Math 0-1: Probability For Data Science & Machine Learning

Math 0-1: Probability For Data Science & Machine Learning
Published 9/2024
MP4 | Video: h264, 1920×1080 | Audio: AAC, 44.1 KHz

What you’ll learn

Conditional probability, Independence, and Bayes’ Rule

Use of Venn diagrams and probability trees to visualize probability problems

Cumulative distribution functions (CDFs), probability mass functions (PMFs), probability density functions (PDFs)

Joint, marginal, and conditional distributions

Skewness, kurtosis, and moments

Moment generating functions (MGF) and characteristic functions

Convergence in probability, convergence in distribution, almost sure convergence

Law of large numbers and the Central Limit Theorem (CLT)

Applications of probability in machine learning, data science, and reinforcement learning

Requirements

Description

Overview

Section 1: Welcome

Lecture 1 Introduction

Lecture 2 Outline

Lecture 3 How to Succeed in this Course

Section 2: Probability Basics

Lecture 4 What Is Probability?

Lecture 5 Wrong Definition of Probability (Common Mistake)

Lecture 6 Wrong Definition of Probability (Example)

Lecture 7 Probability Models

Lecture 8 Venn Diagrams

Lecture 9 Properties of Probability Models

Lecture 10 Union Example

Lecture 11 Law of Total Probability

Lecture 12 Conditional Probability

Lecture 13 Bayes’ Rule

Lecture 14 Bayes’ Rule Example

Lecture 15 Independence

Lecture 16 Mutual Independence Example

Lecture 17 Probability Tree Diagrams

Lecture 19 The Bernoulli Distribution

Lecture 20 The Categorical Distribution

Lecture 21 The Binomial Distribution

Lecture 22 The Geometric Distribution

Lecture 23 The Poisson Distribution

Lecture 25 Physics Analogy

Lecture 26 More About Continuous Distributions

Lecture 27 The Uniform Distribution

Lecture 28 The Exponential Distribution

Lecture 29 The Normal Distribution (Gaussian Distribution)

Lecture 30 The Laplace (Double Exponential) Distribution

Lecture 31 Cumulative Distribution Function (CDF)

Lecture 32 Exercise: CDF of Geometric Distribution

Lecture 34 Exercise: CDF of Normal Distribution

Lecture 37 Joint and Marginal Distributions pt 1

Lecture 38 Joint and Marginal Distributions pt 2

Lecture 40 Conditional Distributions and Bayes’ Rule

Lecture 41 Independence

Lecture 45 Multinomial Distribution

Section 6: Expectation and Expected Values

Lecture 52 Expected Value and Mean

Lecture 53 Properties of the Expected Value

Lecture 59 Moments, Skewness and Kurtosis

Lecture 60 Exercise: Kurtosis of Normal Distribution

Lecture 63 Exercise: Zero Correlation Does Not Imply Independence

Lecture 64 Exercise: Correlation Measures Linear Relationships

Lecture 65 Conditional Expectation pt 1

Lecture 66 Conditional Expectation pt 2

Lecture 67 Law of Total Expectation

Lecture 68 Exercise: Linear Combination of Normals

Section 7: Generating Functions

Lecture 70 Moment Generating Functions (MGF)

Lecture 71 Exercise: MGF of Exponential

Lecture 72 Exercise: MGF of Normal

Lecture 73 Characteristic Functions

Lecture 74 Exercise: MGF Doesn’t Exist

Lecture 75 Exercise: Characteristic Function of Normal

Lecture 79 Moment Generating Functions for Random Vectors

Lecture 80 Characteristic Functions for Random Vectors

Lecture 81 Exercise: Weighted Sums of Normals

Section 8: Inequalities

Lecture 82 Monotonicity

Lecture 83 Markov Inequality

Lecture 84 Chebyshev Inequality

Section 9: Limit Theorems

Lecture 86 Convergence In Probability

Lecture 87 Weak Law of Large Numbers

Lecture 88 Convergence With Probability 1 (Almost Sure Convergence)

Lecture 89 Strong Law of Large Numbers

Lecture 90 Application: Frequentist Perspective Revisited

Lecture 91 Convergence In Distribution

Lecture 92 Central Limit Theorem

Section 10: Advanced and Other Topics

Lecture 93 The Gamma Distribution

Lecture 94 The Beta Distribution