Sequential and adaptive Bayesian computation for inference and optimization

With the advent of cheap and ubiquitous measurement devices, today more data is measured, recorded, and archived in a relatively short span of time than all data recorded throughout history. Moreover, advances in computation have made it possible to model much more complicated phenomena and to use the vast amounts of data to calibrate the resulting high-dimensional models. In this thesis, we are interested in two fundamental problems which are repeatedly being faced in practice as the dimension of the models and datasets are growing steadily: the problem of inference in high-dimensional models and the problem of optimization for problems when the number of data points is very large. The inference problem gets difficult when the model one wants to calibrate and estimate is defined in a high-dimensional space. The behavior of computational algorithms in high-dimensional spaces is complicated and defies intuition. Computational methods which work accurately for inferring low-dimensional models, for example, may fail to generalize the same performance to high-dimensional models. In recent years, due to the significant interest in high-dimensional models, there has been a plethora of work in signal processing and machine learning to develop computational methods which are robust in high-dimensional spaces. In particular, the high-dimensional stochastic filtering problem has attracted significant attention as it arises in multiple fields which are of crucial importance such as geophysics, aerospace, control. In particular, a class of algorithms called particle filters has received attention and become a fruitful field of research because of their accuracy and robustness in low-dimensional systems. In short, these methods keep a cloud of particles (samples in a state space), which describe the empirical probability distribution over the state variable of interest. The particle filters use a model of the phenomenon of interest to propagate and predict the future states and use an observation model to assimilate the observations to correct the state estimates. The most common particle filter, called the bootstrap particle filter (BPF), consists of an iterative sampling-weighting-resampling scheme. However, BPFs also largely fail at inferring high-dimensional dynamical systems due to a number of reasons. In this work, we propose a novel particle filter, named the nudged particle filter (NuPF), which specifically aims at improving the performance of particle filters in high-dimensional systems. The algorithm relies on the idea of nudging, which has been widely used in the geophysics literature to tackle high-dimensional inference problems. In particular, in addition to standard sampling-weighting-resampling steps of the particle filter, we define a general nudging step based on the gradient of the likelihoods, which generalize some of the nudging schemes proposed in the literature. This step is based on modifying the particles, generated in the sampling step, using the gradients of the likelihoods. In particular, the nudging step moves a fraction of the particles to the regions under which they have high-likelihoods. This scheme results in significantly improved behavior in high-dimensional models. The resulting NuPF is able to track high-dimensional systems successfully. Unlike the proposed nudging schemes in the literature, the NuPF does not rely on Gaussianity assumptions and can be defined for a general likelihood. We analytically prove that, because we only move a fraction of the particles and not all of them, the algorithm has a convergence rate that matches standard Monte Carlo algorithms. More precisely, the NuPF has the same asymptotic convergence guarantees as the bootstrap particle filter. As a byproduct, we also show that the nudging step improves the robustness of the particle filter against model misspecification. In particular, model misspecification occurs when the true data-generating system and the model posed by the user of the algorithm differ significantly. In this case, a majority of computational inference methods fail due to the discrepancy between the modeling assumptions and the observed data. We show that the nudging step increases the robustness of particle filters against model misspecification. Specifically, we prove that the NuPF generates particle systems which have provably higher marginal likelihoods compared to the standard bootstrap particle filter. This theoretical result is attained by showing that the NuPF can be interpreted as a bootstrap particle filter for a modified state-space model. Finally, we demonstrate the empirical behavior of the NuPF with several examples. In particular, we show results on high-dimensional linear state-space models, a misspecified Lorenz 63 model, a high-dimensional Lorenz 96 model, and a misspecified object tracking model. In all examples, the NuPF infers the states successfully. The second problem, the so-called scability problem in optimization, occurs because of the large number of data points in modern datasets. With the increasing abundance of data, many problems in signal processing, statistical