We propose a parametric version of Independent Component Analysis (ICA) via Copulas - families of multivariate distributions that join univariate margins to multivariate distributions. Our procedure exploits the role for copula models in information theory and in measures of association, specifically: the use of copulae densities as parametric mutual information, and as measures of association on the rank statistics.The copula approach offers a unified view of component analysis procedures, in particular, by parameterizing multivariate dependence. ICA then, via the copula, is a generalization of Principal Component Analysis (PCA) - where the copula model may be non-Gaussian. Generally, the goal is to orthogonalize a measure of multivariate dispersion, yielding an orthogonal basis for a multivariate data set. The flexibility of the copula approach allows for parameterizations of non-gaussian, non-monotone dependence. Additionally, we note a possible use for the Copula approach in generalized component extraction procedures (such as Canonical Correlation Analysis). We apply one version of the CICA approach to the 2002 Environmental Sustainability Index (ESI), an aggregation of 64 environmental variables on 142 countries.

Independent component analysis (ICA) is a modern factor analysis tool de- veloped in the last two decades. Given p-dimensional data, we search for that linear combination of data which creates (almost) independent components. Here copulae are used to model the p-dimensional data and then independent components are found by optimizing the copula parameters. Based on this idea, we propose the COPICA method for searching independent components. We illustrate this method using several blind source separation examples, which are mathematically equivalent to ICA problems. Finally performances of our method and FastICA are compared to explore the advantages of this method.

This book constitutes the refereed proceedings of the 7th International Conference on Independent Component Analysis and Blind Source Separation, ICA 2007, held in London, UK, in September 2007. It covers algorithms and architectures, applications, medical applications, speech and signal processing, theory, and visual and sensory processing.

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.

This book is a practical guide for individuals interested in exploring and implementing smart home applications using Python. Comprising six chapters enriched with hands-on codes, it seamlessly navigates from foundational concepts to cutting-edge technologies, balancing theoretical insights and practical coding experiences. In short, it is a gateway to the dynamic intersection of Python programming, smart home technology, and advanced machine learning applications, making it an invaluable resource for those eager to explore this rapidly growing field. Key Features: Throughout the book, practicality takes precedence, with hands-on coding examples accompanying each concept to facilitate an interactive learning journey Striking a harmonious balance between theoretical foundations and practical coding, the book caters to a diverse audience, including smart home enthusiasts and researchers The content prioritizes real-world applications, ensuring readers can immediately apply the knowledge gained to enhance smart home functionalities Covering Python basics, feature extraction, deep learning, and XAI, the book provides a comprehensive guide, offering an overall understanding of smart home applications

User care at home is a matter of great concern since unforeseen circumstances might occur that affect people's well-being. Technologies that assist people in independent living are essential for enhancing care in a cost-effective and reliable manner. Assisted care applications often demand real-time observation of the environment and the resident’s activities using an event-driven system. As an emerging area of research and development, it is necessary to explore the approaches of the user care system in the literature to identify current practices for future research directions. Therefore, this book is aimed at a comprehensive review of data sources (e.g., sensors) with machine learning for various smart user care systems. To encourage the readers in the field, insights of practical essence of different machine learning algorithms with sensor data (e.g., publicly available datasets) are also discussed. Some code segments are also included to motivate the researchers of the related fields to practically implement the features and machine learning techniques. It is an effort to obtain knowledge of different types of sensor-based user monitoring technologies in-home environments. With the aim of adopting these technologies, research works, and their outcomes are reported. Besides, up to date references are included for the user monitoring technologies with the aim of facilitating independent living. Research that is related to the use of user monitoring technologies in assisted living is very widespread, but it is still consists mostly of limited-scale studies. Hence, user monitoring technology is a very promising field, especially for long-term care. However, monitoring of the users for smart assisted technologies should be taken to the next level with more detailed studies that evaluate and demonstrate their potential to contribute to prolonging the independent living of people. The target of this book is to contribute towards that direction.

The latest tools and techniques for pricing and risk management This book introduces readers to the use of copula functions to represent the dynamics of financial assets and risk factors, integrated temporal and cross-section applications. The first part of the book will briefly introduce the standard the theory of copula functions, before examining the link between copulas and Markov processes. It will then introduce new techniques to design Markov processes that are suited to represent the dynamics of market risk factors and their co-movement, providing techniques to both estimate and simulate such dynamics. The second part of the book will show readers how to apply these methods to the evaluation of pricing of multivariate derivative contracts in the equity and credit markets. It will then move on to explore the applications of joint temporal and cross-section aggregation to the problem of risk integration.