Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse

A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the evaluation of the function is expensive, the task is computationally challenging because the standard approach is based on a Monte Carlo method which converges slowly. We present a different approach that exploits the pattern correlation, if present, between the diagonal of the inverse of the matrix and the diagonal of some approximate inverse that can be computed inexpensively. We leverage various sampling and fitting techniques to fit the diagonal of the approximation to the diagonal of the inverse. Depending on the quality of the approximate inverse, our method may serve as a standalone kernel for providing a fast trace estimate with a small number of samples. Furthermore, the method can be used as a variance reduction method for Monte Carlo in some cases. This is decided dynamically by our algorithm. An extensive set of experiments with various technique combinations on several matrices from some real applications demonstrate the potential of our method. (C) 2016 Published by Elsevier Inc

Roughness of molecular property landscapes and its impact on modellability

In molecular discovery and drug design, structure-property relationships and activity landscapes are often qualitatively or quantitatively analyzed to guide the navigation of chemical space. The roughness (or smoothness) of these molecular property landscapes is one of their most studied geometric attributes, as it can characterize the presence of activity cliffs, with rougher landscapes generally expected to pose tougher optimization challenges. Here, we introduce a general, quantitative measure for describing the roughness of molecular property landscapes. The proposed roughness index (ROGI) is loosely inspired by the concept of fractal dimension and strongly correlates with the out-of-sample error achieved by machine learning models on numerous regression tasks.Comment: 17 pages, 6 figures, 2 tables (SI with 17 pages, 16 figures

Digital watermarking in medical images

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 05/12/2005.This thesis addresses authenticity and integrity of medical images using watermarking. Hospital Information Systems (HIS), Radiology Information Systems (RIS) and Picture Archiving and Communication Systems (P ACS) now form the information infrastructure for today's healthcare as these provide new ways to store, access and distribute medical data that also involve some security risk. Watermarking can be seen as an additional tool for security measures. As the medical tradition is very strict with the quality of biomedical images, the watermarking method must be reversible or if not, region of Interest (ROI) needs to be defined and left intact. Watermarking should also serve as an integrity control and should be able to authenticate the medical image. Three watermarking techniques were proposed. First, Strict Authentication Watermarking (SAW) embeds the digital signature of the image in the ROI and the image can be reverted back to its original value bit by bit if required. Second, Strict Authentication Watermarking with JPEG Compression (SAW-JPEG) uses the same principal as SAW, but is able to survive some degree of JPEG compression. Third, Authentication Watermarking with Tamper Detection and Recovery (AW-TDR) is able to localise tampering, whilst simultaneously reconstructing the original image

Digital watermarking in medical images

This thesis addresses authenticity and integrity of medical images using watermarking. Hospital Information Systems (HIS), Radiology Information Systems (RIS) and Picture Archiving and Communication Systems (P ACS) now form the information infrastructure for today's healthcare as these provide new ways to store, access and distribute medical data that also involve some security risk. Watermarking can be seen as an additional tool for security measures. As the medical tradition is very strict with the quality of biomedical images, the watermarking method must be reversible or if not, region of Interest (ROI) needs to be defined and left intact. Watermarking should also serve as an integrity control and should be able to authenticate the medical image. Three watermarking techniques were proposed. First, Strict Authentication Watermarking (SAW) embeds the digital signature of the image in the ROI and the image can be reverted back to its original value bit by bit if required. Second, Strict Authentication Watermarking with JPEG Compression (SAW-JPEG) uses the same principal as SAW, but is able to survive some degree of JPEG compression. Third, Authentication Watermarking with Tamper Detection and Recovery (AW-TDR) is able to localise tampering, whilst simultaneously reconstructing the original image.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Fair learning : une approche basée sur le transport optimale