inference, and machine learning turn into a large-scale optimization problems. For example, in signal processing, one might be interested in estimating a sparse signal given a large number of corrupted observations. Similarly, maximum-likelihood inference problems in statistics result in large-scale optimization problems. Another significant application domain is machine learning, where all important training methods are defined as optimization problems. To tackle these problems, computational optimization methods developed over the past decades are inefficient since they need to compute function evaluations or gradients over all the data for a single iteration. Because of this reason, a class of optimization methods, termed stochastic optimization methods, have emerged. The algorithms of this class are designed to tackle problems which are defined over a big number of data points. In short, these methods utilize a subsample of the dataset in order to update the parameter estimate and do so iteratively until some convergence criterion is met. However, there is a major difficulty that has to be addressed: Although the convergence theory for these algorithms is understood, they can have unstable behavior in practice. In particular, the most commonly used stochastic optimization method, namely the stochastic gradient descent, can diverge easily if its step-size is poorly set. Over the years, practitioners have developed a number of rules of thumb to alleviate stability issues. We argue in this thesis that one way to develop robust stochastic optimization methods is to frame them as inference methods. In particular, we show that stochastic optimization schemes can be recast as inference methods and can be understood as inference algorithms. Framing the problem as an inference problem opens the way to compare these methods to the optimal inference algorithms and understand why they might be failing or producing unstable behavior. In this vein, we show that there is an intrinsic relationship between a class of stochastic optimization methods, called incremental proximal methods, and Kalman (and extended Kalman) filters. The filtering approach to stochastic optimization results in an automatic calibration of the step-size, which removes the instability problems depending on the step-sizes. The probabilistic interpretation of stochastic optimization problems also paves the way to develop new optimization methods based on strategies which are popular in the inference literature. In particular, one can use a set of sampling methods in order to solve the inference problem and hence obtain the global minimum. In this manner, we propose a parallel sequential Monte Carlo optimizer (PSMCO), which is aiming at solving stochastic optimization problems. The PSMCO is designed as a zeroth order method which does not use gradients. It only uses subsets of the data points in order to move at each iteration. The PSMCO obtains an estimate of a global minimum at each iteration by utilizing a cheap kernel density estimator. We prove that the resulting estimator converges to a global minimum almost surely as the number of Monte Carlo samples tends to infinity. We also empirically demonstrate that the algorithm is able to reconstruct multiple global minima and solve difficult global optimization problems. By further exploiting the relationship between inference and optimization, we also propose a probabilistic and online matrix factorization method, termed the dictionary filter to solve large-scale matrix factorization problems. Matrix factorization methods have received significant interest from the machine learning community due to their expressive representations of high-dimensional data and interpretability of their estimates. As the majority of the matrix factorization methods are defined as optimization problems, they suffer from the same issues as stochastic optimization methods. In particular, when using stochastic gradient descent, one might need to try and err many times before deciding to use a step-size. To alleviate these problems, we introduce a matrix-variate probabilistic model for which inference results in a matrix factorization scheme. The scheme is online, in the sense that it only uses a single data point at a time to update the factors. The algorithm bears relationship with optimization schemes, namely with the incremental proximal method defined over a matrix-variate cost function. By way of intuition we developed for the optimization-inference relationship, we devise a model which results in similar update rules for matrix factorization as for the incremental proximal method. However, the probabilistic updates are more stable and efficient. Moreover, the algorithm does not have a step-size parameter to tune, as its role is played by the posterior covariance matrix. We demonstrate the utility of the algorithm on a missing data problem and a video processing problem. We show that the algorithm can be successfully used in machine learning problems and several promising extensions of the method can be constructed easily.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Ricardo Cao Abad.- Secretario: Michael Peter Wiper.- Vocal: Nicholas Paul Whitele

