EM Algorithm
[Variational Inference](https://texonom.com/variational-inference-05563e34ddec467c95c9bda931770d50) 


## **Expectation Maximization Method**
iterative algorithm that has two main steps
![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F4b910c41-80ad-45d4-a933-e9c550f4e282%2FUntitled.png?table=block&id=6e1f4715-426b-4168-9c91-b30d6f6d292e&cache=v2)
## Until Convergence
### E Step ([ELBO](https://texonom.com/elbo-bb7352bbce42480298d501c2ae1076d1), ‣)
**calculates the expected complete log likelihood with posterior for fixed parameters**
**That is why Expectation maximization because It is same to maximize expectation **$**E[logp]**$
calculates the expected complete-data log-likelihood for fixed parameters A and Σ
각 데이터 포인트가 어떤 분포에서 생성되었는지에 대한 확률을 추정
$$l(\theta) \ge ELBO(x^{(i)};Q_i, \theta) = $$


### M Step
re-estimates next step’s fixed parameters to maximizing the expected complete-data log-likelihood (derivative)
확률과 함께 모델 파라미터를 업데이트
$$\theta := argmax_\theta $$





> [ML simple works - A Step by Step Introduction to EM Algorithm](https://metamath1.github.io/blog/posts/em/em_algorithm.html)






