Maximum A Posteriori Estimate (MAP) for Bernoulli | Derivation & 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.

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.

-------

-------

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

[Mrtmm]

This was perfect explanation that I needed. Thankyou infinitely for the derivation :D

[edizferitkula]

Awsome video, thank you very much. I have been watching videos about this topic and this one was the best explanation by far.

[vipingautam]

hi what does theta raise to power "i" implies here...would be helpful if you could explain sorry for this silly question.