Machine Learning Mathematics

Machine Learning is the field of study that gives computers the capability to learn without being explicitly programmed. Math is the core concept in machine learning which is used to express the idea within the machine learning model.

Mathematics for Machine Learning

In this tutorial, we will look at different mathematics concepts and will learn about these modules from basic to advance with the help particular algorithm.

Linear Algebra and Matrix

Linear Algebra is an algebra extension to an undefined number of dimensions. Linear Algebra concerns the focus on linear equation systems. 

• System of Linear Equation
• Matrix Operation
  • Addition, Multiplication, Division Using Python
  • Addition, Multiplication, Division Using NumPy
  • Inverse
  • Transpose
• Properties of Matrix
• Solving Linear Equation using Gaussian Elimination 
• LU Decomposition of Linear Equation
• Row Echelon Form
• Determinant
• Trace
  • With Numpy
• Eigenvalues and Eigenvectors
• Eigenspace
• Orthogonal and Orthonormal Vectors
• Cholesky Decomposition
  • With NumPy
• Eigen Decomposition
• Diagonalization
• Singular Value Decomposition — Implementation
• Matrix Approximation
• Vector Operations
• Linear Mappings
• Affine Spaces

Statistics

Statistics is the collection of data, tabulation, and interpretation of numerical data, and it applied mathematics concerned with data collection analysis, interpretation, and presentation.

• Mean, Standard Deviation and Variance — Implementation
• Sample Error and True Error
• Bias Vs Variance and Its Trade-Off
• Hypothesis Testing
  • T-test
  • Paired T-test
  • p-value
  • F-Test
  • z-test
• Confidence Intervals
• Correlation and Covariance
• Correlation Coefficient
• Covariance Matrix
• Pearson Correlation
• Normal Probability Plot
• Q-Q Plot
• Residuals Leverage Plot
• Pearson Product-Moment Correlations
• Spearman’s Rank Correlation Measure
• Kendall Rank Correlation Measure
• Robust Correlations
• Evaluation Metrics – Accuracy, Precision, Recall, F1-Score, MAE, MSE
• RMSE and R-Squared Error
• Precision-Recall Curve
• ROC-AUC curve

Geometry

Geometry is the branch of mathematics that deals with the forms, angles, measurements, and proportions of ordinary objects

• Vector Norms
• Inner, Outer, Cross Products
• Lengths and Angles
• Orthogonality and Orthonormal Vectors
• Orthogonal Projections
• Rotations
  • With NumPy
• Piecewise Functions
• Constraints and Splines
• Box-Cox Transformation using Python
• Fourier transformation
• Inverse Fast Fourier Transformation

Calculus

Calculus is a subset of mathematics concerned with the study of continuous transition. Calculus is also known as infinitesimal calculus or “infinite calculus.” The analysis of continuous change of functions is known as classical calculus

• Function Differentiation
• Implicit Differentiation
• Inverse Trigonometric Functions Differentiation
• Logarithmic Differentiation
• Partial Differentiation
• Advanced Differentiation
• Gradients
• Gradients of Matrices
• Useful Identities for Gradient computation
• Backpropagation
  • Gradient Descent Algorithm
• Higher-Order Derivatives
• Multivariate Taylor Series

Probability and Distributions

Probability and distributions are statistical function that describes all the possible values.

• Probability
• Chance and Probability
• Discrete and Continuous Probabilities
• Addition Rule for Probability
• Law of total probability
• Sum Rule, Product Rule, and Bayes’ Theorem
• Uniform Distribution
• Normal Distribution
• Poisson Distribution
• Exponential Distribution
• Binomial Distribution
• Gaussian Distribution
• Central Limit Theorem
• Conjugacy and the Exponential Family
• Change of Variables/Inverse Transformation

Regression

Regression is a statistical process for estimating the relationships between the dependent variables or criterion variables 

• Parameter Estimation
• Bayesian Linear Regression
• Normal Equation in Linear Regression
• Maximum Likelihood as Orthogonal Projection

Dimensionality Reduction

Dimensionality reduction is a technique to reduce the number of input variables in training data.

• Introduction to Dimensionality Reduction
• Projection Perspective
• Eigenvector Computation and Low-Rank Approximations
• Principal Component Analysis (PCA)
• PCA implementation in Python
• Latent Variable Perspective
• Low-Rank Approximations
• Overview of Linear Discriminant Analysis (LDA)
• Mathematical Explanation of Linear Discriminant Analysis (LDA)
• Generalized Discriminant Analysis (GDA)
• TSNE Algorithm

Vector Models

Vector is a supervised learning system is used for classification and regression problems.

• Separating Hyperplanes
• Primal Support Vector Machine
• Dual Support Vector Machine
• Kernels

Miscellaneous

• Uni-variate Optimisation
• Multivariate Optimisation
• Constrained Optimization
• Unconstrained Optimization
• Convex Optimization
• Lagrange Multipliers
• Lagrange’s Interpolation
• Latent-Variable Perspective