Application of backpropagation-like generative algorithms to various problems.

Thesis (M.Sc.)-University of Natal, Durban, 1992.Artificial neural networks (ANNs) were originally inspired by networks of biological neurons and the interactions present in networks of these neurons. The recent revival of interest in ANNs has again focused attention on the apparent ability of ANNs to solve difficult problems, such as machine vision, in novel ways. There are many types of ANNs which differ in architecture and learning algorithms, and the list grows annually. This study was restricted to feed-forward architectures and Backpropagation- like (BP-like) learning algorithms. However, it is well known that the learning problem for such networks is NP-complete. Thus generative and incremental learning algorithms, which have various advantages and to which the NP-completeness analysis used for BP-like networks may not apply, were also studied. Various algorithms were investigated and the performance compared. Finally, the better algorithms were applied to a number of problems including music composition, image binarization and navigation and goal satisfaction in an artificial environment. These tasks were chosen to investigate different aspects of ANN behaviour. The results, where appropriate, were compared to those resulting from non-ANN methods, and varied from poor to very encouraging

Advances in Computer Recognition, Image Processing and Communications, Selected Papers from CORES 2021 and IP&C 2021

As almost all human activities have been moved online due to the pandemic, novel robust and efficient approaches and further research have been in higher demand in the field of computer science and telecommunication. Therefore, this (reprint) book contains 13 high-quality papers presenting advancements in theoretical and practical aspects of computer recognition, pattern recognition, image processing and machine learning (shallow and deep), including, in particular, novel implementations of these techniques in the areas of modern telecommunications and cybersecurity

Application and Theory of Multimedia Signal Processing Using Machine Learning or Advanced Methods

This Special Issue is a book composed by collecting documents published through peer review on the research of various advanced technologies related to applications and theories of signal processing for multimedia systems using ML or advanced methods. Multimedia signals include image, video, audio, character recognition and optimization of communication channels for networks. The specific contents included in this book are data hiding, encryption, object detection, image classification, and character recognition. Academics and colleagues who are interested in these topics will find it interesting to read

Advanced Biometrics with Deep Learning

Biometrics, such as fingerprint, iris, face, hand print, hand vein, speech and gait recognition, etc., as a means of identity management have become commonplace nowadays for various applications. Biometric systems follow a typical pipeline, that is composed of separate preprocessing, feature extraction and classification. Deep learning as a data-driven representation learning approach has been shown to be a promising alternative to conventional data-agnostic and handcrafted pre-processing and feature extraction for biometric systems. Furthermore, deep learning offers an end-to-end learning paradigm to unify preprocessing, feature extraction, and recognition, based solely on biometric data. This Special Issue has collected 12 high-quality, state-of-the-art research papers that deal with challenging issues in advanced biometric systems based on deep learning. The 12 papers can be divided into 4 categories according to biometric modality; namely, face biometrics, medical electronic signals (EEG and ECG), voice print, and others

Rare-Event Estimation and Calibration for Large-Scale Stochastic Simulation Models

Stochastic simulation has been widely applied in many domains. More recently, however, the rapid surge of sophisticated problems such as safety evaluation of intelligent systems has posed various challenges to conventional statistical methods. Motivated by these challenges, in this thesis, we develop novel methodologies with theoretical guarantees and numerical applications to tackle them from different perspectives. In particular, our works can be categorized into two areas: (1) rare-event estimation (Chapters 2 to 5) where we develop approaches to estimating the probabilities of rare events via simulation; (2) model calibration (Chapters 6 and 7) where we aim at calibrating the simulation model so that it is close to reality. In Chapter 2, we study rare-event simulation for a class of problems where the target hitting sets of interest are defined via modern machine learning tools such as neural networks and random forests. We investigate an importance sampling scheme that integrates the dominating point machinery in large deviations and sequential mixed integer programming to locate the underlying dominating points. We provide efficiency guarantees and numerical demonstration of our approach. In Chapter 3, we propose a new efficiency criterion for importance sampling, which we call probabilistic efficiency. Conventionally, an estimator is regarded as efficient if its relative error is sufficiently controlled. It is widely known that when a rare-event set contains multiple "important regions" encoded by the dominating points, importance sampling needs to account for all of them via mixing to achieve efficiency. We argue that the traditional analysis recipe could suffer from intrinsic looseness by using relative error as an efficiency criterion. Thus, we propose the new efficiency notion to tighten this gap. In particular, we show that under the standard Gartner-Ellis large deviations regime, an importance sampling that uses only the most significant dominating points is sufficient to attain this efficiency notion. In Chapter 4, we consider the estimation of rare-event probabilities using sample proportions output by crude Monte Carlo. Due to the recent surge of sophisticated rare-event problems, efficiency-guaranteed variance reduction may face implementation challenges, which motivate one to look at naive estimators. In this chapter we construct confidence intervals for the target probability using this naive estimator from various techniques, and then analyze their validity as well as tightness respectively quantified by the coverage probability and relative half-width. In Chapter 5, we propose the use of extreme value analysis, in particular the peak-over-threshold method which is popularly employed for extremal estimation of real datasets, in the simulation setting. More specifically, we view crude Monte Carlo samples as data to fit on a generalized Pareto distribution. We test this idea on several numerical examples. The results show that in the absence of efficient variance reduction schemes, it appears to offer potential benefits to enhance crude Monte Carlo estimates. In Chapter 6, we investigate a framework to develop calibration schemes in parametric settings, which satisfies rigorous frequentist statistical guarantees via a basic notion that we call eligibility set designed to bypass non-identifiability via a set-based estimation. We investigate a feature extraction-then-aggregation approach to construct these sets that target at multivariate outputs. We demonstrate our methodology on several numerical examples, including an application to calibration of a limit order book market simulator. In Chapter 7, we study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge, a model calibration problem under both aleatory and epistemic uncertainties. Our methodology is based on an integration of distributionally robust optimization and importance sampling. The main computation machinery in this integrated methodology amounts to solving sampled linear programs. We present theoretical statistical guarantees of our approach via connections to nonparametric hypothesis testing, and numerical performances including parameter calibration and downstream decision and risk evaluation tasks

Representational Capabilities of Feed-forward and Sequential Neural Architectures

Despite the widespread empirical success of deep neural networks over the past decade, a comprehensive understanding of their mathematical properties remains elusive, which limits the abilities of practitioners to train neural networks in a principled manner. This dissertation provides a representational characterization of a variety of neural network architectures, including fully-connected feed-forward networks and sequential models like transformers. The representational capabilities of neural networks are most famously characterized by the universal approximation theorem, which states that sufficiently large neural networks can closely approximate any well-behaved target function. However, the universal approximation theorem applies exclusively to two-layer neural networks of unbounded size and fails to capture the comparative strengths and weaknesses of different architectures. The thesis addresses these limitations by quantifying the representational consequences of random features, weight regularization, and model depth on feed-forward architectures. It further investigates and contrasts the expressive powers of transformers and other sequential neural architectures. Taken together, these results apply a wide range of theoretical tools—including approximation theory, discrete dynamical systems, and communication complexity—to prove rigorous separations between different neural architectures and scaling regimes