155 research outputs found
Bayesian Learning for Neural Networks: an algorithmic survey
The last decade witnessed a growing interest in Bayesian learning. Yet, the
technicality of the topic and the multitude of ingredients involved therein,
besides the complexity of turning theory into practical implementations, limit
the use of the Bayesian learning paradigm, preventing its widespread adoption
across different fields and applications. This self-contained survey engages
and introduces readers to the principles and algorithms of Bayesian Learning
for Neural Networks. It provides an introduction to the topic from an
accessible, practical-algorithmic perspective. Upon providing a general
introduction to Bayesian Neural Networks, we discuss and present both standard
and recent approaches for Bayesian inference, with an emphasis on solutions
relying on Variational Inference and the use of Natural gradients. We also
discuss the use of manifold optimization as a state-of-the-art approach to
Bayesian learning. We examine the characteristic properties of all the
discussed methods, and provide pseudo-codes for their implementation, paying
attention to practical aspects, such as the computation of the gradient
Information Geometry
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience
The Statistical Foundations of Entropy
In the last two decades, the understanding of complex dynamical systems underwent important conceptual shifts. The catalyst was the infusion of new ideas from the theory of critical phenomena (scaling laws, renormalization group, etc.), (multi)fractals and trees, random matrix theory, network theory, and non-Shannonian information theory. The usual Boltzmann–Gibbs statistics were proven to be grossly inadequate in this context. While successful in describing stationary systems characterized by ergodicity or metric transitivity, Boltzmann–Gibbs statistics fail to reproduce the complex statistical behavior of many real-world systems in biology, astrophysics, geology, and the economic and social sciences.The aim of this Special Issue was to extend the state of the art by original contributions that could contribute to an ongoing discussion on the statistical foundations of entropy, with a particular emphasis on non-conventional entropies that go significantly beyond Boltzmann, Gibbs, and Shannon paradigms. The accepted contributions addressed various aspects including information theoretic, thermodynamic and quantum aspects of complex systems and found several important applications of generalized entropies in various systems
Statistical Foundations of Actuarial Learning and its Applications
This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus
Information geometry
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience
High-dimensional variable selection for GLMs and survival models
De focus van het proefschrift is op de statistische numerieke benaderingen om geringe genoomgegevens te passen met GLM- en overlevingsgegevens. Het proefschrift beschrijft de selectie van verklarende variabelen die een univariate uitkomst kunnen beïnvloeden. Het resultaat heeft een kansverdeling die valt in de klasse van de exponentiële dispersie familie. De aanpak die wordt onderzocht is de regressie van de differentiaalgeometrie van de minimale hoek (dgLARS) die is ontwikkeld voor genormaliseerde lineaire modellen. De dgLARS-aanpak wordt vergeleken met alternatieve methoden voor variabele selectie in algemene lineaire modellen. De numerieke procedures van dgLARS zijn verbeterd voor de algemene instelling, en wordt aangeduid als de uitgebreide dgLARS. Bovendien onderzoeken we hoe goed de dispersieparameter van de familie van exponentiële verdelingen kan worden geschat. In de tussentijd richten we ons op overlevingsgegevens en de genomische invloed, met behulp van de relatieve risicofunctie. In alle hoofdstukken blijkt dat de verbeterde en ontwikkelde numerieke procedures snel en accuraat zijn bij het schatten van parameters. Uiteindelijk wordt een volledige beschrijving van het pakket code{R} dat is ontwikkeld om alle analyses te doen, gepresenteerd
Statistical Foundations of Actuarial Learning and its Applications
This open access book discusses the statistical modeling of insurance problems, a process which comprises data collection, data analysis and statistical model building to forecast insured events that may happen in the future. It presents the mathematical foundations behind these fundamental statistical concepts and how they can be applied in daily actuarial practice. Statistical modeling has a wide range of applications, and, depending on the application, the theoretical aspects may be weighted differently: here the main focus is on prediction rather than explanation. Starting with a presentation of state-of-the-art actuarial models, such as generalized linear models, the book then dives into modern machine learning tools such as neural networks and text recognition to improve predictive modeling with complex features. Providing practitioners with detailed guidance on how to apply machine learning methods to real-world data sets, and how to interpret the results without losing sight of the mathematical assumptions on which these methods are based, the book can serve as a modern basis for an actuarial education syllabus
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