2,604 research outputs found

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    Quantifying Equity Risk Premia: Financial Economic Theory and High-Dimensional Statistical Methods

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    The overarching question of this dissertation is how to quantify the unobservable risk premium of a stock when its return distribution varies over time. The first chapter, titled “Theory-based versus machine learning-implied stock risk premia”, starts with a comparison of two competing strands of the literature. The approach advocated by Martin and Wagner (2019) relies on financial economic theory to derive a closed-form approximation of conditional risk premia using information embedded in the prices of European options. The other approach, exemplified by the study of Gu et al. (2020), draws on the flexibility of machine learning methods and vast amounts of historical data to determine the unknown functional form. The goal of this study is to determine which of the two approaches produces more accurate measurements of stock risk premia. In addition, we present a novel hybrid approach that employs machine learning to overcome the approximation errors induced by the theory-based approach. We find that our hybrid approach is competitive especially at longer investment horizons. The second chapter, titled “The uncertainty principle in asset pricing”, introduces a representation of the conditional capital asset pricing model (CAPM) in which the betas and the equity premium are jointly characterized by the information embedded in option prices. A unique feature of our model is that its implied components represent valid measurements of their physical counterparts without the need for any further risk adjustment. Moreover, because the model’s time-varying parameters are directly observable, the model can be tested without any of the complications that typically arise from statistical estimation. One of the main empirical findings is that the well-known flat relationship between average predicted and realized excess returns of beta-sorted portfolios can be explained by the uncertainty governing market excess returns. In the third chapter, titled “Multi-task learning in cross-sectional regressions”, we challenge the way in which cross-sectional regressions are used to test factor models with time-varying loadings. More specifically, we extend the procedure by Fama and MacBeth (1973) by systematically selecting stock characteristics using a combination of l1- and l2-regularization, known as the multi-task Lasso, and addressing the bias that is induced by selection via repeated sample splitting. In the empirical part of this chapter, we apply our testing procedure to the option-implied CAPM from chapter two, and find that, while variants of the momentum effect lead to a rejection of the model, the implied beta is by far the most important predictor of cross-sectional return variation

    Backpropagation Beyond the Gradient

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    Automatic differentiation is a key enabler of deep learning: previously, practitioners were limited to models for which they could manually compute derivatives. Now, they can create sophisticated models with almost no restrictions and train them using first-order, i. e. gradient, information. Popular libraries like PyTorch and TensorFlow compute this gradient efficiently, automatically, and conveniently with a single line of code. Under the hood, reverse-mode automatic differentiation, or gradient backpropagation, powers the gradient computation in these libraries. Their entire design centers around gradient backpropagation. These frameworks are specialized around one specific task—computing the average gradient in a mini-batch. This specialization often complicates the extraction of other information like higher-order statistical moments of the gradient, or higher-order derivatives like the Hessian. It limits practitioners and researchers to methods that rely on the gradient. Arguably, this hampers the field from exploring the potential of higher-order information and there is evidence that focusing solely on the gradient has not lead to significant recent advances in deep learning optimization. To advance algorithmic research and inspire novel ideas, information beyond the batch-averaged gradient must be made available at the same level of computational efficiency, automation, and convenience. This thesis presents approaches to simplify experimentation with rich information beyond the gradient by making it more readily accessible. We present an implementation of these ideas as an extension to the backpropagation procedure in PyTorch. Using this newly accessible information, we demonstrate possible use cases by (i) showing how it can inform our understanding of neural network training by building a diagnostic tool, and (ii) enabling novel methods to efficiently compute and approximate curvature information. First, we extend gradient backpropagation for sequential feedforward models to Hessian backpropagation which enables computing approximate per-layer curvature. This perspective unifies recently proposed block- diagonal curvature approximations. Like gradient backpropagation, the computation of these second-order derivatives is modular, and therefore simple to automate and extend to new operations. Based on the insight that rich information beyond the gradient can be computed efficiently and at the same time, we extend the backpropagation in PyTorch with the BackPACK library. It provides efficient and convenient access to statistical moments of the gradient and approximate curvature information, often at a small overhead compared to computing just the gradient. Next, we showcase the utility of such information to better understand neural network training. We build the Cockpit library that visualizes what is happening inside the model during training through various instruments that rely on BackPACK’s statistics. We show how Cockpit provides a meaningful statistical summary report to the deep learning engineer to identify bugs in their machine learning pipeline, guide hyperparameter tuning, and study deep learning phenomena. Finally, we use BackPACK’s extended automatic differentiation functionality to develop ViViT, an approach to efficiently compute curvature information, in particular curvature noise. It uses the low-rank structure of the generalized Gauss-Newton approximation to the Hessian and addresses shortcomings in existing curvature approximations. Through monitoring curvature noise, we demonstrate how ViViT’s information helps in understanding challenges to make second-order optimization methods work in practice. This work develops new tools to experiment more easily with higher-order information in complex deep learning models. These tools have impacted works on Bayesian applications with Laplace approximations, out-of-distribution generalization, differential privacy, and the design of automatic differentia- tion systems. They constitute one important step towards developing and establishing more efficient deep learning algorithms

