From 5ba9b9cb86d4c16cccbe07edc3196f7b8cf7b97a Mon Sep 17 00:00:00 2001 From: benjas <909336740@qq.com> Date: Tue, 23 Feb 2021 12:24:28 +0800 Subject: [PATCH] Add. Gradient Descent --- .../1. 线性回归原理.md | 20 +++++++++++++++--- .../assets/1614044218548.png | Bin 0 -> 22061 bytes .../assets/1614044234709.png | Bin 0 -> 62388 bytes .../assets/1614044250549.png | Bin 0 -> 5883 bytes .../assets/1614051473653.png | Bin 0 -> 28023 bytes .../assets/1614053992861.png | Bin 0 -> 9614 bytes .../assets/1614054121928.png | Bin 0 -> 123615 bytes 7 files changed, 17 insertions(+), 3 deletions(-) create mode 100644 机器学习算法理论及应用/第一章——线性回归/assets/1614044218548.png create mode 100644 机器学习算法理论及应用/第一章——线性回归/assets/1614044234709.png create mode 100644 机器学习算法理论及应用/第一章——线性回归/assets/1614044250549.png create mode 100644 机器学习算法理论及应用/第一章——线性回归/assets/1614051473653.png create mode 100644 机器学习算法理论及应用/第一章——线性回归/assets/1614053992861.png create mode 100644 机器学习算法理论及应用/第一章——线性回归/assets/1614054121928.png diff --git a/机器学习算法理论及应用/第一章——线性回归/1. 线性回归原理.md b/机器学习算法理论及应用/第一章——线性回归/1. 线性回归原理.md index 2d3681d..43de6d6 100644 --- a/机器学习算法理论及应用/第一章——线性回归/1. 线性回归原理.md +++ b/机器学习算法理论及应用/第一章——线性回归/1. 线性回归原理.md @@ -67,17 +67,25 @@ #### 似然函数的作用 -- 预测值与误差:![1613978116054](assets/1613978116054.png) -- 由于误差服从高斯分布:![1613978136136](assets/1613978136136.png) +- 预测值与误差(1):![1613978116054](assets/1613978116054.png) + + > y是真实值、x是预测值、ε误差值,现在我们要求的就是θ,它应该怎么求解 + +- 由于误差服从高斯分布(2):![1613978136136](assets/1613978136136.png) + + > 高斯分布的公式,这里我们要求的是θ,所以把θ移动到左边,变成y - θX = ε,即演变成 + - 将(1)式带入(2)式:![1613978160407](assets/1613978160407.png) + > 这里我们希望左边的x和θ组合完后,和真实值y越解决越好,即成为y的可能性越大越好 + - 似然函数:![1613978566334](assets/1613978566334.png) 解释:什么样的参数跟我们的数据组合后恰好是真实值 - 对数似然:![1613978607945](assets/1613978607945.png) - 解释:乘法难解:加法就容易了,对数里乘法可以转换成加法 + 解释:乘法难解,加法就容易了,对数里乘法可以转换成加法 - 展开化简:![1613980700874](assets/1613980700874.png) @@ -85,3 +93,9 @@ ![1613980821171](assets/1613980821171.png)(最小二乘法) +#### 参数求解 + +- 目标函数:![1614044218548](assets/1614044218548.png) +- 求偏导:![1614044234709](assets/1614044234709.png) +- 偏导等于0:![1614044250549](assets/1614044250549.png) + diff --git 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