From e77257c776781fe943e23d044ef534d0b21e2241 Mon Sep 17 00:00:00 2001
From: Shine wOng <1551885@tongji.edu.cn>
Date: Wed, 8 Jan 2020 21:46:16 +0800
Subject: [PATCH] modify tex formulas.

---
 ml/linear regression/linear regression.md | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

diff --git a/ml/linear regression/linear regression.md b/ml/linear regression/linear regression.md
index 4b11fcb..433fbb1 100644
--- a/ml/linear regression/linear regression.md	
+++ b/ml/linear regression/linear regression.md	
@@ -79,8 +79,7 @@ $$
 因此可以写出似然函数$L(\theta)$
 
 $$
-L(\theta) = \Pi_{i = 1}^m f(y^{(i)}|x^{(i)}) = (\frac{1}{\sqrt{2\pi}\sigma})^m\cdot e^{-\frac{1}{2\sigma^2}\Sigma_{i = 1}^m (y^{(i)} - \theta^Tx^{(i)})^2}\\
-
+L(\theta) = \Pi_{i = 1}^m f(y^{(i)}|x^{(i)}) = (\frac{1}{\sqrt{2\pi}\sigma})^m\cdot e^{-\frac{1}{2\sigma^2}\Sigma_{i = 1}^m (y^{(i)} - \theta^Tx^{(i)})^2}\\\
 lnL(\theta) = -mln(\sqrt{2\pi}\sigma) - \frac{1}{2\sigma^2}\Sigma_{i = 1}^m(y^{(i)} - \theta^Tx^{(i)})^2
 $$
 
@@ -169,11 +168,8 @@ $$
 H = \frac{1}{m}\left[
 	\begin{matrix}
 		\Sigma_{i = 1}^mx_0^{(i)^2} & \Sigma_{i = 1}^mx_0^{(i)}x_1^{(i)} & \cdots & \Sigma_{i = 1}^mx_0^{(i)}x_n^{(i)}\\
-		
-		\Sigma_{i = 1}^mx_1^{(i)}x_0^{(i)} & \Sigma_{i = 1}^mx_1^{(i)^2} & \cdots & \Sigma_{i = 1}^mx_1^{(i)}x_n^{(i)}\\
-		
-		\vdots & \vdots &  & \vdots&\\
-		
+		\Sigma_{i = 1}^mx_1^{(i)}x_0^{(i)} & \Sigma_{i = 1}^mx_1^{(i)^2} & \cdots & \Sigma_{i = 1}^mx_1^{(i)}x_n^{(i)}\\	
+		\vdots & \vdots &  & \vdots&\\	
 		\Sigma_{i = 1}^mx_n^{(i)}x_0^{(i)} & \Sigma_{i = 1}^mx_n^{(i)}x_1^{(i)} & \cdots & \Sigma_{i = 1}^mx_n^{(i)^2}\\
 	\end{matrix}
 \right]