L'objectif de cette thèse est double. D'une part, les méthodes de transport optimal sont étudiées pour l'inférence statistique. D'autre part, le récent problème de l'apprentissage équitable est considéré avec des contributions à travers le prisme de la théorie du transport optimal. L'utilisation généralisée des applications basées sur les modèles d'apprentissage automatique dans la vie quotidienne et le monde professionnel s'est accompagnée de préoccupations quant aux questions éthiques qui peuvent découler de l'adoption de ces technologies. Dans la première partie de cette thèse, nous motivons le problème de l'équité en présentant quelques résultats statistiques complets en étudiant le critère statistical parity par l'analyse de l'indice disparate impact sur l'ensemble de données réel Adult income. Il est important de noter que nous montrons qu'il peut être particulièrement difficile de créer des modèles d'apprentissage machine équitables, surtout lorsque les observations de formation contiennent des biais. Ensuite, une revue des mathématiques pour l'équité dans l'apprentissage machine est donné dans un cadre général, avec également quelques contributions nouvelles dans l'analyse du prix pour l'équité dans la régression et la classification. Dans cette dernière, nous terminons cette première partie en reformulant les liens entre l'équité et la prévisibilité en termes de mesures de probabilité. Nous analysons les méthodes de réparation basées sur le transport de distributions conditionnelles vers le barycentre de Wasserstein. Enfin, nous proposons le random repair qui permet de trouver un compromis entre une perte minimale d'information et un certain degré d'équité. La deuxième partie est dédiée à la théorie asymptotique du coût de transport empirique. Nous fournissons un Théorème de Limite Centrale pour la distance de Monge-Kantorovich entre deux distributions empiriques de tailles différentes n et m, Wp(Pn,Qm), p > = 1, avec observations sur R. Dans le cas de p > 1, nos hypothèses sont nettes en termes de moments et de régularité. Nous prouvons des résultats portant sur le choix des constantes de centrage. Nous fournissons une estimation consistente de la variance asymptotique qui permet de construire tests à deux échantillons et des intervalles de confiance pour certifier la similarité entre deux distributions. Ceux-ci sont ensuite utilisés pour évaluer un nouveau critère d'équité de l'ensemble des données dans la classification. En outre, nous fournissons un principe de déviations modérées pour le coût de transport empirique dans la dimension générale. Enfin, les barycentres de Wasserstein et le critère de variance en termes de la distance de Wasserstein sont utilisés dans de nombreux problèmes pour analyser l'homogénéité des ensembles de distributions et les relations structurelles entre les observations. Nous proposons l'estimation des quantiles du processus empirique de la variation de Wasserstein en utilisant une procédure bootstrap. Ensuite, nous utilisons ces résultats pour l'inférence statistique sur un modèle d'enregistrement de distribution avec des fonctions de déformation générale. Les tests sont basés sur la variance des distributions par rapport à leurs barycentres de Wasserstein pour lesquels nous prouvons les théorèmes de limite centrale, y compris les versions bootstrap.The aim of this thesis is two-fold. On the one hand, optimal transportation methods are studied for statistical inference purposes. On the other hand, the recent problem of fair learning is addressed through the prism of optimal transport theory. The generalization of applications based on machine learning models in the everyday life and the professional world has been accompanied by concerns about the ethical issues that may arise from the adoption of these technologies. In the first part of the thesis, we motivate the fairness problem by presenting some comprehensive results from the study of the statistical parity criterion through the analysis of the disparate impact index on the real and well-known Adult Income dataset. Importantly, we show that trying to make fair machine learning models may be a particularly challenging task, especially when the training observations contain bias. Then a review of Mathematics for fairness in machine learning is given in a general setting, with some novel contributions in the analysis of the price for fairness in regression and classification. In the latter, we finish this first part by recasting the links between fairness and predictability in terms of probability metrics. We analyze repair methods based on mapping conditional distributions to the Wasserstein barycenter. Finally, we propose a random repair which yields a tradeoff between minimal information loss and a certain amount of fairness. The second part is devoted to the asymptotic theory of the empirical transportation cost. We provide a Central Limit Theorem for the Monge-Kantorovich distance between two empirical distributions with different sizes n and m, Wp(Pn,Qm), p > = 1, for observations on R. In the case p > 1 our assumptions are sharp in terms of moments and smoothness. We prove results dealing with the choice of centering constants. We provide a consistent estimate of the asymptotic variance which enables to build two sample tests and confidence intervals to certify the similarity between two distributions. These are then used to assess a new criterion of data set fairness in classification. Additionally, we provide a moderate deviation principle for the empirical transportation cost in general dimension. Finally, Wasserstein barycenters and variance-like criterion using Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the estimation of the quantiles of the empirical process of the Wasserstein's variation using a bootstrap procedure. Then we use these results for statistical inference on a distribution registration model for general deformation functions. The tests are based on the variance of the distributions with respect to their Wasserstein's barycenters for which we prove central limit theorems, including bootstrap versions