New optimized electrical architectures of photovoltaic generators with high conversion efficiency

L'objectif de cette thèse est l'optimisation du rendement des chaînes de conversion photovoltaïques (PV). Différentes améliorations de l'architecture électriques et de ses algorithmes de commande ont été développées afin d'obtenir un haut rendement de conversion sur une grande plage de puissance d'entrée. Ces travaux portent également sur l'allongement de la durée de vie de l'étage de conversion électrique. Les avantages et les inconvénients d'un système composé de convertisseurs connectés en parallèle ont été montrés notamment à travers une analyse de pertes. Ces études ont permis la conception d'une nouvelle architecture constituée par des convertisseurs parallélisés. Cette dernière est appelée "Convertisseur Multi-Phase Adaptative" (MPAC). Sa singularité réside dans ses algorithmes de commande qui adaptent les phases actives selon la production de puissance en temps réel et recherchent la configuration la plus efficiente à chaque instant. De cette façon, le MPAC garantit un haut rendement de conversion sur toute la plage de puissance de fonctionnement. Une autre loi de commande permet quant à elle d'uniformiser le temps de fonctionnement de chaque phase par l'implémentation d'un algorithme de rotation de phase. Ainsi, le stress des composants de ces phases est maintenu homogène, assurant un vieillissement homogène pour chacune des phases. Etant donné alors le faible stress appliqué sur chaque composant, la structure MPAC présente une durée de vie plus importante. Les améliorations de l'étage de conversion de puissance ont pu montrer par la réalisation d'un prototype expérimental et par la réalisation de tests expérimentaux la validation globale du système. Pour finir, des tests comparatifs entre une chaîne de conversion PV classique et notre système ont montré une amélioration significative du rendement de conversion.This thesis focuses in the optimization of the efficiency of photovoltaic power conversion chain. In this way, different improvements have been proposed in the electrical architecture and its control algorithms in order to obtain high efficiency in a large rage of input power and long life-time of PV power conversion system. Using loss analysis, the benefits and drawbacks of parallel connection of power structures has been shown. This analysis has allowed the conception of a new optimized architecture constituted by parallelized power converters, called Multi-Phase Adaptive Converter (MPAC). The singularity of these power structures consists on the adaptation of the phases of the converter depending on the power production in real-time and looking for the most efficient configuration all time. In this way, the MPAC guarantees high conversion efficiency for all power ranges. Another control law is also implemented which guarantees a rotation of the phases to keep their working time uniform. Thus, the stress of the components of all the phases is kept homogenous, assuring a homogeneous aging of the phases. Since the global stress of the component is lower, the MPAC presents a longer life-time. The improvements in the power conversion stage are shown by experimental prototypes. Experimental tests have been done for global validation. Comparison with a classical power conversion stage shows the improvement in the global conversion efficiency

High-Performance Placement and Routing for the Nanometer Scale.

Modern semiconductor manufacturing facilitates single-chip electronic systems that only five years ago required ten to twenty chips. Naturally, design complexity has grown within this period. In contrast to this growth, it is becoming common in the industry to limit design team size which places a heavier burden on design automation tools. Our work identifies new objectives, constraints and concerns in the physical design of systems-on-chip, and develops new computational techniques to address them. In addition to faster and more relevant design optimizations, we demonstrate that traditional design flows based on ``separation of concerns'' produce unnecessarily suboptimal layouts. We develop new integrated optimizations that streamline traditional chains of loosely-linked design tools. In particular, we bridge the gap between mixed-size placement and routing by updating the objective of global and detail placement to a more accurate estimate of routed wirelength. To this we add sophisticated whitespace allocation, and the combination provides increased routability, faster routing, shorter routed wirelength, and the best via counts of published techniques. To further improve post-routing design metrics, we present new global routing techniques based on Discrete Lagrange Multipliers (DLM) which produce the best routed wirelength results on recent benchmarks. Our work culminates in the integration of our routing techniques within an incremental placement flow to improve detailed routing solutions, shrink die sizes and reduce total chip cost. Not only do our techniques improve the quality and cost of designs, but also simplify design automation software implementation in many cases. Ultimately, we reduce the time needed for design closure through improved tool fidelity and the use of our incremental techniques for placement and routing.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/64639/1/royj_1.pd

Nesting optimization with adversarial games, meta-learning, and deep equilibrium models