    Language integrated relational lenses

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    Relational databases are ubiquitous. Such monolithic databases accumulate large amounts of data, yet applications typically only work on small portions of the data at a time. A subset of the database defined as a computation on the underlying tables is called a view. Querying views is helpful, but it is also desirable to update them and have these changes be applied to the underlying database. This view update problem has been the subject of much previous work before, but support by database servers is limited and only rarely available. Lenses are a popular approach to bidirectional transformations, a generalization of the view update problem in databases to arbitrary data. However, perhaps surprisingly, lenses have seldom actually been used to implement updatable views in databases. Bohannon, Pierce and Vaughan propose an approach to updatable views called relational lenses. However, to the best of our knowledge this proposal has not been implemented or evaluated prior to the work reported in this thesis. This thesis proposes programming language support for relational lenses. Language integrated relational lenses support expressive and efficient view updates, without relying on updatable view support from the database server. By integrating relational lenses into the programming language, application development becomes easier and less error-prone, avoiding the impedance mismatch of having two programming languages. Integrating relational lenses into the language poses additional challenges. As defined by Bohannon et al. relational lenses completely recompute the database, making them inefficient as the database scales. The other challenge is that some parts of the well-formedness conditions are too general for implementation. Bohannon et al. specify predicates using possibly infinite abstract sets and define the type checking rules using relational algebra. Incremental relational lenses equip relational lenses with change-propagating semantics that map small changes to the view into (potentially) small changes to the source tables. We prove that our incremental semantics are functionally equivalent to the non-incremental semantics, and our experimental results show orders of magnitude improvement over the non-incremental approach. This thesis introduces a concrete predicate syntax and shows how the required checks are performed on these predicates and show that they satisfy the abstract predicate specifications. We discuss trade-offs between static predicates that are fully known at compile time vs dynamic predicates that are only known during execution and introduce hybrid predicates taking inspiration from both approaches. This thesis adapts the typing rules for relational lenses from sequential composition to a functional style of sub-expressions. We prove that any well-typed functional relational lens expression can derive a well-typed sequential lens. We use these additions to relational lenses as the foundation for two practical implementations: an extension of the Links functional language and a library written in Haskell. The second implementation demonstrates how type-level computation can be used to implement relational lenses without changes to the compiler. These two implementations attest to the possibility of turning relational lenses into a practical language feature

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Space-Efficient Parameterized Algorithms on Graphs of Low Shrubdepth

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    Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming uses space that is exponential in the decomposition's width, and there are good reasons to believe that this is necessary. However, it has been shown that in graphs of low treedepth it is possible to design algorithms which achieve polynomial space complexity without requiring worse time complexity than their counterparts working on tree decompositions of bounded width. Here, treedepth is a graph parameter that, intuitively speaking, takes into account both the depth and the width of a tree decomposition of the graph, rather than the width alone. Motivated by the above, we consider graphs that admit clique expressions with bounded depth and label count, or equivalently, graphs of low shrubdepth (sd). Here, sd is a bounded-depth analogue of cliquewidth, in the same way as td is a bounded-depth analogue of treewidth. We show that also in this setting, bounding the depth of the decomposition is a deciding factor for improving the space complexity. Precisely, we prove that on nn-vertex graphs equipped with a tree-model (a decomposition notion underlying sd) of depth dd and using kk labels, we can solve - Independent Set in time 2O(dk)nO(1)2^{O(dk)}\cdot n^{O(1)} using O(dk2logn)O(dk^2\log n) space; - Max Cut in time nO(dk)n^{O(dk)} using O(dklogn)O(dk\log n) space; and - Dominating Set in time 2O(dk)nO(1)2^{O(dk)}\cdot n^{O(1)} using nO(1)n^{O(1)} space via a randomized algorithm. We also establish a lower bound, conditional on a certain assumption about the complexity of Longest Common Subsequence, which shows that at least in the case of IS the exponent of the parametric factor in the time complexity has to grow with dd if one wishes to keep the space complexity polynomial.Comment: Conference version to appear at the European Symposium on Algorithms (ESA 2023

