Multinomial Distribution | Intuition & Introduction | example in TensorFlow Probability

Video Description

You observe 2 out 7 days cloudy, 1 out of 7 days rainy, 4 out of 7 days sunny weather. The Multinomial helps us to calculate the probability of that. Here are the notes: https://raw.githubusercontent.com/Ceyron/machine-learning-and-simulation/main/english/essential_pmf_pdf/multinomial_intro.pdf The Multinomial Distribution is the natural extension of the Binomial Distribution for collection of discrete observations. Similarly, to the Categorical generalizing the Bernoulli, the Multinomial considers discrete random variables that can take more than 3 states (think of the weather which, for instance, can be cloudy, rainy, sunny). In general, there are multiple paths/sequences of observing certain weather combinations. The Multinomial will consider all of them by the help of the Multinomial coefficient, which itself is also just a generalization of the Binomial coefficient. In this video, I provide an intuition to this distribution. We then derive the probability mass function (=pmf). Lastly, we see how to use the Multinomial distribution in TensorFlow Probability. ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-learning-and-simulation 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff: https://www.linkedin.com/in/felix-koehler and https://twitter.com/felix_m_koehler 💸 : If you want to support my work on the channel, you can become a Patreon here: https://www.patreon.com/MLsim ------- Timestamps 00:00 Introduction 00:43 Motivation and Naive Approach 02:12 Multiple Paths/Sequences 03:55 Constructing the pmf 05:21 Confusion Multinomial and Categorical 05:41 Encoding Multinomial Events 07:15 The pmf 08:29 Parameters of the Multinomial 09:02 Restrictions 09:54 What a dataset looks like 10:22 TFP: Creating a Multinomial 10:57 TFP: Sampling the Multinomial 11:11 TFP: Querying the probability 12:25 Outro As an Amazon Associate I earn from qualifying purchases.