tasks, which is then instantiated to the standard interval domain approximating the range of numerical features, to verify its robustness and stability properties. This verification approach has been fully implemented and evaluated on several datasets, including standard benchmark datasets for individual fairness verification, and then compared with some related works finding adversarial examples on kNNs. The experimental results turned out to be very promising and showed high percentages of provable robustness and stability in most of the reference datasets, thus making a step forward in the current state-of-the-art of formal verification of machine learning models

APPROXIMATION OF LIMIT STATE SURFACES IN MONOTONIC MONTE CARLO SETTINGS

International audienceThis article investigates the theoretical convergence properties of the estimators produced by a numerical exploration of a monotonic function with multivariate random inputs in a structural reliability framework.The quantity to be estimated is a probability typically associated to an undesirable (unsafe) event and the function is usually implemented as a computer model. The estimators produced by a Monte Carlo numerical design are two subsets of inputs leading to safe and unsafe situations, the measures of which can be traduced as deterministic bounds for the probability. Several situations are considered, when the design is independent, identically distributed or not, or sequential. As a major consequence, a consistent estimator of the (limit state) surface separating the subsets under isotonicity and regularity arguments can be built, and its convergence speed can be exhibited. This estimator is built by aggregating semi-supervized binary classifiers chosen as constrained Support Vector Machines. Numerical experiments conducted on toy examples highlight that they work faster than recently developed monotonic neural networks with comparable predictable power. They are therefore more adapted when the computational time is a key issue

Applications of frequency domain stability criteria in the design of nonlinear feedback systems

The Popov criterion for absolute stability of nonlinear feedback systems is applied to several example problems. Model transformations such as pole shifting and zero shifting extend the class of systems to which the criterion applies. Extensions of the criterion having simple graphical interpretations yield stronger results for systems with constant monotonic slope-bounded nonlinearities. Additional extensions lacking simple graphical interpretations in the complex plane are also demonstrated by example. Stability throughout a region in parameter space is discussed, and the Kalman conjecture is verified for a new class of systems. The Popov criterion is also used to prove BIBO stability, process stability, and degree of stability. The conservatism of the criterion, i. e., the margin of actual performance beyond guaranteed performance, is discussed in the light of simulation results. An interactive computer program is developed to make the Popov criterion, along with two of its extensions, a convenient tool for the design of stable systems. The user has the options of completely automatic parameter adjustment or intervention at any stage of the procedure --Abstract, page ii

Measurement uncertainty in machine learning - uncertainty propagation and influence on performance

Industry 4.0 is based on the intelligent networking of machines and processes in industry and makes a decisive contribution to increasing competitiveness. For this, reliable measurements of used sensors and sensor systems are essential. Metrology deals with the definition of internationally accepted measurement units and standards. In order to internationally compare measurement results, the Guide to the Expression of Uncertainty in Measurement (GUM) provides the basis for evaluating and interpreting measurement uncertainty. At the same time, measurement uncertainty also provides data quality information, which is important when machine learning is applied in the digitalized factory. However, measurement uncertainty in line with the GUM has been mostly neglected in machine learning or only estimated by cross-validation. Therefore, this dissertation aims to combine measurement uncertainty based on the principles of the GUM and machine learning. For performing machine learning, a data pipeline that fuses raw data from different measurement systems and determines measurement uncertainties from dynamic calibration information is presented. Furthermore, a previously published automated toolbox for machine learning is extended to include uncertainty propagation based on the GUM and its supplements. Using this uncertainty-aware toolbox, the influence of measurement uncertainty on machine learning results is investigated, and approaches to improve these results are discussed.Industrie 4.0 basiert auf der intelligenten Vernetzung von Maschinen und Prozessen und trägt zur Steigerung der Wettbewerbsfähigkeit entscheidend bei. Zuverlässige Messungen der eingesetzten Sensoren und Sensorsysteme sind dabei unerlässlich. Die Metrologie befasst sich mit der Festlegung international anerkannter Maßeinheiten und Standards. Um Messergebnisse international zu vergleichen, stellt der Guide to the Expression of Uncertainty in Measurement (GUM) die Basis zur Bewertung von Messunsicherheit bereit. Gleichzeitig liefert die Messunsicherheit auch Informationen zur Datenqualität, welche wiederum wichtig ist, wenn maschinelles Lernen in der digitalisierten Fabrik zur Anwendung kommt. Bisher wurde die Messunsicherheit im Bereich des maschinellen Lernens jedoch meist vernachlässigt oder nur mittels Kreuzvalidierung geschätzt. Ziel dieser Dissertation ist es daher, Messunsicherheit basierend auf dem GUM und maschinelles Lernen zu vereinen. Zur Durchführung des maschinellen Lernens wird eine Datenpipeline vorgestellt, welche Rohdaten verschiedener Messsysteme fusioniert und Messunsicherheiten aus dynamischen Kalibrierinformationen bestimmt. Des Weiteren wird eine bereits publizierte automatisierte Toolbox für maschinelles Lernen um Unsicherheitsfortpflanzungen nach dem GUM erweitert. Unter Verwendung dieser Toolbox werden der Einfluss der Messunsicherheit auf die Ergebnisse des maschinellen Lernens untersucht und Ansätze zur Verbesserung dieser Ergebnisse aufgezeigt