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Foundations of Statistical Learning & Algorithms · LearnSpace
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Foundations of Statistical Learning & Algorithms

Курс от Northeastern University
Уровень не указан≈ 21.4 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course covers linear algebra, probability, and optimization. It begins with systems of equations, matrix operations, vector spaces, and eigenvalues. Advanced topics include Cholesky and singular value decomposition. Probability modules address Bayes' theorem, Gaussian distribution, and inference techniques. The course concludes with model selection methods and an introduction to optimization.

Навыки, которые вы освоите

Linear AlgebraBayesian StatisticsModel OptimizationProbabilityDimensionality ReductionApplied MathematicsMachine Learning AlgorithmsAlgebraModel EvaluationProbability DistributionProbability & StatisticsStatistical InferenceMachine LearningMachine Learning MethodsStatistical Machine LearningStatistical ModelingStatistical MethodsVerification And Validation

Программа курса

4 модулей · 72 учебных материалов

01Introduction to Linear Algebra and Vector Spaces29 материалов

Getting Started

Course IntroductionВидеоCourse OverviewЧтениеSyllabusЧтениеMeet Your InstructorВидео

Учитесь у экспертов

Rehab Ali

Преподаватель курса

Foundations of Statistical Learning & Algorithms
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Обучение на Coursera

≈ 21.4 ч

4 модулей

Язык: Английский

Субтитры: Узбекский, Казахский

Часть программы вашего университета
Meet Your Fellow LearnersОбсуждение
Academic IntegrityЧтение

Lesson 1: Introduction to Linear Algebra

Introduction to Machine LearningЧтениеIntroduction to Linear AlgebraЧтениеWhy Linear Algebra and Mathematics?ЧтениеNotationЧтение

Lesson 2: Systems of Linear Equations

Foundational Concepts of Systems of Linear EquationsЧтение[H5P] System of Linear EquationsВнешний инструментSolved Example and Recommended ResourcesЧтениеCheck Your Knowledge: System of Linear EquationsЗадание

Lesson 3: Matrices

Matrices and Matrix OperationsЧтениеMatricesВидеоHelpful Resources and Solved ExamplesЧтениеCheck Your Knowledge: MatricesЗадание

Lesson 4: Vector Spaces

Foundations of Vector Spaces: Operations and SubspacesЧтениеVector SpaceВидеоVector Space PropertiesЧтениеSubspaceЧтениеCheck Your Knowledge: Vector SpacesЗадание

Lesson 5: Orthogonal Complement and Projection

Introduction to Orthogonal ComplementЧтениеIntroduction to Orthogonal ProjectionsЧтениеImportance of ProjectionsЧтениеProjection Onto One-Dimensional Subspaces (Lines)ЧтениеProjection Onto General SubspacesЧтениеProjections Case StudyЧтение
02Linear Transformation and Matrix Decomposition 15 материалов

Linear Independence

Understanding Linear Independence in Vector SpacesЧтениеLinear Independence, Basis, and RankВнешний инструментLinear IndependenceЧтение

Linear Mapping

Exploring Transformations: Understanding Linear MappingsЧтениеLinear Mapping: Part 1ВидеоLinear Mapping: Part 2ВидеоLinear MappingЧтениеMatrix RepresentationЧтениеPractice Quiz: Linear MappingЗадание

Lesson 3: Eigenvalues and Eigenvectors

Introduction to Eigenvalues and Eigenvectors ЧтениеEigenvectors and Eigenvalues: Examples and ApplicationsЧтение

Lesson 4: Cholesky Decomposition

Cholesky DecompositionЧтениеSolved ExamplesЧтение

Lesson 5: Singular Value Decomposition

Introduction to Singular Value Decomposition (SVD)ЧтениеDerivation of Singular Value Decomposition (SVD) from Eigenvalues and EigenvectorsЧтение
03Probability Foundations for Statistical Learning12 материалов

Lesson 1: Sum Rule, Product Rule, and Bayes' Theorem

Sum Rule, Product Rule, and Bayes’ TheoremЧтениеSum RuleЧтениеProduct Rule (Chain Rule)ЧтениеBayes’ TheoremЧтение

Lesson 2: Gaussian Distribution

Univariate Gaussian DistributionЧтениеGaussian Distribution: Foundations and ApplicationsЧтениеMultivariate Gaussian DistributionЧтениеConditional and Marginal Multivariate Gaussian DistributionsЧтениеProduct of Gaussian DensitiesЧтение

Lesson 3: Inference Techniques

Bayesian InferenceЧтениеLatent-Variable ModelsЧтениеCheck Your Knowledge: Inference TechniquesЗадание
04Introduction to Model Evaluation and Optimization16 материалов

Lesson 1: Model Selection Techniques

Introduction to Model SelectionЧтение Bayesian Model SelectionЧтениеBayesian Model Selection ReadingsЧтение

Lesson 2: Cross Validation

Introduction to Cross-ValidationЧтениеK-Fold Cross-ValidationЧтениеLeave-One-Out Cross-Validation (LOOCV)Чтение

Lesson 3: Introduction to Optimization Techniques

Introduction to Optimization TechniquesЧтениеOptimization Using Gradient DescentЧтениеGradient Descent with MomentumЧтениеStochastic Gradient Descent (SGD)ЧтениеConstrained OptimizationЧтениеLagrange MultipliersЧтение
Convex OptimizationЧтение
Linear ProgrammingЧтение
Quadratic ProgrammingЧтение
Check Your Knowledge: Optimization TechniquesЗадание