Multinomial Distribution | Intuition & Introduction | example in TensorFlow Probability

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.

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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.

[longfellowrose]

In 7:15 of this video, the k is [2, 8, 23], but n=31, it should be 33😉

[ЕкатеринаК-хът]

Thank you for the video, especially for examples with tfp)

[orjihvy]

The explanation on number of path was really helpful.

[orjihvy]

Is that a bug why tensor flow probability didn’t raise an error?