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Probability and Statistics for Machine Learning

Start your career with the Probability & Statistics for Machine Learning course. Learn how to design, evaluate, and understand the next generation of AI models.

(PS-ML.AU1)
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About This Course

Are you tired of treating machine learning models like black boxes? This statistics course gives you the rigorous foundation to simply build, evaluate & troubleshoot AI algorithms. Therefore, the power of modern data science & AI lies in the mathematical principles—especially probability & statistics for machine learning.

Mastering statistics for machine learning is an important differentiator for securing high-end roles in the fields of data science & AI engineering. For anyone aiming to master AI, this is the definition of math for the Machine Learning Program. By understanding the probability for data science, it is no longer optional—it is optional for anyone who is opting for a career in statistics for AI. 

   

Skills You’ll Get

  • Core Probability & Data Analysis: Dive into the essentials of probability, random variables, expected value & common distributions—the statistical backbone for all the machine learning models. You can deepen the probability for data science expertise. 
  • Statistical Inference & Testing: Master hypothesis testing, confidence intervals, and ANOVA, as well as the central limit theorem for rigorous model validation, a key skill in statistics for AI. 
  • Model Building Blocks: Learn the maximum likelihood estimation, the bias-variance trade-off & how to reconstruct common distributions from data, essential for practical statistics for machine learning. 
  • Probabilistic Algorithms: Understand the math behind models such as regression, classification, and unsupervised learning, as well as Markov.
Download Course Outline

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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Data science professionals, machine learning engineers, & anyone who wants to gain a deep understanding of the statistical mathematics underlying AI algorithms, such as neural networks and generative models.

You will master essential topics such as maximum likelihood estimation, hypothesis testing, & probabilistic models for regression & classification, which are important for robust statistics in machine learning.

Absolutely. It covers both the theory & hands-on implementation of concepts like Bayesian methods, Gaussian distributions, and hypothesis testing using data, which makes it perfect for a data science program.

This program is specially designed for AI, directly linking core concepts such as Bias-variance trade-off and Markov processes to modern machine learning techniques, offering you a distinct advantage in statistics for AI. Your true math for machine learning mastery starts here.

Ready to Master the Math for Machine Learning & AI?

  Transform the complex theories into real-world AI solutions with the comprehensive statistics course.

$167.99

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