Probability & Statistics for Machine Learning & Data Science

Probability & Statistics for Machine Learning & Data Science

This course is part of Mathematics for Machine Learning and Data Science Specialization

Instructor: Luis Serrano

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113,086 already enrolled

4 modules

Gain insight into a topic and learn the fundamentals.

686 reviews

Intermediate level

Recommended experience

Flexible schedule

3 weeks at 10 hours a week

Learn at your own pace

93%

Most learners liked this course

4 modules

Gain insight into a topic and learn the fundamentals.

686 reviews

Intermediate level

Recommended experience

Flexible schedule

3 weeks at 10 hours a week

Learn at your own pace

93%

Most learners liked this course

What you'll learn

Describe and quantify the uncertainty inherent in predictions made by machine learning models
Visually and intuitively understand the properties of commonly used probability distributions in machine learning and data science
Apply common statistical methods like maximum likelihood estimation (MLE) and maximum a priori estimation (MAP) to machine learning problems
Assess the performance of machine learning models using interval estimates and margin of errors

Skills you'll gain

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Assessments

8 assignments

Taught in English

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This course is part of the Mathematics for Machine Learning and Data Science Specialization

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There are 4 modules in this course

Newly updated for 2024! Mathematics for Machine Learning and Data Science is a foundational online program created by DeepLearning.AI and taught by Luis Serrano. In machine learning, you apply math concepts through programming. And so, in this specialization, you’ll apply the math concepts you learn using Python programming in hands-on lab exercises. As a learner in this program, you'll need basic to intermediate Python programming skills to be successful.

After completing this course, you will be able to: • Describe and quantify the uncertainty inherent in predictions made by machine learning models, using the concepts of probability, random variables, and probability distributions. • Visually and intuitively understand the properties of commonly used probability distributions in machine learning and data science like Bernoulli, Binomial, and Gaussian distributions • Apply common statistical methods like maximum likelihood estimation (MLE) and maximum a priori estimation (MAP) to machine learning problems • Assess the performance of machine learning models using interval estimates and margin of errors • Apply concepts of statistical hypothesis testing to commonly used tests in data science like AB testing • Perform Exploratory Data Analysis on a dataset to find, validate, and quantify patterns. Many machine learning engineers and data scientists need help with mathematics, and even experienced practitioners can feel held back by a lack of math skills. This Specialization uses innovative pedagogy in mathematics to help you learn quickly and intuitively, with courses that use easy-to-follow visualizations to help you see how the math behind machine learning actually works. We recommend you have a high school level of mathematics (functions, basic algebra) and familiarity with programming (data structures, loops, functions, conditional statements, debugging). Assignments and labs are written in Python but the course introduces all the machine learning libraries you’ll use.

In this week, you will learn about probability of events and various rules of probability to correctly do arithmetic with probabilities. You will learn the concept of conditional probability and the key idea behind Bayes theorem. In lesson 2, we generalize the concept of probability of events to probability distribution over random variables. You will learn about some common probability distributions like the Binomial distribution and the Normal distribution.

What's included

30 videos9 readings2 assignments1 programming assignment4 ungraded labs

30 videosTotal 151 minutes

Course Introduction5 minutes
A note on programming experience1 minute
What is Probability?6 minutes
What is Probability? - Dice Example1 minute
Complement of Probability4 minutes
Sum of Probabilities (Disjoint Events)5 minutes
Sum of Probabilities (Joint Events)8 minutes
Independence7 minutes
Birthday problem5 minutes
Conditional Probability - Part 18 minutes
Conditional Probability - Part 27 minutes
Bayes Theorem - Intuition6 minutes
Bayes Theorem - Mathematical Formula6 minutes
Bayes Theorem - Spam example5 minutes
Bayes Theorem - Prior and Posterior3 minutes
Bayes Theorem - The Naive Bayes Model5 minutes
Probability in Machine Learning6 minutes
Random Variables7 minutes
Probability Distributions (Discrete)4 minutes
Binomial Distribution6 minutes
(Optional) Binomial Coefficient5 minutes
Bernoulli Distribution1 minute
Probability Distributions (Continuous)5 minutes
Probability Density Function6 minutes
Cumulative Distribution Function8 minutes
Uniform Distribution5 minutes
Normal Distribution8 minutes
(Optional) Chi-Squared Distribution3 minutes
Sampling from a Distribution5 minutes
Week 1 - Conclusion0 minutes

9 readingsTotal 92 minutes

Join the DeepLearning.AI Forum to ask questions, get support, or share amazing ideas!2 minutes
Check your knowledge10 minutes
Learning Python: Recommended Resources10 minutes
Interactive Tool: Repeated Experiments15 minutes
Interactive Tool: Relationship between PMF/PDF and CDF of some distributions15 minutes
(Optional) Common Coursera Labs Operations10 minutes
(Optional) Assignment Troubleshooting Tips10 minutes
(Optional) Partial Grading for Assignments10 minutes
Week 1 - Slides10 minutes

2 assignmentsTotal 45 minutes

Week 1 - Practice Quiz15 minutes
Week 1 - Summative quiz30 minutes

1 programming assignmentTotal 240 minutes

Naive Bayes240 minutes

4 ungraded labsTotal 240 minutes

Four Birthday Problems60 minutes
Monty Hall Problem60 minutes
Exploratory Data Analysis - Intro to Pandas60 minutes
Exploratory Data Analysis - Exploring Your Data60 minutes

This week you will learn about different measures to describe probability distributions as well as any dataset. These include measures of central tendency (mean, median, and mode), variance, skewness, and kurtosis. The concept of the expected value of a random variable is introduced to help you understand each of these measures. You will also learn about some visual tools to describe data and distributions. In lesson 2, you will learn about the probability distribution of two or more random variables using concepts like joint distribution, marginal distribution, and conditional distribution. You will end the week by learning about covariance: a generalization of variance to two or more random variables.

What's included

27 videos2 readings2 assignments1 programming assignment3 ungraded labs

27 videosTotal 141 minutes

Expected Value11 minutes
Other measures of central tendency: median and mode6 minutes
Expected value of a Function4 minutes
Sum of expectations7 minutes
Variance11 minutes
Standard Deviation4 minutes
Sum of Gaussians3 minutes
Standardizing a Distribution4 minutes
Skewness and Kurtosis: Moments of a Distribution2 minutes
Skewness and Kurtosis - Skewness8 minutes
Skewness and Kurtosis - Kurtosis7 minutes
Quantiles and Box-Plots3 minutes
Visualizing data: Box-Plots3 minutes
Visualizing data: Kernel density estimation2 minutes
Visualizing data: Violin Plots1 minute
Visualizing data: QQ plots2 minutes
Joint Distribution (Discrete) - Part 15 minutes
Joint Distribution (Discrete) - Part 25 minutes
Joint Distribution (Continuous)5 minutes
Marginal and Conditional Distribution7 minutes
Conditional Distribution5 minutes
Covariance of a Dataset10 minutes
Covariance of a Probability Distribution11 minutes
Covariance Matrix2 minutes
Correlation Coefficient5 minutes
Multivariate Gaussian Distribution6 minutes
Week 2 - Conclusion0 minutes

2 readingsTotal 25 minutes

Interactive Tool: Mean, median and standard deviation15 minutes
Week 2 - Slides10 minutes

2 assignmentsTotal 60 minutes

Week 2 - Practice Quiz30 minutes
Week 2 - Summative Quiz30 minutes

1 programming assignmentTotal 100 minutes

Loaded Dice100 minutes

3 ungraded labsTotal 180 minutes

Summary statistics and visualization of data sets60 minutes
Exploratory Data Analysis - Data Visualization and Summary Statistics60 minutes
Simulating Dice Rolls with Numpy (helper for the assignment, not necessary and not graded)60 minutes

This week shifts its focus from probability to statistics. You will start by learning the concept of a sample and a population and two fundamental results from statistics that concern samples and population: the law of large numbers and the central limit theorem. In lesson 2, you will learn the first and the simplest method of estimation in statistics: point estimation. You will see how maximum likelihood estimation, the most common point estimation method, works and how regularization helps prevent overfitting. You'll then learn how Bayesian Statistics incorporates the concept of prior beliefs into the way data is evaluated and conclusions are reached.

What's included

20 videos3 readings2 assignments2 ungraded labs

20 videosTotal 99 minutes

Population and Sample6 minutes
Sample Mean3 minutes
Sample Proportion2 minutes
Sample Variance11 minutes
Law of Large Numbers4 minutes
Central Limit Theorem - Discrete Random Variable3 minutes
Central Limit Theorem - Continuous Random Variable8 minutes
Point Estimation1 minute
Maximum Likelihood Estimation: Motivation 3 minutes
MLE: Bernoulli Example5 minutes
MLE: Gaussian Example6 minutes
MLE: Linear Regression6 minutes
Regularization3 minutes
Back to "Bayesics"3 minutes
Bayesian Statistics - Frequentist vs. Bayesian3 minutes
Bayesian Statistics - MAP5 minutes
Bayesian Statistics - Updating Priors9 minutes
Bayesian Statistics - Full Worked Example11 minutes
Relationship between MAP, MLE and Regularization6 minutes
Week 3 - Conclusion0 minutes

3 readingsTotal 35 minutes

MLE for Gaussian population10 minutes
Interactive Tool: Likelihood Functions15 minutes
Week 3 - Slides10 minutes

2 assignmentsTotal 90 minutes

Week 3 - Practice Quiz30 minutes
Week 3 - Summative Quiz60 minutes

2 ungraded labsTotal 120 minutes

Sampling data from different distribution and studying the distribution of sample mean60 minutes
Exploratory Data Analysis - Linear Regression60 minutes

This week you will learn another estimation method called interval estimation. The most common interval estimates are confidence intervals and you will see how they are calculated and how to correctly interpret them. In lesson 2, you will learn about hypothesis testing where estimates are formulated as a hypothesis and then tested in the presence of available evidence or a sample of data. You will learn the concept of p-value that helps in making a decision about a hypothesis test and also learn some common tests like the t-test, two-sample t-test, and the paired t-test. You will end the week with an interesting application of hypothesis testing in data science: A/B testing.