Math for Machine Learning

Roadmap of Mathematics for Machine LearningMedium

Statistics Roadmap

1. STATS BASICS

• Types of Data: Nominal, Ordinal, Discrete, Continuous

• Descriptive vs Inferential Stats

• Moments

• Mean, Median, Mode

• Skewness

• Kurtosis

• Range, IQR

• Percentiles, Quartiles

• Mean Deviation

• Standard Deviation

• Variance

• Quartile Deviation

• Standard Error

2. CHARTS

• Frequency Distribution Table

• Line Chart

• Bar Chart

• Histogram

• Frequency Polygon

• Pie Chart

• Ogives

3. PROBABILITY DISTRIBUTION FUNCTIONS

• Random Variables

• Multivariate random variables

• Discrete random variables

• Continuous random variables

• Law of Large Numbers

• Expectation

• PMF — Probability Mass Function

• PDF — Probability Density Function

• CDF — Cumulative Density Function

• Bernoulli Distribution

• Binomial Distribution

• Geometric Distribution

• Poisson Distribution

• Exponential Distribution

• Uniform Distribution

• Gaussian / Normal Distribution

• Chi-Square Distribution

• Power Law Distribution

• Pareto Distribution

• Box-Cox Transformation

• Log-Normal Distribution

• Kernel Density Estimation

• Q-Q plot

4. PROBABILITY

• Basic Probability

• Joint Probability

• Conditional Probability

• Independent Events

• Mutually Exclusive Events

• Bayes’ Theorem

5. TESTS / SAMPLING / POPULATION

• Sampling, Sample Mean & Distribution

• Central Limit Theorem

• Point estimate, Interval estimate

• Confidence Interval

• Population, Population Mean & Distribution

• Hypothesis Testing

• P-value

• Population Proportions

• Critical Value

• Significance Level

• Rejection regions

• Type I vs Type II errors

• One tail vs Two tail

• Z-Test

• T-Test

• ANOVA

• F-Test

• Chi-Square Test

• Monte Carlo Simulation

• A/B Testing

6. RELATIONS / REGRESSION

• Causality

• Covariance

• Covariance Matrix

• Correlation

• Scatter Plots

• Pearson Correlation Coefficient

• Rank / Spearman Correlation Coefficient

• R2 score

• Linear Regression

• OLS

• Factor Analysis

• Logistic Regression

Linear Algebra Roadmap

1. LINEAR EQUATIONS

• Systems of Linear Equations

• Gaussian Elimination

• Echelon Form

• Linear Combination

• Span

• Homogeneous Linear System

• Linear Independence

• Subspace

• Basis

• Affine space

• Linear Transformation

2. MATRIX

• Matrix transformations

• Matrix multiplication

• Inverse Matrix

• Transpose of a matrix

• Rank of a matrix

• Symmetric Matrix

• Orthogonal Matrix

• Adjoint Matrix

• Singular Matrix

• Determinant of a matrix

• Trace of a Matrix

3. VECTORS

• Components of Vector

• Vector Space

• Norm of a vector

• Lengths and distances

• Euclidean Norm

• Manhattan Norm

• Minkowski Distance

• Scalar Multiplication

• Dot Product

• Inner Product

• Cross Product

• Orthogonality

• Orthonormal

• Rotations

4. FACTORIZATION

• Matrix Decomposition

• LU Decomposition

• QR Decomposition

• Cholesky Decomposition

• Eigen Decomposition

• Eigen Values

• Eigen Vector

• Singular Value Decomposition

• Principal Component Analysis

Calculus Roadmap

1. CALCULUS BASICS

• Functions

• Derivatives

• Maxima Minima

• Product and Chain Rule Differentiation

• Composite functions

• Partial Derivatives

• Higher-order derivatives

• Integrals

• Limits

• Infinite series summation

2. OPTIMIZERS

• Gradient Descents

• Optimizers

• Loss Functions

• Taylor’s Series

• Constrained Optimization (Lagrange Multiplier)

• Newton’s method in Optimization

• Convex Optimization

Free YouTube resources:

Credits to 3Blue1Brown, Khan Academy, StatQuest with Josh Starmer.