Machine Learning and Optimization
- Machine learning models optimize the function by minimizing the loss
- The process of optimizaion for the machine learning function represents learning
Linear Regression
- Basic machine learning and statistical analysis method which assumes the linear relationship between input and output
- We estimate the optimal coefficients to minimize the loss function
![](https://velog.velcdn.com/images/psy4072/post/19a3af3f-55da-4b50-9e53-42a2c988febf/image.png)
- Linear regression is one of the basic and fundamental machine learning methods
![](https://velog.velcdn.com/images/psy4072/post/1ea46664-04a0-491b-bffd-74dc84ed31f1/image.png)
![](https://velog.velcdn.com/images/psy4072/post/105acff1-4946-4eba-99d7-d15b3845f1ad/image.png)
![](https://velog.velcdn.com/images/psy4072/post/8e3509c3-6af0-4679-b90d-564d3e0d3fe8/image.png)
➡️ y = 2x
➡️ Learning is Optimization !!
Loss Function of Neural Networks
![](https://velog.velcdn.com/images/psy4072/post/ee40eaa2-a86a-4399-8aae-72fbc0e48b01/image.png)
Iterative Algorithm-based Optimization
Gradient Descent
![](https://velog.velcdn.com/images/psy4072/post/b0535f8b-8282-4fb4-9177-853aa4bf4a97/image.png)
- loss 최소 부분을 찾는 것이 머신러닝의 핵심
![](https://velog.velcdn.com/images/psy4072/post/447579b0-427e-4a25-b116-4f5957add0ae/image.png)
등고선 Contour
- 3차원 -> 2차원
![](https://velog.velcdn.com/images/psy4072/post/341a4399-c816-4237-8fa8-9e771a17f883/image.png)
경사 하강법 심화
Learning Rate
![](https://velog.velcdn.com/images/psy4072/post/9051d240-0d82-4186-ab56-26c5899d1b53/image.png)
- Learning Rate 를 적절하게 책정해야 한다.
- 너무 작아도 문제, 너무 커도 문제
![](https://velog.velcdn.com/images/psy4072/post/0d5d9948-f4b0-4bee-ab54-74e70abe077f/image.png)
Stochastic Gradient Descent
- Consider minimizing an average of functions
![](https://velog.velcdn.com/images/psy4072/post/4de09b73-e563-4ffe-a519-3251c473fdda/image.png)
Global vs Local Minimum
![](https://velog.velcdn.com/images/psy4072/post/af125e30-73ba-4275-9f97-8e7fc1b1f9d8/image.png)
Momentum
![](https://velog.velcdn.com/images/psy4072/post/877be8fc-f49e-426d-ab1a-7fdd953150e3/image.png)
reference : K-MOOC 실습으로 배우는 머신러닝