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
Independent vs. Dependent Events
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- The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, and Jerome Friedman, 2009 (Springer) - Comprehensive coverage of statistical learning methods, including the probabilistic foundations and assumptions in models.
- Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) DOI: 10.1007/978-0-387-44958-6 - Offers a detailed probabilistic perspective on machine learning, with a strong emphasis on Bayesian methods and the role of independence.
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems, Aurélien Géron, 2022 (O'Reilly Media) - Provides practical examples and explanations of machine learning models, including the Naive Bayes classifier and its independence assumptions.