Variational Inference - Deriving ELBO

This post describes two approaches for deriving the Expected Lower Bound (ELBO) used in variational inference. Let us begin with a little bit of motivation. Consider a probabilistic model where we are interested in maximizing the marginal likelihood $p(X)$ for which direct optimization is difficult, but optimizing complete-data likelihood $p(X, Z)$ is significantly easier. In a bayesian setting, we condition on the data $X$ and compute the posterior distribution $p(Z | X)$ over the latent variables given our observed data.

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Visualizing TensorFlow Graphs in Jupyter Notebooks

TensorFlow operations form a computation graph. And while for small examples you might be able to look at the code and immediately see what is going on, larger computation graphs might not be so obvious. Visualizing the graph can help both in diagnosing issues with the computation itself, but also in understanding how certain operations in TensorFlow work and how are things put together.