    Development, Implementation, and Optimization of a Modern, Subsonic/Supersonic Panel Method

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    In the early stages of aircraft design, engineers consider many different design concepts, examining the trade-offs between different component arrangements and sizes, thrust and power requirements, etc. Because so many different designs are considered, it is best in the early stages of design to use simulation tools that are fast; accuracy is secondary. A common simulation tool for early design and analysis is the panel method. Panel methods were first developed in the 1950s and 1960s with the advent of modern computers. Despite being reasonably accurate and very fast, their development was abandoned in the late 1980s in favor of more complex and accurate simulation methods. The panel methods developed in the 1980s are still in use by aircraft designers today because of their accuracy and speed. However, they are cumbersome to use and limited in applicability. The purpose of this work is to reexamine panel methods in a modern context. In particular, this work focuses on the application of panel methods to supersonic aircraft (a supersonic aircraft is one that flies faster than the speed of sound). Various aspects of the panel method, including the distributions of the unknown flow variables on the surface of the aircraft and efficiently solving for these unknowns, are discussed. Trade-offs between alternative formulations are examined and recommendations given. This work also serves to bring together, clarify, and condense much of the literature previously published regarding panel methods so as to assist future developers of panel methods

    Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5

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    This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well

    On the Utility of Representation Learning Algorithms for Myoelectric Interfacing

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    Electrical activity produced by muscles during voluntary movement is a reflection of the firing patterns of relevant motor neurons and, by extension, the latent motor intent driving the movement. Once transduced via electromyography (EMG) and converted into digital form, this activity can be processed to provide an estimate of the original motor intent and is as such a feasible basis for non-invasive efferent neural interfacing. EMG-based motor intent decoding has so far received the most attention in the field of upper-limb prosthetics, where alternative means of interfacing are scarce and the utility of better control apparent. Whereas myoelectric prostheses have been available since the 1960s, available EMG control interfaces still lag behind the mechanical capabilities of the artificial limbs they are intended to steer—a gap at least partially due to limitations in current methods for translating EMG into appropriate motion commands. As the relationship between EMG signals and concurrent effector kinematics is highly non-linear and apparently stochastic, finding ways to accurately extract and combine relevant information from across electrode sites is still an active area of inquiry.This dissertation comprises an introduction and eight papers that explore issues afflicting the status quo of myoelectric decoding and possible solutions, all related through their use of learning algorithms and deep Artificial Neural Network (ANN) models. Paper I presents a Convolutional Neural Network (CNN) for multi-label movement decoding of high-density surface EMG (HD-sEMG) signals. Inspired by the successful use of CNNs in Paper I and the work of others, Paper II presents a method for automatic design of CNN architectures for use in myocontrol. Paper III introduces an ANN architecture with an appertaining training framework from which simultaneous and proportional control emerges. Paper Iv introduce a dataset of HD-sEMG signals for use with learning algorithms. Paper v applies a Recurrent Neural Network (RNN) model to decode finger forces from intramuscular EMG. Paper vI introduces a Transformer model for myoelectric interfacing that do not need additional training data to function with previously unseen users. Paper vII compares the performance of a Long Short-Term Memory (LSTM) network to that of classical pattern recognition algorithms. Lastly, paper vIII describes a framework for synthesizing EMG from multi-articulate gestures intended to reduce training burden

    Machine learning in solar physics

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    The application of machine learning in solar physics has the potential to greatly enhance our understanding of the complex processes that take place in the atmosphere of the Sun. By using techniques such as deep learning, we are now in the position to analyze large amounts of data from solar observations and identify patterns and trends that may not have been apparent using traditional methods. This can help us improve our understanding of explosive events like solar flares, which can have a strong effect on the Earth environment. Predicting hazardous events on Earth becomes crucial for our technological society. Machine learning can also improve our understanding of the inner workings of the sun itself by allowing us to go deeper into the data and to propose more complex models to explain them. Additionally, the use of machine learning can help to automate the analysis of solar data, reducing the need for manual labor and increasing the efficiency of research in this field.Comment: 100 pages, 13 figures, 286 references, accepted for publication as a Living Review in Solar Physics (LRSP
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