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
Point Estimation
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- Statistical Inference, George Casella, Roger L. Berger, 2002 (Duxbury Thomson Learning) DOI: 10.1201/9781003456285 - A comprehensive text on statistical inference, covering the theoretical underpinnings of point estimation, properties of estimators, and methods for finding good estimators.
- Probability and Statistics, Morris H. DeGroot and Mark J. Schervish, 2012 (Pearson) - Offers a clear explanation of point estimation, differentiating between population parameters and sample statistics, and illustrating common estimators.
- Practical Statistics for Data Scientists: 50 Essential Concepts, Peter Bruce, Andrew Bruce, Peter Gedeck, 2020 (O'Reilly Media) - Discusses estimates of location and variability, providing practical context for how point estimates are used in data science and machine learning applications.
- Introduction to Probability and Statistics, Jeremy Orloff, Jonathan Bloom, 2014 (MIT OpenCourseWare) - Free online course materials from MIT covering fundamental concepts of statistical inference, including parameters, statistics, and point estimation.