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Aldo Faisal, and Cheng Soon Ong builds a bridge between foundational math and practical machine learning. The text starts with mathematical foundations—linear algebra, analytic geometry, matrix decompositions, vector calculus, probability and distributions, and continuous optimization—then connects them to central machine learning problems. Key topics include model-data interaction, empirical risk minimization, parameter estimation, graphical models, linear regression, PCA, Gaussian mixture density estimation, and support vector machines, supported by exercises and further reading.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematics-for-machine-learning/319314/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematics-for-machine-learning/319314.png","ImageObject",300,407,{"name":92,"@type":93},"Riley","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":36},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What prerequisite knowledge does the book emphasize for understanding machine learning?","Question",{"text":112,"@type":113},"The book emphasizes prerequisite programming/data analysis tools, large-scale computation frameworks, and mathematics and statistics, explaining how machine learning builds on them.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What core mathematical topics are covered in Part I?",{"text":117,"@type":113},"Part I covers linear algebra, analytic geometry, matrix decompositions, vector calculus, probability and distributions, and continuous optimization, each with subtopics and exercises.",{"name":119,"@type":110,"acceptedAnswer":120},"Which central machine learning problems are addressed in Part II?",{"text":121,"@type":113},"Part II connects the foundations to problems such as data-model learning, empirical risk minimization and parameter estimation, linear regression, PCA-based dimensionality reduction, Gaussian mixture density estimation, and classification with support vector machines.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},319314,1790376626,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":36,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},1374391975076,"https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051","MATHEMATICS FOR MACHINE LEARNING  \nMarc Peter Deisenroth  \nA. Aldo Faisal Cheng Soon Ong  \nContents  \nForeword 1  \nPart I Mathematical Foundations 9  \n1 Introduction and Motivation 11  \n1.1 Finding Words for Intuitions 12  \n1.2 Two Ways to Read This Book 13  \n1.3 Exercises and Feedback 16  \n2 Linear Algebra 17  \n2.1 Systems of Linear Equations 19  \n2.2 Matrices 22  \n2.3 Solving Systems of Linear Equations 27  \n2.4 Vector Spaces 35  \n2.5 Linear Independence 40  \n2.6 Basis and Rank 44  \n2.7 Linear Mappings 48  \n2.8 Affine Spaces 61  \n2.9 Further Reading 63  \nExercises 64  \n3 Analytic Geometry 70  \n3.1 Norms 71  \n3.2 Inner Products 72  \n3.3 Lengths and Distances 75  \n3.4 Angles and Orthogonality 76  \n3.5 Orthonormal Basis 78  \n3.6 Orthogonal Complement 79  \n3.7 Inner Product of Functions 80  \n3.8 Orthogonal Projections 81  \n3.9 Rotations 91  \n3.10 Further Reading 94  \nExercises 96  \n4 Matrix Decompositions 98  \n4.1 Determinant and Trace 99  \ni  \nThis material is published by Cambridge University Press as Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong (2020) . This version is free to view and download for personal use only. Not for re-distribution, re-sale, or use in derivative works.©by M. P. Deisenroth, A. A. Faisal, and C. S. Ong, 2024. [https://mml-book.com](https://mml-book.com).  \nii Contents  \n4.2 Eigenvalues and Eigenvectors 105  \n4.3 Cholesky Decomposition 114  \n4.4 Eigendecomposition and Diagonalization 115  \n4.5 Singular Value Decomposition 119  \n4.6 Matrix Approximation 129  \n4.7 Matrix Phylogeny 134  \n4.8 Further Reading 135  \nExercises 137  \n5 Vector Calculus 139  \n5.1 Differentiation of Univariate Functions 141  \n5.2 Partial Differentiation and Gradients 146  \n5.3 Gradients of Vector-Valued Functions 149  \n5.4 Gradients of Matrices 155  \n5.5 Useful Identities for Computing Gradients 158  \n5.6 Backpropagation and Automatic Differentiation 159  \n5.7 Higher-Order Derivatives 164  \n5.8 Linearization and Multivariate Taylor Series 165  \n5.9 Further Reading 170  \nExercises 170  \n6 Probability and Distributions 172  \n6.1 Construction of a Probability Space 172  \n6.2 Discrete and Continuous Probabilities 178  \n6.3 Sum Rule, Product Rule, and Bayes’ Theorem 183  \n6.4 Summary Statistics and Independence 186  \n6.5 Gaussian Distribution 197  \n6.6 Conjugacy and the Exponential Family 205  \n6.7 Change of Variables/Inverse Transform 214  \n6.8 Further Reading 221  \nExercises 222  \n7 Continuous Optimization 225  \n7.1 Optimization Using Gradient Descent 227  \n7.2 Constrained Optimization and Lagrange Multipliers 233  \n7.3 Convex Optimization 236  \n7.4 Further Reading 246  \nExercises 247  \nPart II Central Machine Learning Problems 249  \n8 When Models Meet Data 251  \n8.1 Data, Models, and Learning 251  \n8.2 Empirical Risk Minimization 258  \n8.3 Parameter Estimation 265  \n8.4 Probabilistic Modeling and Inference 272  \n8.5 Directed Graphical Models 278  \nDraft (2024-01-15) of“Mathematics for Machine Learning”. Feedback: [https://mml-book.com](https://mml-book.com).  \nContents iii  \n8.6 Model Selection 283  \n9 Linear Regression 289  \n9.1 Problem Formulation 291  \n9.2 Parameter Estimation 292  \n9.3 Bayesian Linear Regression 303  \n9.4 Maximum Likelihood as Orthogonal Projection 313  \n9.5 Further Reading 315  \n10 Dimensionality Reduction with Principal Component Analysis 317  \n10.1 Problem Setting 318  \n10.2 Maximum Variance Perspective 320  \n10.3 Projection Perspective 325  \n10.4 Eigenvector Computation and Low-Rank Approximations 333  \n10.5 PCA in High Dimensions 335  \n10.6 Key Steps of PCA in Practice 336  \n10.7 Latent Variable Perspective 339  \n10.8 Further Reading 343  \n11 Density Estimation with Gaussian Mixture Models 348  \n11.1 Gaussian Mixture Model 349  \n11.2 Parameter Learning via Maximum Likelihood 350  \n11.3 EM Algorithm 360  \n11.4 Latent-Variable Perspective 363  \n11.5 Further Reading 368  \n12 Classification with Support Vector Machines 370  \n12.1 Separating Hyperplanes 372  \n12.2","cbCaiju25opLDqOh","https://ap.wps.com/l/cbCaiju25opLDqOh","pdf",17565898,417,"English","# Foreword\n# Part I Mathematical Foundations\n## Introduction and Motivation\n## Linear Algebra\n## Analytic Geometry\n## Matrix Decompositions\n## Vector Calculus\n## Probability and Distributions\n## Continuous Optimization\n# Part II Central Machine Learning Problems\n## When Models Meet Data\n## Linear Regression\n## Dimensionality Reduction with Principal Component Analysis\n## Density Estimation with Gaussian Mixture Models\n## Classification with Support Vector Machines","[{\"question\":\"What prerequisite knowledge does the book emphasize for understanding machine learning?\",\"answer\":\"The book emphasizes prerequisite programming/data analysis tools, large-scale computation frameworks, and mathematics and statistics, explaining how machine learning builds on them.\"},{\"question\":\"What core mathematical topics are covered in Part I?\",\"answer\":\"Part I covers linear algebra, analytic geometry, matrix decompositions, vector calculus, probability and distributions, and continuous optimization, each with subtopics and exercises.\"},{\"question\":\"Which central machine learning problems are addressed in Part II?\",\"answer\":\"Part II connects the foundations to problems such as data-model learning, empirical risk minimization and parameter estimation, linear regression, PCA-based dimensionality reduction, Gaussian mixture density estimation, and classification with support vector machines.\"}]","Mathematics for Machine Learning | PDF",1789942667,1051]