Statistical Methods for Machine Learning

Copyright Contents Preface I Introduction II Statistics Introduction to Statistics Statistics is Required Prerequisite Why Learn Statistics? What is Statistics? Further Reading Summary Statistics vs Machine Learning Machine Learning Predictive Modeling Statistical Learning Two Cultures Further Reading Summary Examples of Statistics in Machine Learning Overview Problem Framing Data Understanding Data Cleaning Data Selection Data Preparation Model Evaluation Model Configuration Model Selection Model Presentation Model Predictions Summary III Foundation Gaussian and Summary Stats Tutorial Overview Gaussian Distribution Sample vs Population Test Dataset Central Tendency Variance Describing a Gaussian Extensions Further Reading Summary Simple Data Visualization Tutorial Overview Data Visualization Introduction to Matplotlib Line Plot Bar Chart Histogram Plot Box and Whisker Plot Scatter Plot Extensions Further Reading Summary Random Numbers Tutorial Overview Randomness in Machine Learning Pseudorandom Number Generators Random Numbers with Python Random Numbers with NumPy When to Seed the Random Number Generator How to Control for Randomness Common Questions Extensions Further Reading Summary Law of Large Numbers Tutorial Overview Law of Large Numbers Worked Example Implications in Machine Learning Extensions Further Reading Summary Central Limit Theorem Tutorial Overview Central Limit Theorem Worked Example with Dice Impact on Machine Learning Extensions Further Reading Summary IV Hypothesis Testing Statistical Hypothesis Testing Tutorial Overview Statistical Hypothesis Testing Statistical Test Interpretation Errors in Statistical Tests Degrees of Freedom in Statistics Extensions Further Reading Summary Statistical Distributions Tutorial Overview Distributions Gaussian Distribution Student's t-Distribution Chi-Squared Distribution Extensions Further Reading Summary Critical Values Tutorial Overview Why Do We Need Critical Values? What Is a Critical Value? How to Use Critical Values How to Calculate Critical Values Extensions Further Reading Summary Covariance and Correlation Tutorial Overview What is Correlation? Test Dataset Covariance Pearson's Correlation Extensions Further Reading Summary Significance Tests Tutorial Overview Parametric Statistical Significance Tests Test Data Student's t-Test Paired Student's t-Test Analysis of Variance Test Repeated Measures ANOVA Test Extensions Further Reading Summary Effect Size Tutorial Overview The Need to Report Effect Size What Is Effect Size? How to Calculate Effect Size Extensions Further Reading Summary Statistical Power Tutorial Overview Statistical Hypothesis Testing What Is Statistical Power? Power Analysis Student's t-Test Power Analysis Extensions Further Reading Summary V Resampling Methods Introduction to Resampling Tutorial Overview Statistical Sampling Statistical Resampling Extensions Further Reading Summary Estimation with Bootstrap Tutorial Overview Bootstrap Method Configuration of the Bootstrap Worked Example Bootstrap in Python Extensions Further Reading Summary Estimation with Cross-Validation Tutorial Overview k-Fold Cross-Validation Configuration of k Worked Example Cross-Validation in Python Variations on Cross-Validation Extensions Further Reading Summary VI Estimation Statistics Introduction to Estimation Statistics Tutorial Overview Problems with Hypothesis Testing Estimation Statistics Effect Size Interval Estimation Meta-Analysis Extensions Further Reading Summary Tolerance Intervals Tutorial Overview Bounds on Data What Are Statistical Tolerance Intervals? How to Calculate Tolerance Intervals Tolerance Interval for Gaussian Distribution Extensions Further Reading Summary Confidence Intervals Tutorial Overview What is a Confidence Interval? Interval for Classification Accuracy Nonparametric Confidence Interval Extensions Further Reading Summary Prediction Intervals Tutorial Overview Why Calculate a Prediction Interval? What Is a Prediction Interval? How to Calculate a Prediction Interval Prediction Interval for Linear Regression Worked Example Extensions Further Reading Summary VII Nonparametric Methods Rank Data Tutorial Overview Parametric Data Nonparametric Data Ranking Data Working with Ranked Data Extensions Further Reading Summary Normality Tests Tutorial Overview Normality Assumption Test Dataset Visual Normality Checks Statistical Normality Tests What Test Should You Use? Extensions Further Reading Summary Make Data Normal Tutorial Overview Gaussian and Gaussian-Like Sample Size Data Resolution Extreme Values Long Tails Power Transforms Use Anyway Extensions Further Reading Summary 5-Number Summary Tutorial Overview Nonparametric Data Summarization Five-Number Summary How to Calculate the Five-Number Summary Use of the Five-Number Summary Extensions Further Reading Summary Rank Correlation Tutorial Overview Rank Correlation Test Dataset Spearman's Rank Correlation Kendall's Rank Correlation Extensions Further Reading Summary Rank Significance Tests Tutorial Overview Nonparametric Statistical Significance Tests Test Dataset Mann-Whitney U Test Wilcoxon Signed-Rank Test Kruskal-Wallis H Test Friedman Test Extensions Further Reading Independence Test Tutorial Overview Contingency Table Pearson's Chi-Squared Test Example Chi-Squared Test Extensions Further Reading Summary VIII Appendix Getting Help Statistics on Wikipedia Statistics Textbooks Python API Resources Ask Questions About Statistics How to Ask Questions Contact the Author How to Setup a Workstation for Python Overview Download Anaconda Install Anaconda Start and Update Anaconda Further Reading Summary Basic Math Notation Tutorial Overview The Frustration with Math Notation Arithmetic Notation Greek Alphabet Sequence Notation Set Notation Other Notation Tips for Getting More Help Further Reading Summary IX Conclusions How Far You Have Come