‘Mathematical Foundations of Machine Learning’ delves into the fundamental mathematical concepts that underpin the field of machine learning, providing a comprehensive exploration of the mathematical principles behind algorithms and models. Whether you’re a data scientist, researcher, or enthusiast seeking a deeper understanding of the mathematical intricacies driving machine learning, this book equips you with the knowledge and insights necessary to navigate the complex landscape of modern AI.
- Core Mathematical Concepts: Explore the essential mathematical foundations essential for understanding machine learning, including linear algebra, calculus, probability theory, and optimization. Gain a solid grasp of these fundamental concepts and their applications in designing, analyzing, and interpreting machine learning algorithms and models.
- Rigorous Theoretical Framework: Delve into the theoretical underpinnings of machine learning, uncovering the mathematical frameworks that govern the behavior and performance of algorithms. From convex optimization and kernel methods to spectral graph theory and manifold learning, this book provides a rigorous treatment of key topics essential for mastering machine learning theory.
- Algorithmic Insights: Gain insights into the mathematical principles behind popular machine learning algorithms and techniques, such as linear regression, support vector machines, neural networks, and deep learning. Understand how mathematical formulations drive algorithm design, parameter optimization, and model evaluation, enabling you to apply mathematical reasoning to solve real-world problems effectively.
- Advanced Topics: Explore advanced mathematical concepts and techniques shaping the cutting edge of machine learning research, including Bayesian inference, reinforcement learning, and probabilistic graphical models. Dive into the mathematical intricacies of these advanced topics and learn how to leverage them to tackle complex challenges and push the boundaries of AI.
- Practical Applications: Bridge the gap between theory and practice by applying mathematical principles to real-world machine learning problems and projects. With practical examples, code snippets, and exercises, this book equips you with the skills and confidence to implement mathematical concepts in your own machine learning projects and experiments.
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Cuprins
Mathematical Foundations of Machine Learning v
Introduction vi
Chapter 1: Introduction to Machine Learning 1
Types of Machine Learning 3
Unsupervised Machine Learning 5
Semi-Supervised Machine Learning 6
Reinforcement Machine Learning 7
Importance of Machine Learning 7
Core Concepts of Machine Learning 8
Representation 9
Evaluation 11
Optimization 11
Statistical Learning Framework 11
Prediction and Inference 12
Parametric and Non-parametric Techniques 13
Predictions Accuracy and Model Interpretability 15
Assessing Model Accuracy 17
Chapter 2: Machine Learning Algorithms 19
Regression 20
Types of ‘Naïve Bayes classifier’ 31
Applications of ‘Naïve Bayes’ 32
Chapter 3: Neural Network Learning Models 33
Hyperparameter of ANN 35
Unsupervised Training 43
Candidate Model Evaluation 44
Model Deployment 45
Model Scoring 45
Applications of Neural Network Models 47
Chapter 4: Learning Through Uniform Convergence 50
Impact of Uniform Convergence on Learnability 54
Learnability without Uniform Convergence 56
Chapter 5: Data Science Lifecycle and Technologies 61
Data Science Lifecycle 62
Stage I – Business Understanding 64
Stage II – Data Acquisition and Understanding 66
Stage III – Modeling 68
Importance of Data Science 70
Business Intelligence vs. Data Science 73
Conclusion 77
Despre autor
David Mackay is a renowned mathematician and computer scientist based in London. With a wealth of experience in both academia and industry, Mackay has been instrumental in advancing the field of machine learning. He has authored numerous research papers and books, making complex mathematical concepts accessible to a wide audience.
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