Probability & Statistics Fundamentals for Machine Learning
Chapter 1: Introduction to Probability and Statistics for Machine Learning
What are Probability and Statistics?
Relevance in Machine Learning
Understanding Data Types
Populations and Samples
Setting Up the Python Environment
Hands-on Practical: Loading and Inspecting Data
Quiz for Chapter 1
Chapter 2: Descriptive Statistics: Summarizing Data
Measuring the Center: Mean, Median, and Mode
Measuring Spread: Variance and Standard Deviation
Measuring Spread: Range
Understanding Percentiles and Quartiles
Visualizing Distributions: Histograms
Visualizing Summaries: Box Plots
Calculating Descriptive Statistics with Python
Practice: Summarizing a Dataset
Quiz for Chapter 2
Chapter 3: Basic Probability Concepts
Understanding Probability: Events and Sample Spaces
Calculating Simple Probabilities
Introduction to Set Theory for Probability
Conditional Probability Explained
Independent vs. Dependent Events
Introduction to Bayes' Theorem
Practice: Probability Calculations
Quiz for Chapter 3
Chapter 4: Probability Distributions
What are Probability Distributions?
Probability Mass Function (PMF) for Discrete Distributions
Discrete Distribution: Bernoulli
Discrete Distribution: Binomial
Probability Density Function (PDF) for Continuous Distributions
Continuous Distribution: Uniform
Continuous Distribution: Normal (Gaussian)
The Central Limit Theorem
Generating Samples from Distributions using Python
Practice: Working with Distributions
Quiz for Chapter 4
Chapter 5: Introduction to Statistical Inference
Drawing Conclusions from Data
Point Estimation
Interval Estimation: Confidence Intervals
Hypothesis Testing: The Basic Idea
Null and Alternative Hypotheses
Understanding P-values
Connecting Inference to Machine Learning Evaluation
Practice: Interpreting Statistical Results
Quiz for Chapter 5
Discrete Distribution: Binomial
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- A First Course in Probability, Sheldon M. Ross, 2019 (Pearson) - A widely-used textbook offering a comprehensive and rigorous introduction to probability theory, including a detailed treatment of discrete distributions such as the binomial distribution.
- Lecture 4: Discrete Random Variables (Part 1 and 2) from 6.041SC Probabilistic Systems Analysis and Applied Probability, John Tsitsiklis and Patrick Jaillet, 2010 (MIT OpenCourseWare) - Provides high-quality lecture materials and video explanations from an MIT course, offering an academic approach to understanding discrete probability distributions, including the binomial distribution.
- All of Statistics: A Concise Course in Statistical Inference, Larry Wasserman, 2004 (Springer) DOI: 10.1007/978-0-387-21736-9 - A foundational textbook that covers the essential concepts of statistics with a focus on statistical inference, highly relevant for machine learning practitioners seeking a solid theoretical background on distributions like the binomial.
- Probability and Statistics, Morris H. DeGroot, Mark J. Schervish, 2012 (Pearson) - A classic and widely-respected textbook that offers a thorough and accessible introduction to probability theory and statistical inference, with detailed chapters on discrete distributions.