A coherent point drift algorithm for breast image registration via surface markers

Breast Magnetic Resonance Imaging (MRI) is a reliable imaging tool for localization and evaluation of lesions prior to breast conserving surgery (BCS). MR images typically will be used to determine the size and location of the tumours before making the incision in order to minimize the amount of tissue excised. The arm position and configuration of the breast during and prior to surgery are different and one question is whether it would be possible to match the two configurations. This matching process can potentially be used in development of tools to guide surgeons in the incision process. Recently, a Thin- Plate-Spline (TPS) algorithm has been proposed to assess the feasibility of breast tissue matching using fiducial surface markers in two different arm positions. The registration algorithm uses the surface markers only and does not employ the image intensities. In this Thesis, I apply and evaluate a coherent point drift (CPD) algorithm for registration of 3D breast MR images of six patient volunteers. In particular, we evaluate the results of the previous TPS registration technique to the proposed rigid, affine, and deformable CPD registration algorithms on the same patient datasets. The results suggest that the CPD deformable registration algorithm is superior in correcting the motion of the breast compared to CPD rigid, affine and TPS registration algorithms. The CPD registration results reported in this thesis took 0.2 to 0.4 seconds, which is significantly lower than the computation time using TPS (under a minute)

Efficient Quasi-Newton Methods in Trust-Region Frameworks for Training Deep Neural Networks

Deep Learning (DL), utilizing Deep Neural Networks (DNNs), has gained significant popularity in Machine Learning (ML) due to its wide range of applications in various domains. DL applications typically involve large-scale, highly nonlinear, and non-convex optimization problems. The objective of these optimization problems, often expressed as a finite-sum function, is to minimize the overall prediction error by optimizing the parameters of the neural network. In order to solve a DL optimization problem, interpreted as DNN training, stochastic second-order methods have recently attracted much attention. These methods leverage curvature information from the objective function and employ practical subsampling schemes to approximately evaluate the objective function and its gradient using random subsets of the available (training) data. Within this context, active research is focused on exploring strategies based on Quasi-Newton methods within both line-search and trust-region optimization frameworks. A trust-region approach is often preferred over the former one due to its ability to make progress even when some iterates are rejected, as well as its compatibility with both positive definite and indefinite Hessian approximations. Considering Quasi-Newton Hessian approximations, the thesis studies two classes of second-order trust-region methods in stochastic expansions for training DNNs as follows. In the class of standard trust-region methods, we consider well-known limited memory Quasi-Newton Hessian matrices, namely L-BFGS and L-SR1, and apply a half-overlapping subsampling for computations. We present an extensive experimental study on the resulting methods, discussing the effect of various factors on the training of different DNNs and filling a gap regarding which method yields more effective training. Then, we present a modified L-BFGS trust-region method by introducing a simple modification to the secant condition, which enhances the curvature information of the objective function, and extend it in a stochastic setting for training tasks. Finally, we devise a novel stochastic method that combines a trust-region L-SR1 second-order direction with a first-order variance-reduced stochastic gradient. Our focus in the second class is to develop standard trust-region methods for both non-monotone and stochastic expansions. Using regular fixed sample size subsampling, we investigate the efficiency of a non-monotone L-SR1 trust-region method in training through different approaches for computing the curvature information. We eventually propose a non-monotone trust-region algorithm that involves an additional sampling strategy in order to control the resulting error in function and gradient approximations due to subsampling. This novel method enjoys an adaptive sample size procedure and achieves almost sure convergence under standard assumptions. The efficiency of the algorithms presented in this study, implemented in MATLAB, is assessed by training different DNNs to solve specific problems such as image recognition and regression, and comparing their performance to well-known first- and second-order methods, including Adam and STORM.Deep Learning (DL), utilizing Deep Neural Networks (DNNs), has gained significant popularity in Machine Learning (ML) due to its wide range of applications in various domains. DL applications typically involve large-scale, highly nonlinear, and non-convex optimization problems. The objective of these optimization problems, often expressed as a finite-sum function, is to minimize the overall prediction error by optimizing the parameters of the neural network. In order to solve a DL optimization problem, interpreted as DNN training, stochastic second-order methods have recently attracted much attention. These methods leverage curvature information from the objective function and employ practical subsampling schemes to approximately evaluate the objective function and its gradient using random subsets of the available (training) data. Within this context, active research is focused on exploring strategies based on Quasi-Newton methods within both line-search and trust-region optimization frameworks. A trust-region approach is often preferred over the former one due to its ability to make progress even when some iterates are rejected, as well as its compatibility with both positive definite and indefinite Hessian approximations. Considering Quasi-Newton Hessian approximations, the thesis studies two classes of second-order trust-region methods in stochastic expansions for training DNNs as follows. In the class of standard trust-region methods, we consider well-known limited memory Quasi-Newton Hessian matrices, namely L-BFGS and L-SR1, and apply a half-overlapping subsampling for computations. We present an extensive experimental study on the resulting methods, discussing the effect of various factors on the training of different DNNs and filling a gap regarding which method yields more effective training. Then, we present a modified L-BFGS trust-region method by introducing a simple modification to the secant condition, which enhances the curvature information of the objective function, and extend it in a stochastic setting for training tasks. Finally, we devise a novel stochastic method that combines a trust-region L-SR1 second-order direction with a first-order variance-reduced stochastic gradient. Our focus in the second class is to develop standard trust-region methods for both non-monotone and stochastic expansions. Using regular fixed sample size subsampling, we investigate the efficiency of a non-monotone L-SR1 trust-region method in training through different approaches for computing the curvature information. We eventually propose a non-monotone trust-region algorithm that involves an additional sampling strategy in order to control the resulting error in function and gradient approximations due to subsampling. This novel method enjoys an adaptive sample size procedure and achieves almost sure convergence under standard assumptions. The efficiency of the algorithms presented in this study, implemented in MATLAB, is assessed by training different DNNs to solve specific problems such as image recognition and regression, and comparing their performance to well-known first- and second-order methods, including Adam and STORM

