Mathematics is the foundation of machine learning and helps explain how models learn from data, represent information and improve their performance. Concepts from areas like linear algebra, calculus, probability and statistics provide the theoretical base required to design, train and optimize machine learning algorithms effectively.
- Linear Algebra: for representing data using vectors, matrices and performing transformations
- Statistics & Probability: for modeling uncertainty, analyzing data and making predictions
- Calculus: for optimization and understanding how models learn and update parameters
Probability for Machine Learning
Probability helps measure uncertainty and model randomness in data. It is used in machine learning to understand data distributions and make predictions based on likelihood.
- Basic probability: Sample space, Types of events, Probability Rules
- Joint, Conditional & Marginal probability
- Bayes' theorem
- Probability Distributions
- Sampling Distributions
- t -Distribution
Statistics for Machine Learning
Statistics helps summarize, analyze and interpret data. It is essential for understanding data patterns, evaluating models and making data-driven decisions.
- Descriptive Statistics : Mean, Median, Mode, Variance, Standard deviation
- Inferential Statistics: Confidence Interval, Central Limit Theorem
- Correlation and Covariance
- Hypothesis testing
- Confidence intervals
- P-Value
- Skewness and Kurtosis
- Parametric Test : T-test, F-Test, Z-test, Chi-square Test
- Bias & Variance tradeoff
- Maximum Likelihood Estimation (MLE)
- Mean Squared Error
Linear Algebra for Machine Learning
Linear algebra is used to represent and manipulate data using vectors and matrices. Many machine learning algorithms rely on these operations for computations and transformations.
- Vectors
- Matrices and Matrix operations
- Dot Product
- Euclidean distance
- Manhattan distance
- Eigenvalues and Eigenvectors
- Singular Value Decomposition (SVD)
- Cosine Similarity
- Jaccard Similarity
- Orthogonality and Projections
Calculus for Machine Learning
Calculus is used to optimize machine learning models. Concepts like derivatives and gradients help minimize loss functions and improve model performance during training.
- Fundamental Calculus Concepts
- Gradient
- Higher-Order Derivatives
- Multivariable calculus
- Chain rule
- Jacobian & Hessian Matrices
- Gradient descent
- Stochastic gradient descent