Routine procedure for the assessment of rail-induced vibration

Railway induced ground-borne vibration is among the most common and widespread sources of perceptible environmental vibration, adversely impacting on human activity and the operation of sensitive equipment. The rising demand for building new railway lines or upgrading existing lines in order to meet increasing traffic flows has furthered the need for adequate vibration assessment tools during scheme planning and design. In recent years many studies of rail and ground dynamics have produced many vibration prediction techniques which have given rise to a variety of procedures for estimating rail-induced vibration on adjacent buildings. Each method shows potential for application at different levels of complexity and at different stages of a scheme. However, for the majority of the procedures significant challenges arise in obtaining the required input data, which can compromise their routine use in Environmental Impact Assessment (EIA). Moreover, as the majority of prediction procedures do not provide levels of uncertainty (i.e. expected spread of data), little is available on their effectiveness. Additionally, some procedures are restricted in that they require specific modelling approaches or proprietary software. Therefore, from an industrial point of view there is a need for a robust and flexible rail-induced vibration EIA procedure that can be routinely used with a degree of confidence. Based on an existing framework for assessing rail-induced vibration offered by the USA department of transportation (FTA) this project investigates, revises and establishes an empirical procedure capable of predicting rail-induced vibration in nearby buildings that can be routinely applied by the sponsoring company. Special attention is given to the degree of variability inherent to rail-induced vibration prediction, bringing forward the degrees of uncertainty, at all levels (i.e. measuring, analysis and scenario characterisation) that may impact on the procedure performance. The research shows a diminishing confidence when predicting rail-induced absolute vibration levels. It was found that ground-to-transducer coupling method, which is a critical step for acquiring data for characterising the ground, can impact on the results by as much as 10 dB. The ground decay rate, when derived through transfer functions, also showed to vary significantly in accordance to the assessment approach. Here it is shown the extent to which track conditions, which are difficult to account for, can affect predictions; variability in vibration levels of up to 10 dB, at some frequency bands, was found to occur simply due to track issues. The thesis offers general curves that represent modern UK buildings; however, a 15 dB variation should be expected. For urban areas, where the ground structure is significantly heterogeneous, the thesis proposes an empirical modelling technique capable of shortening the FTA procedure, whilst maintain the uncertainty levels within limits. Based on the finding and acknowledging the inherent degree of variability mentioned above, this study proposes a resilient empirical vibration analysis model, where its flexibility is established by balancing the significance of each modelling component with the uncertainty levels likely to arise due to randomness in the system

Biometrics & [and] Security:Combining Fingerprints, Smart Cards and Cryptography

Since the beginning of this brand new century, and especially since the 2001 Sept 11 events in the U.S, several biometric technologies are considered mature enough to be a new tool for security. Generally associated to a personal device for privacy protection, biometric references are stored in secured electronic devices such as smart cards, and systems are using cryptographic tools to communicate with the smart card and securely exchange biometric data. After a general introduction about biometrics, smart cards and cryptography, a second part will introduce our work with fake finger attacks on fingerprint sensors and tests done with different materials. The third part will present our approach for a lightweight fingerprint recognition algorithm for smart cards. The fourth part will detail security protocols used in different applications such as Personal Identity Verification cards. We will discuss our implementation such as the one we developed for the NIST to be used in PIV smart cards. Finally, a fifth part will address Cryptography-Biometrics interaction. We will highlight the antagonism between Cryptography – determinism, stable data – and Biometrics – statistical, error-prone –. Then we will present our application of challenge-response protocol to biometric data for easing the fingerprint recognition process

The image of the Incarnation as motif for development practice in West Java, Indonesia

Beginning with the proposition that the incarnation is not simply theologically descriptive but also strategically prescriptive, this thesis proposes utilising this motif in order to analyse and critique participatory development practice as it is undertaken today, both by Christians as well as those who are not. After first illustrating the value of incarnational involvement by presenting the results of field research undertaken amongst a particular community of the Sundanese people residing in a specific hamlet in the city of Tasikmalaya, West Java, Indonesia, a template comprised of six distinguishing marks and three overarching characteristics is then developed in order to appraise the Incarnational motif in terms of its tangible applicability. Thereafter, four disciplines are examined and appraised in terms of their incarnational, participatory value-the discipline of development studies (focussing on the work of Robert Chambers), the discipline of anthropology (focussing on the work of Clifford Geertz), the logic of Critical Theory (focussing on the work of Jürgen Habermas) and the thought of a leading Indonesian Islamic theorist, Abdurrahman Wahid. Key, buttressing points in each of these are selected as sources of validation for the incarational motif. Furthermore, the image of participation found in each is critiqued by comparing them to the six distinguishing marks and the three overarching characteristics. Finally, a tangible example of incarnational participation previously undertaken in West Java, Indonesia by the author is offered as a picture of how the incarnational thesis might be utilised in social practice. Both the complexities encountered as well as promises experienced are highlighted so as to present a realistic and useful model

CORPORATE SOCIAL RESPONSIBILITY IN ROMANIA

The purpose of this paper is to identify the main opportunities and limitations of corporate social responsibility (CSR). The survey was defined with the aim to involve the highest possible number of relevant CSR topics and give the issue a more wholesome perspective. It provides a basis for further comprehension and deeper analyses of specific CSR areas. The conditions determining the success of CSR in Romania have been defined in the paper on the basis of the previously cumulative knowledge as well as the results of various researches. This paper provides knowledge which may be useful in the programs promoting CSR.Corporate social responsibility, Supportive policies, Romania