A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization

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Operations research modeling environment for an ERP system

Estágio realizado na AlumniEI e Microsoft Development Center CopenhagenTese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 200

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.In the literature of optimization problems under uncertainty a common approach of dealing with two- and multi-stage problems is to use scenario analysis. To do so, the uncertainty of some data in the problem is modeled by stage specific random vectors with finite supports. Each realization is called a scenario. By using scenarios, it is possible to study smaller versions (subproblems) of the underlying problem. As a scenario decomposition technique, the progressive hedging algorithm is one of the most popular methods in multi-stage stochastic programming problems. In spite of full decomposition over scenarios, progressive hedging efficiency is greatly sensitive to some practical aspects, such as the choice of the penalty parameter and handling the quadratic term in the augmented Lagrangian objective function. For the choice of the penalty parameter, we review some of the popular methods, and design a novel adaptive strategy that aims to better follow the algorithm process. Numerical experiments on linear multistage stochastic test problems suggest that most of the existing techniques may exhibit premature convergence to a sub-optimal solution or converge to the optimal solution, but at a very slow rate. In contrast, the new strategy appears to be robust and efficient, converging to optimality in all our experiments and being the fastest in most of them. For the question of handling the quadratic term, we review some existing techniques and we suggest to replace the quadratic term with a linear one. Although this method has yet to be tested, we have the intuition that it will reduce some numerical and theoretical difficulties of progressive hedging in linear problems

Self-Learning Longitudinal Control for On-Road Vehicles

Fahrerassistenzsysteme (Advanced Driver Assistance Systems) sind ein wichtiges Verkaufsargument für PKWs, fordern jedoch hohe Entwicklungskosten. Insbesondere die Parametrierung für Längsregelung, die einen wichtigen Baustein für Fahrerassistenzsysteme darstellt, benötigt viel Zeit und Geld, um die richtige Balance zwischen Insassenkomfort und Regelgüte zu treffen. Reinforcement Learning scheint ein vielversprechender Ansatz zu sein, um dies zu automatisieren. Diese Klasse von Algorithmen wurde bislang allerdings vorwiegend auf simulierte Aufgaben angewendet, die unter idealen Bedingungen stattfinden und nahezu unbegrenzte Trainingszeit ermöglichen. Unter den größten Herausforderungen für die Anwendung von Reinforcement Learning in einem realen Fahrzeug sind Trajektorienfolgeregelung und unvollständige Zustandsinformationen aufgrund von nur teilweise beobachteter Dynamik. Darüber hinaus muss ein Algorithmus, der in realen Systemen angewandt wird, innerhalb von Minuten zu einem Ergebnis kommen. Außerdem kann das Regelziel sich während der Laufzeit beliebig ändern, was eine zusätzliche Schwierigkeit für Reinforcement Learning Methoden darstellt. Diese Arbeit stellt zwei Algorithmen vor, die wenig Rechenleistung benötigen und diese Hürden überwinden. Einerseits wird ein modellfreier Reinforcement Learning Ansatz vorgeschlagen, der auf der Actor-Critic-Architektur basiert und eine spezielle Struktur in der Zustandsaktionswertfunktion verwendet, um mit teilweise beobachteten Systemen eingesetzt werden zu können. Um eine Vorsteuerung zu lernen, wird ein Regler vorgeschlagen, der sich auf eine Projektion und Trainingsdatenmanipulation stützt. Andererseits wird ein modellbasierter Algorithmus vorgeschlagen, der auf Policy Search basiert. Diesem wird eine automatisierte Entwurfsmethode für eine inversionsbasierte Vorsteuerung zur Seite gestellt. Die vorgeschlagenen Algorithmen werden in einer Reihe von Szenarien verglichen, in denen sie online, d.h. während der Fahrt und bei geschlossenem Regelkreis, in einem realen Fahrzeug lernen. Obwohl die Algorithmen etwas unterschiedlich auf verschiedene Randbedingungen reagieren, lernen beide robust und zügig und sind in der Lage, sich an verschiedene Betriebspunkte, wie zum Beispiel Geschwindigkeiten und Gänge, anzupassen, auch wenn Störungen während des Trainings einwirken. Nach bestem Wissen des Autors ist dies die erste erfolgreiche Anwendung eines Reinforcement Learning Algorithmus, der online in einem realen Fahrzeug lernt