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
Relevance in Machine Learning
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- The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, Jerome Friedman, 2009 (Springer) - This textbook provides a comprehensive introduction to statistical learning methods, outlining the statistical and probabilistic foundations of many machine learning algorithms.
- Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) - This book presents machine learning from a unified Bayesian probabilistic perspective, describing the statistical underpinnings of various models and algorithms.
- Practical Statistics for Data Scientists: 50 Essential Concepts, Peter Bruce, Andrew Bruce, Peter Gedeck, 2020 (O'Reilly Media) - This reference connects statistical concepts with their practical application in data science and machine learning, offering core insights for data exploration and model evaluation.
- Probability and Statistics for Engineers and Scientists, Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying E. Ye, 2021 (Pearson) - A standard textbook providing a strong foundation in probability theory and statistical inference, fundamental for understanding the mathematical basis of machine learning.