Nested optimization, whereby an optimization problem is constrained by the solutions of other optimization problems, has recently seen a surge in its application to Deep Learning. While the study of such problems started nearly a century ago in the context of market theory, many of the algorithms developed since do not scale to modern Deep Learning applications. In this thesis, I push the understanding and applicability of nested optimization to three machine learning domains: 1) adversarial games, 2) meta-learning and 3) deep equilibrium models. For each domain, I tackle a particular goal. In 1) I adversarially learn model compression, in the case where training data isn't available, in 2) I meta-learn hyperparameters for long optimization processes without introducing greediness, and in 3) I use deep equilibrium models to improve temporal coherence in video landmark detection. The first part of my thesis deals with casting model compression as an adversarial game. Performing knowledge transfer from a large teacher network to a smaller student is a popular task in deep learning. However, due to growing dataset sizes and stricter privacy regulations, it is increasingly common not to have access to the data that was used to train the teacher. I propose a novel method which trains a student to match the predictions of its teacher without using any data or metadata. This is achieved by nesting the training optimization of the student with that of an adversarial generator, which searches for images on which the student poorly matches the teacher. These images are used to train the student in an online fashion. The student closely approximates its teacher for simple datasets like SVHN, and on CIFAR10 I improve on the state-of-the-art for few-shot distillation (with $100$ images per class), despite using no data. Finally, I also propose a metric to quantify the degree of belief matching between teacher and student in the vicinity of decision boundaries, and observe a significantly higher match between the zero-shot student and the teacher, than between a student distilled with real data and the teacher. The second part of my thesis deals with meta-learning hyperparameters in the case when the nested optimization to be differentiated is itself solved by many gradient steps. Gradient-based hyperparameter optimization has earned a widespread popularity in the context of few-shot meta-learning, but remains broadly impractical for tasks with long horizons (many gradient steps), due to memory scaling and gradient degradation issues. A common workaround is to learn hyperparameters online, but this introduces greediness which comes with a significant performance drop. I propose forward-mode differentiation with sharing (FDS), a simple and efficient algorithm which tackles memory scaling issues with forward-mode differentiation, and gradient degradation issues by sharing hyperparameters that are contiguous in time. I provide theoretical guarantees about the noise reduction properties of my algorithm, and demonstrate its efficiency empirically by differentiating through $\sim 10^4$ gradient steps of unrolled optimization. I consider large hyperparameter search ranges on CIFAR-10 where I significantly outperform greedy gradient-based alternatives, while achieving $\times 20$ speedups compared to the state-of-the-art black-box methods. The third part of my thesis deals with converting deep equilibrium models to a form of nested optimization in order to perform robust video landmark detection. Cascaded computation, whereby predictions are recurrently refined over several stages, has been a persistent theme throughout the development of landmark detection models. I show that the recently proposed deep equilibrium model (DEQ) can be naturally adapted to this form of computation, given appropriate regularization. My landmark model achieves state-of-the-art performance on the challenging WFLW facial landmark dataset, reaching $3.92$ normalized mean error with fewer parameters and a training memory cost of $\mathcal{O}(1)$ in the number of recurrent modules. Furthermore, I show that DEQs are particularly suited for landmark detection in videos. In this setting, it is typical to train on still images due to the lack of labeled videos. This can lead to a ``flickering'' effect at inference time on video, whereby a model can rapidly oscillate between different plausible solutions across consecutive frames. I show that the DEQ root solving problem can be turned into a constrained optimization problem in a way that emulates recurrence at inference time, despite not having access to temporal data at training time. I call this "Recurrence without Recurrence'', and demonstrate that it helps reduce landmark flicker by introducing a new metric, and contributing a new facial landmark video dataset targeting landmark uncertainty. On the hard subset of this new dataset, made up of $500$ videos, my model improves the accuracy and temporal coherence by $10$ and $13\%$ respectively, compared to the strongest previously published model using a hand-tuned conventional filter

Fundamental Approaches to Software Engineering

This open access book constitutes the proceedings of the 24th International Conference on Fundamental Approaches to Software Engineering, FASE 2021, which took place during March 27–April 1, 2021, and was held as part of the Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg but changed to an online format due to the COVID-19 pandemic. The 16 full papers presented in this volume were carefully reviewed and selected from 52 submissions. The book also contains 4 Test-Comp contributions

