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
Connecting Inference to Machine Learning Evaluation
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- The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, Jerome Friedman, 2009 (Springer) - This canonical reference for statistical learning covers theoretical foundations and practical algorithms. Its chapter on model assessment and selection is essential for understanding uncertainty in ML model evaluation.
- An Introduction to Statistical Learning: With Applications in R, Gareth James, Daniela Witten, Trevor Hastie, Rob Tibshirani, 2013 (Springer) - A more accessible introduction to statistical learning, this book provides a solid foundation for understanding how statistical inference applies to machine learning model assessment, covering concepts like test sets and performance metrics.
- Approximate Statistical Tests for Comparing Supervised Classification Learning Algorithms, Thomas G. Dietterich, 1998 Neural Computation, Vol. 10 (MIT Press) DOI: 10.1162/089976698300017197 - This foundational paper presents approximate statistical tests, such as the McNemar test and paired t-tests, for comparing the performance of two supervised classification algorithms, directly addressing the need for rigorous hypothesis testing in machine learning evaluation.
- Probability and Statistics for Engineering and the Sciences, Jay L. Devore, 2021 (Cengage Learning) - This comprehensive textbook provides a thorough introduction to probability theory and statistical inference, including detailed explanations of point estimation, confidence intervals, and hypothesis testing, serving as a strong foundation for the statistical concepts discussed.