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
Understanding Probability: Events and Sample Spaces
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- A First Course in Probability, Sheldon Ross, 2019 (Pearson) - Standard undergraduate text covering fundamental probability concepts like experiments, outcomes, sample spaces, and events. (10th edition)
- Introduction to Probability (Course 6.041SC), John Tsitsiklis, Patrick Jaillet, 2018 (MIT OpenCourseWare) - Foundational university course material providing lectures and problem sets on basic probability theory.
- Introduction to Probability, Charles M. Grinstead and J. Laurie Snell, 2006 (American Mathematical Society) - Highly regarded textbook offering a clear and accessible introduction to probability theory, including definitions of experiments, outcomes, sample spaces, and events.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Chapter 3 introduces essential probability theory concepts foundational for machine learning, including experiments, outcomes, sample spaces, and events.