Maximum A Posteriori Estimate (MAP) for Bernoulli: Derivation and Implementation with TensorFlow Probability

In this video, we derive the Maximum A Posteriori Estimate (MAP). This estimate is not only based on the dataset, but also prior knowledge encoded in terms of the hyperparameter of the prior distribution over the parameters. It is therefore more robust against corrupt, noisy or incomplete data, but requires expert knowledge on the choice of the hyperparameters.

You can find the notes here: https://raw.githubusercontent.com/Ceyron/machine-learning-and-simulation/main/english/essential_pmf_pdf/bernoulli_maximum_a_posteriori_estimate.pdf

After the derivation, we then check our results in TensorFlow Probability with a clean and a corrupt dataset. In both cases, our informed MAP is superior over the uninformed MLE.

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📝 : 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

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Timestamps:
0:00 Opening
0:17 Intro
03:31 MLE vs MAP
07:20 Posterior
11:48 Log-Posterior
15:07 Maximizing the Log-Posterior
22:08 TensorFlow Probability