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Part 2: Scalable Approximate Inference
Session 1:
- Variational Inference
Session 2:
- Sampling methods
Approximate and Scalable Inference for Complex
Probabilistic Models in Recommender Systems
Introduction
Motivation: bayesian mixture model
Main idea
KL-Divergence
KL of the posterior
KL-Divergence
ELBO e KL-Divergence
Jensen inequality
concave (log)
KL of the posterior
Evidence lower
bound (ELBO)
+
+
KL and ELBO
Choose family of variational distributions such that the
expectations of log(q(z)) and log(p(x,z)) are
computable
Mean-field
Optimizing a functional
Euler-lagrange equation
Mean-field
Variational Inference
Structured variational inference

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Variational Inference