Self-study course: approximate and scalable inference for complex probabilistic models in recommender systems. part 2: scalable aproximate inference session 1: variational inference

1. Part 2: Scalable Approximate Inference
Session 1:
- Variational Inference
Session 2:
- Sampling methods
Approximate and Scalable Inference for Complex
Probabilistic Models in Recommender Systems

2. Introduction

3. Motivation: bayesian mixture model

4. Main idea

5. KL-Divergence
KL of the posterior

6. KL-Divergence

7. ELBO e KL-Divergence
Jensen inequality
concave (log)
KL of the posterior
Evidence lower
bound (ELBO)
+
+

8. KL and ELBO
Choose family of variational distributions such that the
expectations of log(q(z)) and log(p(x,z)) are
computable

9. Mean-field

10. Optimizing a functional
Euler-lagrange equation

11. Mean-field

13. Structured variational inference