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Artículo: AMZ-B0DKD826QD
Measure Theory and Probability Spaces in Machine Learning With Python (Mastering Machine Learning)
Format:
Hardcover
Detalles del producto
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En stock
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0.73 kg
0.73 kg
Devolución
Si
Si
Condición
Nuevo
Nuevo
Producto de
Amazon
Amazon
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USA
USA
Sobre este producto
- Discover an illuminating journey through the profound world of measure theory and probability spaces, meticulously tailored for applications in machine learning. This comprehensive resource seamlessly blends theoretical foundations with practical implementations, featuring Python code examples that breathe life into advanced mathematical concepts.Key Features:Delve into the core principles of measure theory and its pivotal role in understanding probability spaces.Empower your machine learning models with sophisticated probability and statistics techniques grounded in rigorous mathematical foundations.Master practical applications with Python code, demonstrating each concept's real-world utility and significance.Ideal for data scientists, statisticians, researchers, and students eager to deepen their understanding of theoretical underpinnings in machine learning.Book Description:Immerse yourself in the foundational elements of measure theory and probability spaces, vital for navigating the complexities of modern machine learning. This insightful guide introduces key concepts such as sigma-algebras, measurable functions, and probability measures, while offering practical Python applications to bridge theory with practice. Traverse through a rich tapestry of topics, from Monte Carlo methods and Gaussian processes to reinforcement learning and stochastic calculus, and gain a solid footing in the mathematical structures that underpin data-driven decision-making.What You Will Learn:Understand the foundational building blocks of sigma-algebras and their critical role in measure theory.Explore the creation and application of measures and measurable functions in data analysis.Gain insight into advanced techniques for constructing measures, including Carathéodory's extension theorem.Discover the unique properties and construction of Lebesgue measure.Analyze Borel sets and their significance in probability spaces.Develop a thorough comprehension of probability spaces, encompassing sample spaces, events, and probability measures.Conceptualize random variables as measurable functions within probability theory.Master the expectation of random variables through integrals with respect to probability measures.Unveil the principles of conditional probability within the framework of measure theory.Define the independence of events and random variables using sigma-algebras and probability measures.Study various concepts of convergence, such as convergence in probability and almost sure convergence.Explore convergence in Lp spaces, essential for analyzing random variables.Dive into weak convergence and its application in probability measures.Learn about characteristic functions and their role in understanding distribution properties.Investigate the Law of Large Numbers and its implications for statistical reliability.Grasp the Central Limit Theorem's centrality in statistics and its impact on machine learning.Uncover the intriguing realm of martingales, their basic properties, and associated theorems like the Optional Stopping Theorem.Explore measure-preserving transformations and their applications in various fields.Delve into the concepts of ergodicity and ergodic theorems in dynamical systems.Gain insights into the applications of the Radon-Nikodym theorem in complex analyses.Comprehend the utility of Fubini’s theorem in product space integration.
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