Dirichlet Distribution | Intuition & Intro | w\ example in TensorFlow Probability
The parameter to the Categorical is a vector of parameters. Can we put a distribution on it? Yes, we can. That's the Dirichlet. Here are the notes: https://raw.githubusercontent.com/Cey... The Parameter vector to the Categorical is of the dimension equal to the number of states of the Categorical. For example, we model the weather as the three states: Cloudy, Rainy or Sunny then we need a parameter (a probability) for each of the states. There are two requirements on this probability vector: (1) all entries must be chosen from the interval [0, 1] (since they are probabilities), (2) the vector's components have to sum up to one. In this video, we will see that this implies the that the D-dimensional parameter vector is distributed over a (D-1)-dimensional simplex in D dimensions. The Dirichlet describes a probability density distribution over this simplex. It is parameterized by an alpha-vector with also D-components which we can use to move the probability mass around over the simplex Here is the website I showed in the video: https://chart-studio.plotly.com/~davi... ------- 📝 : 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-lea... 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff:   / felix-koehler  and   / felix_m_koehler  💸 : If you want to support my work on the channel, you can become a Patreon here:   / mlsim  ------- Timestamps: 00:00 Introduction 00:33 Restrictions on the Parameter Vector 02:00 Visualizing 2-State Parameter Vector 05:56 Connection to the Beta Distribution 07:03 Visualizing 3-State Parameter Vector 09:25 General D-State Parameter Vector 10:37 Probability Density Function 11:56 Parameters of the Dirichlet 12:24 Plot: Exploring alpha values 15:58 TFP: Creating the Dirichlet Distribution 16:49 TFP: Sampling the Dirichlet 17:16 TFP: Querying the pdf 17:55 TF: Calculating Multivariate Beta Function 18:47 Outro
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