Math 0-1: Probability For Data Science & Machine Learning
Published 9/2024
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 12.73 GB | Duration: 17h 30m
A Casual Guide for Artificial Intelligence, Deep Learning, and Python Programmers
[b]What you'll learn[/b]
Conditional probability, Independence, and Bayes' Rule
Use of Venn diagrams and probability trees to visualize probability problems
Discrete random variables and distributions: Bernoulli, categorical, binomial, geometric, Poisson
Continuous random variables and distributions: uniform, exponential, normal (Gaussian), Laplace, Gamma, Beta
Cumulative distribution functions (CDFs), probability mass functions (PMFs), probability density functions (PDFs)
Joint, marginal, and conditional distributions
Multivariate distributions, random vectors
Functions of random variables, sums of random variables, convolution
Expected values, expectation, mean, and variance
Skewness, kurtosis, and moments
Covariance and correlation, covariance matrix, correlation matrix
Moment generating functions (MGF) and characteristic functions
Key inequalities like Markov, Chebyshev, Cauchy-Schwartz, Jensen
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
[b]Requirements[/b]
College / University-level Calculus (for most parts of the course)
College / University-level Linear Algebra (for some parts of the course)
[b]Description[/b]
Common scenario: You try to get into machine learning and data science, but there's SO MUCH MATH.Either you never studied this math, or you studied it so long ago you've forgotten it all.What do you do?Well my friends, that is why I created this course.Probability is one of the most important math prerequisites for data science and machine learning. It's required to understand essentially everything we do, from the latest LLMs like ChatGPT, to diffusion models like Stable Diffusion and Midjourney, to statistics (what I like to call "probability part 2").Markov chains, an important concept in probability, form the basis of popular models like the Hidden Markov Model (with applications in speech recognition, DNA analysis, and stock trading) and the Markov Decision Process or MDP (the basis for Reinforcement Learning).Machine learning (statistical learning) itself has a probabilistic foundation. Specific models, like Linear Regression, K-Means Clustering, Principal Components Analysis, and Neural Networks, all make use of probability.In short, probability cannot be avoided!If you want to do machine learning beyond just copying library code from blogs and tutorials, you must know probability.This course will cover everything that you'd learn (and maybe a bit more) in an undergraduate-level probability class. This includes random variables and random vectors, discrete and continuous probability distributions, functions of random variables, multivariate distributions, expectation, generating functions, the law of large numbers, and the central limit theorem.Most important theorems will be derived from scratch. Don't worry, as long as you meet the prerequisites, they won't be difficult to understand. This will ensure you have the strongest foundation possible in this subject. No more memorizing "rules" only to apply them incorrectly / inappropriately in the future! This course will provide you with a deep understanding of probability so that you can apply it correctly and effectively in data science, machine learning, and beyond.Are you ready?Let's go!Suggested prerequisites:Differential calculus, integral calculus, and vector calculusLinear algebraGeneral comfort with university/collegelevel mathematics
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
Section 3: Random Variables and Probability Distributions
Lecture 18 What is a Random Variable?
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
Section 4: Continuous Random Variables and Probability Density Functions
Lecture 24 Continuous Random Variables and Continuous Distributions
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
Section 5: More About Probability Distributions and Random Variables
Lecture 31 Cumulative Distribution Function (CDF)
Lecture 32 Exercise: CDF of Geometric Distribution
Lecture 33 CDFs for Continuous Random Variables
Lecture 34 Exercise: CDF of Normal Distribution
Lecture 35 Change of Variables (Functions of Random Variables) pt 1
Lecture 36 Change of Variables (Functions of Random Variables) pt 2
Lecture 37 Joint and Marginal Distributions pt 1
Lecture 38 Joint and Marginal Distributions pt 2
Lecture 39 Exercise: Marginal of Bivariate Normal
Lecture 40 Conditional Distributions and Bayes' Rule
Lecture 41 Independence
Lecture 42 Exercise: Bivariate Normal with Zero Correlation
Lecture 43 Multivariate Distributions and Random Vectors
Lecture 44 Multivariate Normal Distribution / Vector Gaussian
Lecture 45 Multinomial Distribution
Lecture 46 Exercise: MVN to Bivariate Normal
Lecture 47 Exercise: Multivariate Normal, Zero Correlation Implies Independence
Lecture 48 Multidimensional Change of Variables (Discrete)
Lecture 49 Multidimensional Change of Variables (Continuous)
Lecture 50 Convolution From Adding Random Variables
Lecture 51 Exercise: Sums of Jointly Normal Random Variables (Optional)
Section 6: Expectation and Expected Values
Lecture 52 Expected Value and Mean
Lecture 53 Properties of the Expected Value
Lecture 54 Variance
Lecture 55 Exercise: Mean and Variance of Bernoulli
Lecture 56 Exercise: Mean and Variance of Poisson
Lecture 57 Exercise: Mean and Variance of Normal
Lecture 58 Exercise: Mean and Variance of Exponential
Lecture 59 Moments, Skewness and Kurtosis
Lecture 60 Exercise: Kurtosis of Normal Distribution
Lecture 61 Covariance and Correlation
Lecture 62 Exercise: Covariance and Correlation of Bivariate Normal
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
Lecture 69 Exercise: Mean and Variance of Weighted Sums
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 76 Sums of Independent Random Variables
Lecture 77 Exercise: Distribution of Sum of Poisson Random Variables
Lecture 78 Exercise: Distribution of Sum of Geometric Random Variables
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
Lecture 85 Cauchy-Schwartz 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
Python developers and software developers curious about Data Science,Professionals interested in Machine Learning and Data Science but haven't studied college-level math,Students interested in ML and AI but find they can't keep up with the math,Former STEM students who want to brush up on probability before learning about artificial intelligence
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