Essential Math for Data Science

Spis treści książki

• Preface
  • Conventions Used in This Book
  • Using Code Examples
  • OReilly Online Learning
  • How to Contact Us
  • Acknowledgments
• 1. Basic Math and Calculus Review
  • Number Theory
  • Order of Operations
  • Variables
  • Functions
  • Summations
  • Exponents
  • Logarithms
  • Eulers Number and Natural Logarithms
    • Eulers Number
    • Natural Logarithms
  • Limits
  • Derivatives
    • Partial Derivatives
    • The Chain Rule
  • Integrals
  • Conclusion
  • Exercises
• 2. Probability
  • Understanding Probability
    • Probability Versus Statistics
  • Probability Math
    • Joint Probabilities
    • Union Probabilities
    • Conditional Probability and Bayes Theorem
    • Joint and Union Conditional Probabilities
  • Binomial Distribution
  • Beta Distribution
  • Conclusion
  • Exercises
• 3. Descriptive and Inferential Statistics
  • What Is Data?
  • Descriptive Versus Inferential Statistics
  • Populations, Samples, and Bias
  • Descriptive Statistics
    • Mean and Weighted Mean
    • Median
    • Mode
    • Variance and Standard Deviation
      • Population Variance and Standard Deviation
      • Sample Variance and Standard Deviation
    • The Normal Distribution
      • Discovering the Normal Distribution
      • Properties of a Normal Distribution
      • The Probability Density Function (PDF)
      • The Cumulative Distribution Function (CDF)
    • The Inverse CDF
    • Z-Scores
  • Inferential Statistics
    • The Central Limit Theorem
    • Confidence Intervals
    • Understanding P-Values
    • Hypothesis Testing
      • One-Tailed Test
      • Two-Tailed Test
  • The T-Distribution: Dealing with Small Samples
  • Big Data Considerations and the Texas Sharpshooter Fallacy
  • Conclusion
  • Exercises
• 4. Linear Algebra
  • What Is a Vector?
    • Adding and Combining Vectors
    • Scaling Vectors
    • Span and Linear Dependence
  • Linear Transformations
    • Basis Vectors
    • Matrix Vector Multiplication
  • Matrix Multiplication
  • Determinants
  • Special Types of Matrices
    • Square Matrix
    • Identity Matrix
    • Inverse Matrix
    • Diagonal Matrix
    • Triangular Matrix
    • Sparse Matrix
  • Systems of Equations and Inverse Matrices
  • Eigenvectors and Eigenvalues
  • Conclusion
  • Exercises
• 5. Linear Regression
  • A Basic Linear Regression
    • Basic Linear Regression with SciPy
  • Residuals and Squared Errors
  • Finding the Best Fit Line
    • Closed Form Equation
    • Inverse Matrix Techniques
    • Gradient Descent
      • A Thought Experiment on Gradient Descent
      • Lets Walk Before We Run
      • Gradient Descent and Linear Regression
      • Gradient Descent for Linear Regression Using SymPy
  • Overfitting and Variance
  • Stochastic Gradient Descent
  • The Correlation Coefficient
  • Statistical Significance
  • Coefficient of Determination
  • Standard Error of the Estimate
  • Prediction Intervals
  • Train/Test Splits
  • Multiple Linear Regression
  • Conclusion
  • Exercises
• 6. Logistic Regression and Classification
  • Understanding Logistic Regression
  • Performing a Logistic Regression
    • Logistic Function
    • Fitting the Logistic Curve
      • Using SciPy
      • Using Maximum Likelihood and Gradient Descent
  • Multivariable Logistic Regression
  • Understanding the Log-Odds
  • R-Squared
  • P-Values
  • Train/Test Splits
  • Confusion Matrices
  • Bayes Theorem and Classification
  • Receiver Operator Characteristics/Area Under Curve
  • Class Imbalance
  • Conclusion
  • Exercises
• 7. Neural Networks
  • When to Use Neural Networks and Deep Learning
  • A Simple Neural Network
    • Activation Functions
    • Forward Propagation
  • Backpropagation
    • Calculating the Weight and Bias Derivatives
    • Stochastic Gradient Descent
  • Using scikit-learn
  • Limitations of Neural Networks and Deep Learning
  • Conclusion
  • Exercise
• 8. Career Advice and the Path Forward
  • Redefining Data Science
  • A Brief History of Data Science
  • Finding Your Edge
    • SQL Proficiency
      • What About Pandas and NoSQL?
    • Programming Proficiency
    • Data Visualization
    • Knowing Your Industry
    • Productive Learning
    • Practitioner Versus Advisor
  • What to Watch Out For in Data Science Jobs
    • Role Definition
    • Organizational Focus and Buy-In
    • Adequate Resources
    • Reasonable Objectives
    • Competing with Existing Systems
    • A Role Is Not What You Expected
  • Does Your Dream Job Not Exist?
  • Where Do I Go Now?
  • Conclusion
• A. Supplemental Topics
  • Using LaTeX Rendering with SymPy
  • Binomial Distribution from Scratch
  • Beta Distribution from Scratch
  • Deriving Bayes Theorem
  • CDF and Inverse CDF from Scratch
  • Use e to Predict Event Probability Over Time
  • Hill Climbing and Linear Regression
  • Hill Climbing and Logistic Regression
  • A Brief Intro to Linear Programming
  • MNIST Classifier Using scikit-learn
• B. Exercise Answers
  • Chapter 1
  • Chapter 2
  • Chapter 3
  • Chapter 4
  • Chapter 5
  • Chapter 6
  • Chapter 7
• Index

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