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Variational Bayesian learning is one of the most popular methods in machine learning. Designed for researchers and graduate students in machine learning, this book summarizes recent developments in the non-asymptotic and asymptotic theory of variational Bayesian learning and suggests how this theory can be applied in practice. The authors begin by developing a basic framework with a focus on conjugacy, which enables the reader to derive tractable algorithms. Next, it summarizes non-asymptotic theory, which, although limited in application to bilinear models, precisely describes the behavior of the variational Bayesian solution and reveals its sparsity inducing mechanism. Finally, the text summarizes asymptotic theory, which reveals phase transition phenomena depending on the prior setting, thus providing suggestions on how to set hyperparameters for particular purposes. Detailed derivations allow readers to follow along without prior knowledge of the mathematical techniques specific to Bayesian learning.

Bayesian field theory. --- Probabilities.

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Water quality --- Water quality --- Bayesian field theory.

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This book is an introduction to the mathematical analysis of Bayesian decision-making when the state of the problem is unknown but further data about it can be obtained. The objective of such analysis is to determine the optimal decision or solution that is logically consistent with the preferences of the decision-maker, that can be analyzed using numerical utilities or criteria with the probabilities assigned to the possible state of the problem, such that these probabilities are updated by gathering new information.

Bayesian field theory. --- Field theory, Bayesian --- Statistical physics --- Physical Sciences --- Engineering and Technology --- Mathematics --- Applied Mathematics

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Develop Bayesian Deep Learning models to help make your own applications more robust. Key Features Gain insights into the limitations of typical neural networks Acquire the skill to cultivate neural networks capable of estimating uncertainty Discover how to leverage uncertainty to develop more robust machine learning systems Book Description Deep learning is revolutionizing our lives, impacting content recommendations and playing a key role in mission- and safety-critical applications. Yet, typical deep learning methods lack awareness about uncertainty. Bayesian deep learning offers solutions based on approximate Bayesian inference, enhancing the robustness of deep learning systems by indicating how confident they are in their predictions. This book will guide you in incorporating model predictions within your applications with care. Starting with an introduction to the rapidly growing field of uncertainty-aware deep learning, you'll discover the importance of uncertainty estimation in robust machine learning systems. You'll then explore a variety of popular Bayesian deep learning methods and understand how to implement them through practical Python examples covering a range of application scenarios. By the end of this book, you'll embrace the power of Bayesian deep learning and unlock a new level of confidence in your models for safer, more robust deep learning systems. What you will learn Discern the advantages and disadvantages of Bayesian inference and deep learning Become well-versed with the fundamentals of Bayesian Neural Networks Understand the differences between key BNN implementations and approximations Recognize the merits of probabilistic DNNs in production contexts Master the implementation of a variety of BDL methods in Python code Apply BDL methods to real-world problems Evaluate BDL methods and choose the most suitable approach for a given task Develop proficiency in dealing with unexpected data in deep learning applications Who this book is for This book will cater to researchers and developers looking for ways to develop more robust deep learning models through probabilistic deep learning. You're expected to have a solid understanding of the fundamentals of machine learning and probability, along with prior experience working with machine learning and deep learning models.

Deep learning (Machine learning) --- Neural networks (Computer science) --- Bayesian field theory. --- Mathematical models. --- Mathematical models.

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Measured by the accuracy of its predictions and the scope of its technological applications, quantum mechanics is one of the most successful theories in science—as well as one of the most misunderstood. The deeper meaning of quantum mechanics remains controversial almost a century after its invention. Providing a way past quantum theory’s paradoxes and puzzles, QBism offers a strikingly new interpretation that opens up for the nonspecialist reader the profound implications of quantum mechanics for how we understand and interact with the world. Short for Quantum Bayesianism, QBism adapts many of the conventional features of quantum mechanics in light of a revised understanding of probability. Bayesian probability, unlike the standard “frequentist probability,” is defined as a numerical measure of the degree of an observer’s belief that a future event will occur or that a particular proposition is true. Bayesianism’s advantages over frequentist probability are that it is applicable to singular events, its probability estimates can be updated based on acquisition of new information, and it can effortlessly include frequentist results. But perhaps most important, much of the weirdness associated with quantum theory—the idea that an atom can be in two places at once, or that signals can travel faster than the speed of light, or that Schrödinger’s cat can be simultaneously dead and alive—dissolves under the lens of QBism. Using straightforward language without equations, Hans Christian von Baeyer clarifies the meaning of quantum mechanics in a commonsense way that suggests a new approach to physics in general.

Quantum Bayesianism. --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Qbism --- Bayesian field theory --- Quantum theory