Machine Learning and Deep Learning
Models, math, and neural networks from first principles.
3,538 lessons·First 10 free
- 1Scalars, Vectors, and Matrices: DefinitionsFree
- 2Vector Operations: Addition and Scalar MultiplicationFree
- 3Dot Product and Vector SimilarityFree
- 4Vector Norms and Distance MetricsFree
- 5Matrix-Vector MultiplicationFree
- 6Matrix-Matrix MultiplicationFree
- 7Matrix Transpose and SymmetryFree
- 8Identity Matrix and Matrix InverseFree
- 9Systems of Linear EquationsFree
- 10Linear Independence and SpanFree
- 11Basis and DimensionPro
- 12Column Space and Null SpacePro
- 13Rank of a MatrixPro
- 14Determinants and Their PropertiesPro
- 15Trace of a MatrixPro
- 16Eigenvalues and Eigenvectors: DefinitionsPro
- 17Computing Eigenvalues and EigenvectorsPro
- 18Eigendecomposition of MatricesPro
- 19Diagonalization and Its ApplicationsPro
- 20Orthogonality and Orthonormal VectorsPro
- 21Orthogonal Matrices and Their PropertiesPro
- 22Singular Value Decomposition (SVD): ConceptPro
- 23Computing and Interpreting SVDPro
- 24Matrix Approximation with SVDPro
- 25Positive Definite and Semidefinite MatricesPro
- 26Quadratic FormsPro
- 27Matrix Calculus: Gradients of Matrix ExpressionsPro
- 28Numerical Stability in Linear AlgebraPro
- 29Functions and ContinuityPro
- 30Limits: The Foundation of DerivativesPro
- 31The Derivative DefinitionPro
- 32Geometric Interpretation of DerivativesPro
- 33Basic Differentiation RulesPro
- 34Product and Quotient RulesPro
- 35The Chain RulePro
- 36Derivatives of Exponential FunctionsPro
- 37Derivatives of Logarithmic FunctionsPro
- 38Derivatives of Trigonometric FunctionsPro
- 39Higher-Order DerivativesPro
- 40Implicit DifferentiationPro
- 41Partial Derivatives: IntroductionPro
- 42The Gradient VectorPro
- 43Directional DerivativesPro
- 44The Multivariable Chain RulePro
- 45Critical Points and ExtremaPro
- 46The Hessian MatrixPro
- 47Second Derivative Test in Multiple DimensionsPro
- 48Taylor Series and ApproximationsPro
- 49L'Hôpital's RulePro
- 50The Jacobian MatrixPro
- 51Integration FundamentalsPro
- 52Numerical DifferentiationPro
- 53Sample Spaces and EventsPro
- 54Probability Axioms and Basic RulesPro
- 55Conditional ProbabilityPro
- 56Independence of EventsPro
- 57Bayes' TheoremPro
- 58Random Variables: Discrete and ContinuousPro
- 59Probability Mass FunctionsPro
- 60Probability Density FunctionsPro
- 61Cumulative Distribution FunctionsPro
- 62Expectation and MeanPro
- 63Variance and Standard DeviationPro
- 64Common Discrete Distributions: Bernoulli and BinomialPro
- 65Poisson DistributionPro
- 66Uniform DistributionPro
- 67Normal (Gaussian) DistributionPro
- 68Exponential and Gamma DistributionsPro
- 69Joint Probability DistributionsPro
- 70Marginal and Conditional DistributionsPro
- 71Covariance and CorrelationPro
- 72Independence of Random VariablesPro
- 73Law of Large NumbersPro
- 74Central Limit TheoremPro
- 75Population vs SamplePro
- 76Descriptive Statistics: Central TendencyPro
- 77Descriptive Statistics: Spread and VariabilityPro
- 78Percentiles and QuantilesPro
- 79Covariance and CorrelationPro
- 80The Law of Large NumbersPro
- 81Central Limit TheoremPro
- 82Sampling DistributionsPro
- 83Point Estimation FundamentalsPro
- 84Bias and Variance of EstimatorsPro
- 85Maximum Likelihood EstimationPro
- 86Method of MomentsPro
- 87Confidence IntervalsPro
- 88Bootstrap ResamplingPro
- 89Hypothesis Testing FrameworkPro
- 90Type I and Type II ErrorsPro
- 91Common Statistical TestsPro
- 92Multiple Testing CorrectionPro
- 93What is Mathematical Optimization?Pro
- 94Unconstrained vs Constrained OptimizationPro
- 95Local vs Global OptimaPro
- 96Convex SetsPro
- 97Convex FunctionsPro
- 98First-Order Optimality ConditionsPro
- 99Second-Order Optimality ConditionsPro
- 100The Gradient Descent AlgorithmPro
- 101Learning Rate and Step SizePro
- 102Convergence Guarantees for Gradient DescentPro
- 103Lipschitz Continuity and SmoothnessPro
- 104Strong ConvexityPro
- 105Stochastic Gradient Descent BasicsPro
- 106Momentum MethodsPro
- 107Newton's MethodPro
- 108Quasi-Newton MethodsPro
- 109Coordinate DescentPro
- 110Constrained Optimization and Lagrange MultipliersPro
- 111KKT ConditionsPro
- 112Subgradients and Non-Smooth OptimizationPro