921 research outputs found
Classical and quantum algorithms for scaling problems
This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size
Quantifying Equity Risk Premia: Financial Economic Theory and High-Dimensional Statistical Methods
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
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Advances and Applications of DSmT for Information Fusion. Collected Works, Volume 5
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
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
Quadratic quantum speedup in evaluating bilinear risk functions
Computing nonlinear functions over multilinear forms is a general problem
with applications in risk analysis. For instance in the domain of energy
economics, accurate and timely risk management demands for efficient simulation
of millions of scenarios, largely benefiting from computational speedups. We
develop a novel hybrid quantum-classical algorithm based on polynomial
approximation of nonlinear functions and compare different implementation
variants. We prove a quadratic quantum speedup, up to polylogarithmic factors,
when forms are bilinear and approximating polynomials have second degree, if
efficient loading unitaries are available for the input data sets. We also
enhance the bidirectional encoding, that allows tuning the balance between
circuit depth and width, proposing an improved version that can be exploited
for the calculation of inner products. Lastly, we exploit the dynamic circuit
capabilities, recently introduced on IBM Quantum devices, to reduce the average
depth of the Quantum Hadamard Product circuit. A proof of principle is
implemented and validated on IBM Quantum systems
(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!)
(b2023 to 2014) The UNBELIEVABLE similarities between the ideas of some people (2006-2016) and my ideas (2002-2008) in physics (quantum mechanics, cosmology), cognitive neuroscience, philosophy of mind, and philosophy (this manuscript would require a REVOLUTION in international academy environment!
Performance Analysis Of Data-Driven Algorithms In Detecting Intrusions On Smart Grid
The traditional power grid is no longer a practical solution for power delivery due to several shortcomings, including chronic blackouts, energy storage issues, high cost of assets, and high carbon emissions. Therefore, there is a serious need for better, cheaper, and cleaner power grid technology that addresses the limitations of traditional power grids. A smart grid is a holistic solution to these issues that consists of a variety of operations and energy measures. This technology can deliver energy to end-users through a two-way flow of communication. It is expected to generate reliable, efficient, and clean power by integrating multiple technologies. It promises reliability, improved functionality, and economical means of power transmission and distribution. This technology also decreases greenhouse emissions by transferring clean, affordable, and efficient energy to users. Smart grid provides several benefits, such as increasing grid resilience, self-healing, and improving system performance. Despite these benefits, this network has been the target of a number of cyber-attacks that violate the availability, integrity, confidentiality, and accountability of the network. For instance, in 2021, a cyber-attack targeted a U.S. power system that shut down the power grid, leaving approximately 100,000 people without power. Another threat on U.S. Smart Grids happened in March 2018 which targeted multiple nuclear power plants and water equipment. These instances represent the obvious reasons why a high level of security approaches is needed in Smart Grids to detect and mitigate sophisticated cyber-attacks. For this purpose, the US National Electric Sector Cybersecurity Organization and the Department of Energy have joined their efforts with other federal agencies, including the Cybersecurity for Energy Delivery Systems and the Federal Energy Regulatory Commission, to investigate the security risks of smart grid networks. Their investigation shows that smart grid requires reliable solutions to defend and prevent cyber-attacks and vulnerability issues. This investigation also shows that with the emerging technologies, including 5G and 6G, smart grid may become more vulnerable to multistage cyber-attacks. A number of studies have been done to identify, detect, and investigate the vulnerabilities of smart grid networks. However, the existing techniques have fundamental limitations, such as low detection rates, high rates of false positives, high rates of misdetection, data poisoning, data quality and processing, lack of scalability, and issues regarding handling huge volumes of data. Therefore, these techniques cannot ensure safe, efficient, and dependable communication for smart grid networks. Therefore, the goal of this dissertation is to investigate the efficiency of machine learning in detecting cyber-attacks on smart grids. The proposed methods are based on supervised, unsupervised machine and deep learning, reinforcement learning, and online learning models. These models have to be trained, tested, and validated, using a reliable dataset. In this dissertation, CICDDoS 2019 was used to train, test, and validate the efficiency of the proposed models. The results show that, for supervised machine learning models, the ensemble models outperform other traditional models. Among the deep learning models, densely neural network family provides satisfactory results for detecting and classifying intrusions on smart grid. Among unsupervised models, variational auto-encoder, provides the highest performance compared to the other unsupervised models. In reinforcement learning, the proposed Capsule Q-learning provides higher detection and lower misdetection rates, compared to the other model in literature. In online learning, the Online Sequential Euclidean Distance Routing Capsule Network model provides significantly better results in detecting intrusion attacks on smart grid, compared to the other deep online models
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