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Fix the invalid hyperlink in 09-05-03 Example: FISTA #204

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Expand Up @@ -16,7 +16,8 @@ owner: "Kyeongmin Woo"

> $$\min_\beta \frac{1}{2} \lVert y−X\beta \rVert_2^2 + \lambda \lVert \beta \rVert_1$$
그리고, ISTA의 정의도 기억해 보자. $$S_\lambda (·)$$는 vector soft-thresholding일 떄 Proximal gradient update가 다음과 같이 정의되었었다. ([09-01 Proximal gradient descent](chapter09/2020/01/08/09_01_proximal_gradient_descent/) 참조)
그리고, ISTA의 정의도 기억해 보자. $$S_\lambda (·)$$는 vector soft-thresholding일 떄 Proximal gradient update가 다음과 같이 정의되었었다.
([09-01 Proximal gradient descent]({% post_url contents/chapter09/20-01-08-09_01_proximal_gradient_descent %}) 참조)
> $$\beta^{(k)} = S_{\lambda t_k} (\beta^{(k−1)} + t_kX^T(y − X\beta^{(k−1)})), k = 1,2,3,...$$
이 식에 acceleration을 적용하면 $$\beta$$ 대신에 $$v$$를 계산해서 proximal gradient update를 한다.
Expand All @@ -43,4 +44,4 @@ owner: "Kyeongmin Woo"
</figure>


100가지의 샘플을 토대로 Lasso regression, lasso logistic regression 에 대해 평균을 낸 결과, $$k$$값이 증가할수록 FISTA 기법이 훨씬 더 빠르게 수렴하는 것을 확인할 수 있다.
100가지의 샘플을 토대로 Lasso regression, lasso logistic regression 에 대해 평균을 낸 결과, $$k$$값이 증가할수록 FISTA 기법이 훨씬 더 빠르게 수렴하는 것을 확인할 수 있다.