Machine Learning

2.

Mathematical and Statistical Foundations

2.1.

2.1.1.

Scalars, Vectors, and Matrices

2.1.1.1.

Scalar Operations

2.1.1.2.

Vector Representation

2.1.1.3.

Matrix Representation

2.1.1.4.

Vector and Matrix Notation

2.1.2.

Matrix Operations

2.1.2.1.

Addition and Subtraction

2.1.2.2.

Scalar Multiplication

2.1.2.3.

Matrix Multiplication

2.1.2.4.

2.1.2.5.

2.1.2.6.

2.1.2.7.

2.1.3.

Eigenvectors and Eigenvalues

2.1.3.1.

Definition and Properties

2.1.3.2.

Eigendecomposition

2.1.3.3.

Applications in ML

2.1.3.4.

Computational Methods

2.1.4.

Vector Spaces and Subspaces

2.1.4.1.

Linear Independence

2.1.4.2.

Basis and Dimension

2.1.4.3.

2.1.4.4.

2.1.4.5.

Orthonormal Bases

2.1.4.6.

2.1.5.

Matrix Decompositions

2.1.5.1.

Singular Value Decomposition

2.1.5.2.

QR Decomposition

2.1.5.3.

Cholesky Decomposition

2.1.6.

Norms and Distance Metrics

2.1.6.1.

2.1.6.2.

2.1.6.3.

Distance Functions

2.2.

Probability and Statistics

2.2.1.

Probability Theory Basics

2.2.1.1.

Random Experiments

2.2.1.2.

2.2.1.3.

2.2.1.4.

Probability Axioms

2.2.1.5.

Random Variables

2.2.1.6.

Probability Mass Functions

2.2.1.7.

Probability Density Functions

2.2.2.

Probability Distributions

2.2.2.1.

Discrete Distributions

2.2.2.1.1.

Bernoulli Distribution

2.2.2.1.2.

Binomial Distribution

2.2.2.1.3.

Poisson Distribution

2.2.2.1.4.

Geometric Distribution

2.2.2.2.

Continuous Distributions

2.2.2.2.1.

Uniform Distribution

2.2.2.2.2.

Normal Distribution

2.2.2.2.3.

Exponential Distribution

2.2.2.2.4.

Beta Distribution

2.2.2.2.5.

Gamma Distribution

2.2.3.

Joint and Conditional Probability

2.2.3.1.

Joint Probability

2.2.3.2.

Marginal Probability

2.2.3.3.

Conditional Probability

2.2.3.4.

2.2.3.5.

2.2.3.6.

Law of Total Probability

2.2.4.

Expectation and Moments

2.2.4.1.

2.2.4.2.

2.2.4.3.

2.2.4.4.

2.2.4.5.

Higher-Order Moments

2.2.5.

Descriptive Statistics

2.2.5.1.

Measures of Central Tendency

2.2.5.1.1.

2.2.5.1.2.

2.2.5.1.3.

2.2.5.2.

Measures of Dispersion

2.2.5.2.1.

2.2.5.2.2.

Standard Deviation

2.2.5.2.3.

2.2.5.2.4.

Interquartile Range

2.2.5.3.

Measures of Shape

2.2.5.3.1.

2.2.5.3.2.

2.2.6.

Inferential Statistics

2.2.6.1.

Sampling Theory

2.2.6.2.

Point Estimation

2.2.6.3.

Interval Estimation

2.2.6.4.

Confidence Intervals

2.2.6.5.

Hypothesis Testing

2.2.6.6.

2.2.6.7.

Type I and Type II Errors

2.2.6.8.

Power of a Test

2.2.7.

Correlation and Causation

2.2.7.1.

Pearson Correlation Coefficient

2.2.7.2.

Spearman Rank Correlation

2.2.7.3.

2.2.7.4.

Confounding Variables

2.2.7.5.

Causal Inference

2.3.

Calculus and Optimization

2.3.1.

Functions and Limits

2.3.1.1.

Function Notation

2.3.1.2.

Limits and Continuity

2.3.1.3.

2.3.2.

2.3.2.1.

Definition of Derivative

2.3.2.2.

Differentiation Rules

2.3.2.3.

Partial Derivatives

2.3.2.4.

Gradient Vectors

2.3.2.5.

Directional Derivatives

2.3.3.

2.3.3.1.

Single Variable Chain Rule

2.3.3.2.

Multivariable Chain Rule

2.3.3.3.

Applications in Backpropagation

2.3.4.

Optimization Theory

2.3.4.1.

Local vs. Global Optima

2.3.4.2.

Critical Points

2.3.4.3.

First-Order Conditions

2.3.4.4.

Second-Order Conditions

2.3.4.5.

Convex Functions

2.3.4.6.

Convex Optimization

2.3.5.

Gradient-Based Optimization

2.3.5.1.

Gradient Descent

2.3.5.2.

Learning Rate Selection

2.3.5.3.

Convergence Criteria

2.3.5.4.

Stochastic Gradient Descent

2.3.6.

Multivariate Calculus

2.3.6.1.

Jacobian Matrices

2.3.6.2.

Hessian Matrices

2.3.6.3.

Taylor Series Expansion

2.3.7.

Lagrange Multipliers

2.3.7.1.

Constrained Optimization

2.3.7.2.

Equality Constraints

2.3.7.3.

Inequality Constraints

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3. Data Preprocessing and Feature Engineering