Variational Inference | Evidence Lower Bound (ELBO) | Intuition & Visualization

Published on April 7, 2022

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In real-world applications, the posterior over the latent variables Z given some data D is usually intractable. But we can use a surrogate that is close to it. How do we optimize for it? Here are the notes: https://raw.githubusercontent.com/Ceyron/machine-learning-and-simulation/main/english/probabilistic_machine_learning/vi_and_elbo.pdf

Here is the link to the interactive elbo plot: https://share.streamlit.io/ceyron/machine-learning-and-simulation/main/english/probabilistic_machine_learning/elbo_interactive_plot.py

If you want to run the Python script yourself which requires you to have streamlit, plotly and TensorFlow Probability installed, you can find it here: https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/probabilistic_machine_learning/elbo_interactive_plot.py

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đź“ť : 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

đź“˘ : 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

đź’¸ : If you want to support my work on the channel, you can become a Patreon here: https://www.patreon.com/MLsim

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Timestamps:
00:00 Introduction
00:54 Problem of intractable posteriors
02:10 Fixing the observables X
02:29 The “inference” in variational inference
03:29 The problem of the marginal
05:06 Remedy: A Surrogate Posterior
06:11 The “variational” in variational inference
06:38 Optimizing the surrogate
08:47 Recap: The KL divergence
09:42 We still don’t know the posterior
10:35 Deriving the ELBO
15:17 Discussing the ELBO
17:59 Defining the ELBO explicitly
18:24 When the ELBO equals the evidence
18:56 Equivalent optimization problems
20:38 Rearranging for the ELBO
21:08 Plot: Intro
22:32 Plot: Adjusting the Surrogate
24:02 Summary & Outro

Hidden Divergence Stochastic, Variational Inference | Evidence Lower Bound (ELBO) | Intuition & Visualization.

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