Towards Robust Bipedal Locomotion:From Simple Models To Full-Body Compliance

Thanks to better actuator technologies and control algorithms, humanoid robots to date can perform a wide range of locomotion activities outside lab environments. These robots face various control challenges like high dimensionality, contact switches during locomotion and a floating-base nature which makes them fall all the time. A rich set of sensory inputs and a high-bandwidth actuation are often needed to ensure fast and effective reactions to unforeseen conditions, e.g., terrain variations, external pushes, slippages, unknown payloads, etc. State of the art technologies today seem to provide such valuable hardware components. However, regarding software, there is plenty of room for improvement. Locomotion planning and control problems are often treated separately in conventional humanoid control algorithms. The control challenges mentioned above are probably the main reason for such separation. Here, planning refers to the process of finding consistent open-loop trajectories, which may take arbitrarily long computations off-line. Control, on the other hand, should be done very fast online to ensure stability. In this thesis, we want to link planning and control problems again and enable for online trajectory modification in a meaningful way. First, we propose a new way of describing robot geometries like molecules which breaks the complexity of conventional models. We use this technique and derive a planning algorithm that is fast enough to be used online for multi-contact motion planning. Similarly, we derive 3LP, a simplified linear three-mass model for bipedal walking, which offers orders of magnitude faster computations than full mechanical models. Next, we focus more on walking and use the 3LP model to formulate online control algorithms based on the foot-stepping strategy. The method is based on model predictive control, however, we also propose a faster controller with time-projection that demonstrates a close performance without numerical optimizations. We also deploy an efficient implementation of inverse dynamics together with advanced sensor fusion and actuator control algorithms to ensure a precise and compliant tracking of the simplified 3LP trajectories. Extensive simulations and hardware experiments on COMAN robot demonstrate effectiveness and strengths of our method. This thesis goes beyond humanoid walking applications. We further use the developed modeling tools to analyze and understand principles of human locomotion. Our 3LP model can describe the exchange of energy between human limbs in walking to some extent. We use this property to propose a metabolic-cost model of human walking which successfully describes trends in various conditions. The intrinsic power of the 3LP model to generate walking gaits in all these conditions makes it a handy solution for walking control and gait analysis, despite being yet a simplified model. To fill the reality gap, finally, we propose a kinematic conversion method that takes 3LP trajectories as input and generates more human-like postures. Using this method, the 3LP model, and the time-projecting controller, we introduce a graphical user interface in the end to simulate periodic and transient human-like walking conditions. We hope to use this combination in future to produce faster and more human-like walking gaits, possibly with more capable humanoid robots

Opportunities and obstacles for deep learning in biology and medicine

Deep learning describes a class of machine learning algorithms that are capable of combining raw inputs into layers of intermediate features. These algorithms have recently shown impressive results across a variety of domains. Biology and medicine are data-rich disciplines, but the data are complex and often ill-understood. Hence, deep learning techniques may be particularly well suited to solve problems of these fields. We examine applications of deep learning to a variety of biomedical problems-patient classification, fundamental biological processes and treatment of patients-and discuss whether deep learning will be able to transform these tasks or if the biomedical sphere poses unique challenges. Following from an extensive literature review, we find that deep learning has yet to revolutionize biomedicine or definitively resolve any of the most pressing challenges in the field, but promising advances have been made on the prior state of the art. Even though improvements over previous baselines have been modest in general, the recent progress indicates that deep learning methods will provide valuable means for speeding up or aiding human investigation. Though progress has been made linking a specific neural network\u27s prediction to input features, understanding how users should interpret these models to make testable hypotheses about the system under study remains an open challenge. Furthermore, the limited amount of labelled data for training presents problems in some domains, as do legal and privacy constraints on work with sensitive health records. Nonetheless, we foresee deep learning enabling changes at both bench and bedside with the potential to transform several areas of biology and medicine

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp