Probability & Statistics for Machine Learning & Data Science
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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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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
- Sampling (Statistics)
- Statistical Hypothesis Testing
- Bayesian Statistics
- Statistics
- Statistical Visualization
- Statistical Machine Learning
- Data Science
- Histogram
- Probability Distribution
- Statistical Analysis
- Probability & Statistics
- Probability
- Box Plots
- Statistical Methods
- Exploratory Data Analysis
- Descriptive Statistics
- Statistical Inference
- Correlation Analysis
- A/B Testing
Details to know
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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 videos•Total 151 minutes
- Course Introduction•5 minutes
- A note on programming experience•1 minute
- What is Probability?•6 minutes
- What is Probability? - Dice Example•1 minute
- Complement of Probability•4 minutes
- Sum of Probabilities (Disjoint Events)•5 minutes
- Sum of Probabilities (Joint Events)•8 minutes
- Independence•7 minutes
- Birthday problem•5 minutes
- Conditional Probability - Part 1•8 minutes
- Conditional Probability - Part 2•7 minutes
- Bayes Theorem - Intuition•6 minutes
- Bayes Theorem - Mathematical Formula•6 minutes
- Bayes Theorem - Spam example•5 minutes
- Bayes Theorem - Prior and Posterior•3 minutes
- Bayes Theorem - The Naive Bayes Model•5 minutes
- Probability in Machine Learning•6 minutes
- Random Variables•7 minutes
- Probability Distributions (Discrete)•4 minutes
- Binomial Distribution•6 minutes
- (Optional) Binomial Coefficient•5 minutes
- Bernoulli Distribution•1 minute
- Probability Distributions (Continuous)•5 minutes
- Probability Density Function•6 minutes
- Cumulative Distribution Function•8 minutes
- Uniform Distribution•5 minutes
- Normal Distribution•8 minutes
- (Optional) Chi-Squared Distribution•3 minutes
- Sampling from a Distribution•5 minutes
- Week 1 - Conclusion•0 minutes
9 readings•Total 92 minutes
- Join the DeepLearning.AI Forum to ask questions, get support, or share amazing ideas!•2 minutes
- Check your knowledge•10 minutes
- Learning Python: Recommended Resources•10 minutes
- Interactive Tool: Repeated Experiments•15 minutes
- Interactive Tool: Relationship between PMF/PDF and CDF of some distributions•15 minutes
- (Optional) Common Coursera Labs Operations•10 minutes
- (Optional) Assignment Troubleshooting Tips•10 minutes
- (Optional) Partial Grading for Assignments•10 minutes
- Week 1 - Slides•10 minutes
2 assignments•Total 45 minutes
- Week 1 - Summative quiz•30 minutes
- Week 1 - Practice Quiz•15 minutes
1 programming assignment•Total 240 minutes
- Naive Bayes•240 minutes
4 ungraded labs•Total 240 minutes
- Four Birthday Problems•60 minutes
- Monty Hall Problem•60 minutes
- Exploratory Data Analysis - Intro to Pandas•60 minutes
- Exploratory Data Analysis - Exploring Your Data•60 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 videos•Total 141 minutes
- Expected Value•11 minutes
- Other measures of central tendency: median and mode•6 minutes
- Expected value of a Function•4 minutes
- Sum of expectations•7 minutes
- Variance•11 minutes
- Standard Deviation•4 minutes
- Sum of Gaussians•3 minutes
- Standardizing a Distribution•4 minutes
- Skewness and Kurtosis: Moments of a Distribution•2 minutes
- Skewness and Kurtosis - Skewness•8 minutes
- Skewness and Kurtosis - Kurtosis•7 minutes
- Quantiles and Box-Plots•3 minutes
- Visualizing data: Box-Plots•3 minutes
- Visualizing data: Kernel density estimation•2 minutes
- Visualizing data: Violin Plots•1 minute
- Visualizing data: QQ plots•2 minutes
- Joint Distribution (Discrete) - Part 1•5 minutes
- Joint Distribution (Discrete) - Part 2•5 minutes
- Joint Distribution (Continuous)•5 minutes
- Marginal and Conditional Distribution•7 minutes
- Conditional Distribution•5 minutes
- Covariance of a Dataset•10 minutes
- Covariance of a Probability Distribution•11 minutes
- Covariance Matrix•2 minutes
- Correlation Coefficient•5 minutes
- Multivariate Gaussian Distribution•6 minutes
