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Probability and Statistics for Machine Learning

(PS-ML.AU1)
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1

Preface

  • Prerequisites for the Book
  • Notations
2

Probability and Statistics: An Introduction

  • Introduction
  • Representing Data
  • Summarizing and Visualizing Data
  • The Basics of Probability and Probability Distributions
  • Hypothesis Testing
  • Basic Problems in Machine Learning
  • Summary
  • Exercises
3

Summarizing and Visualizing Data

  • Introduction
  • Summarizing Data
  • Data Visualization
  • Applications to Data Preprocessing
  • Summary
  • Exercises
4

Probability Basics and Random Variables

  • Introduction
  • Sample Spaces and Events
  • The Counting Approach to Probabilities
  • Set-Wise View of Events
  • Conditional Probabilities and Independence
  • The Bayes Rule
  • The Basics of Probability Distributions
  • Distribution Independence and Conditionals
  • Summarizing Distributions
  • Compound Distributions
  • Functions of Random Variables (*)
  • Summary
  • Exercises
5

Probability Distributions

  • Introduction
  • The Uniform Distribution
  • The Bernoulli Distribution
  • The Categorical Distribution
  • The Geometric Distribution
  • The Binomial Distribution
  • The Multinomial Distribution
  • The Exponential Distribution
  • The Poisson Distribution
  • The Normal Distribution
  • The Student’s t-Distribution
  • The χ2-Distribution
  • Mixture Distributions: The Realistic View
  • Moments of Random Variables (*)
  • Summary
  • Exercises
6

Hypothesis Testing and Confidence Interval 

  • Introduction
  • The Central Limit Theorem
  • Sampling Distribution and Standard Error
  • The Basics of Hypothesis Testing
  • Hypothesis Tests For Differences in Means
  • χ2-Hypothesis Tests
  • Analysis of Variance (ANOVA)
  • Machine Learning Applications of Hypothesis Testing
  • Summary
  • Exercises
7

Reconstructing Probability Distributions from Data 

  • Introduction
  • Maximum Likelihood Estimation
  • Reconstructing Common Distributions from Data
  • Mixture of Distributions: The EM Algorithm
  • Kernel Density Estimation
  • Reducing Reconstruction Variance
  • The Bias-Variance Trade-Off
  • Popular Distributions Used as Conjugate Priors (*)
  • Summary
  • Exercises
8

Regression

  • Introduction
  • The Basics of Regression
  • Two Perspectives on Linear Regression
  • Solutions to Linear Regression
  • Handling Categorical Predictors
  • Overfitting and Regularization
  • A Probabilistic View of Regularization
  • Evaluating Linear Regression
  • Nonlinear Regression
  • Summary
  • Exercises
9

Classification: A Probabilistic View

  • Introduction
  • Generative Probabilistic Models
  • Loss-Based Formulations: A Probabilistic View
  • Beyond Classification: Ordered Logit Model
  • Summary
  • Exercises
10

Unsupervised Learning: A Probabilistic View

  • Introduction
  • Mixture Models for Clustering
  • Matrix Factorization
  • Outlier Detection
  • Summary
  • Exercises
11

Discrete State Markov Processes

  • Introduction
  • Markov Chains
  • Machine Learning Applications of Markov Chains
  • Markov Chains to Generative Models
  • Hidden Markov Models
  • Applications of Hidden Markov Models
  • Summary
  • Exercises
12

Probabilistic Inequalities and Approximations

  • Introduction
  • Jensen’s Inequality
  • Markov and Chebyshev Inequalities
  • Approximations for Sums of Random Variables
  • Tail Inequalities Versus Approximation Estimates
  • Summary
  • Exercises

1

Probability and Statistics: An Introduction

  • Preparing Data for Regression and Visualization
  • Performing Hypothesis Testing
  • Modeling Sensor Noise in Robotics
2

Summarizing and Visualizing Data

  • Analyzing Data Using Bar Charts
  • Analyzing Data Using Scatter Plots and Line Plots
  • Analyzing Data Using Histograms
  • Building a Multivariate Model
  • Building a Univariate Model
3

Probability Basics and Random Variables

  • Implementing the Bayes Classifier
  • Training a Naïve Bayes Model
  • Creating a Naïve Bayes Spam Classifier
4

Probability Distributions

  • Generating a Binomial Distribution Plot
  • Generating and Visualizing a Gaussian Distribution
5

Hypothesis Testing and Confidence Interval 

  • Using Sampling to Convert Bimodal Data to a Normal Distribution
  • Evaluating AI Model Accuracy with Statistical Tests
  • Testing Hypotheses: Type I and II Errors
  • Calculating and Interpreting Confidence Intervals
6

Reconstructing Probability Distributions from Data 

  • Implementing the Bias-Variance Trade-Off
  • Working with Conjugate Priors and Estimating Parameters
7

Regression

  • Training a Linear Regression Model
  • Implementing Lasso Regression
  • Implementing Non-Linear Transformations of Predictors
8

Classification: A Probabilistic View

  • Implementing Multinomial Logistic Regression
  • Training a Logistic Regression Model
9

Unsupervised Learning: A Probabilistic View

  • Implementing the Squared Loss Model
  • Implementing PLSA
  • Detecting Outliers Using the Mahalanobis Distance Method
10

Discrete State Markov Processes

  • Using an HMM Model
11

Probabilistic Inequalities and Approximations

  • Applying Markov and Chebyshev Inequalities
  • Applying Chernoff Bounds and Hoeffding Inequalities

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Probability and Statistics for Machine Learning

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