- Week 2 - Conclusion•0 minutes
2 readings•Total 25 minutes
- Interactive Tool: Mean, median and standard deviation•15 minutes
- Week 2 - Slides•10 minutes
2 assignments•Total 60 minutes
- Week 2 - Summative Quiz•30 minutes
- Week 2 - Practice Quiz•30 minutes
1 programming assignment•Total 100 minutes
- Loaded Dice•100 minutes
3 ungraded labs•Total 180 minutes
- Summary statistics and visualization of data sets•60 minutes
- Exploratory Data Analysis - Data Visualization and Summary Statistics•60 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 videos•Total 99 minutes
- Population and Sample•6 minutes
- Sample Mean•3 minutes
- Sample Proportion•2 minutes
- Sample Variance•11 minutes
- Law of Large Numbers•4 minutes
- Central Limit Theorem - Discrete Random Variable•3 minutes
- Central Limit Theorem - Continuous Random Variable•8 minutes
- Point Estimation•1 minute
- Maximum Likelihood Estimation: Motivation •3 minutes
- MLE: Bernoulli Example•5 minutes
- MLE: Gaussian Example•6 minutes
- MLE: Linear Regression•6 minutes
- Regularization•3 minutes
- Back to "Bayesics"•3 minutes
- Bayesian Statistics - Frequentist vs. Bayesian•3 minutes
- Bayesian Statistics - MAP•5 minutes
- Bayesian Statistics - Updating Priors•9 minutes
- Bayesian Statistics - Full Worked Example•11 minutes
- Relationship between MAP, MLE and Regularization•6 minutes
- Week 3 - Conclusion•0 minutes
3 readings•Total 35 minutes
- MLE for Gaussian population•10 minutes
- Interactive Tool: Likelihood Functions•15 minutes
- Week 3 - Slides•10 minutes
2 assignments•Total 90 minutes
- Week 3 - Summative Quiz•60 minutes
- Week 3 - Practice Quiz•30 minutes
2 ungraded labs•Total 120 minutes
- Sampling data from different distribution and studying the distribution of sample mean•60 minutes
- Exploratory Data Analysis - Linear Regression•60 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.
What's included
22 videos8 readings2 assignments1 programming assignment1 ungraded lab
22 videos•Total 112 minutes
- Confidence Intervals - Overview•10 minutes
- Confidence Intervals - Changing the Interval•9 minutes
- Confidence Intervals - Margin of Error•10 minutes
- Confidence Intervals - Calculation Steps•1 minute
- Confidence Intervals - Example•2 minutes
- Calculating Sample Size•3 minutes
- Difference Between Confidence and Probability•2 minutes
- Unknown Standard Deviation•5 minutes
- Confidence Intervals for Proportion•4 minutes
- Defining Hypotheses•3 minutes
- Type I and Type II errors•5 minutes
- Right-Tailed, Left-Tailed, and Two-Tailed Tests•8 minutes
- p-Value•8 minutes
- Critical Values•5 minutes
- Power of a Test•6 minutes
- Interpreting Results•3 minutes
- t-Distribution•4 minutes
- t-Tests•4 minutes
- Two Sample t-Test•6 minutes
- Paired t-Test•5 minutes
- ML Application: A/B Testing•9 minutes
- Week 4 - Conclusion•0 minutes
8 readings•Total 72 minutes
- Interactive Tool: Confidence Intervals•15 minutes
- Test for proportions •10 minutes
- Two sample test for proportions•10 minutes
- [IMPORTANT] Reminder about end of access to Lab Notebooks•2 minutes
- Week 4 - Slides•10 minutes
- Acknowledgments•10 minutes
- (Optional) Opportunity to Mentor Other Learners•5 minutes
- References•10 minutes
2 assignments•Total 45 minutes
- Week 4 - Summative Quiz•30 minutes
- Week 4 - Practice Quiz•15 minutes
1 programming assignment•Total 100 minutes
- A/B Testing•100 minutes
1 ungraded lab•Total 60 minutes
- Exploratory Data Analysis - Confidence Intervals and Hypothesis Testing•60 minutes
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Reviewed on Nov 12, 2023
Very good course! Highly recommended to those who are just starting to learn mathematics for machine learning
Reviewed on May 21, 2025
It was very helpful course. It starts from the bare minimum but gradually you get to the point where you find yourself in Statistopia ???. Big applaud and thanks to Luis and also DeepLearning.AI
Reviewed on Jun 17, 2024
Very thorough and easy to comprehend approach to learning statistical and probability theory which is important foundational knowledge, not just in ML but any field of data analytics!
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