改用图片显示公式

ex1-linear regression/ex1-multiple-variables.ipynb

@@ -24,18 +24,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 代价函数"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\\begin{aligned}\n",
-    "h_\\theta(x)&= \\theta^Tx=\\theta_0+\\theta_1x_1 \\\\\n",
-    "J(\\theta)&=\\frac{1}{2m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)})^2\n",
-    "\\end{aligned}\n",
-    "$$"
+    "## 代价函数\n",
+    "\n",
+    "![](img/cost.png)"
    ]
   },
   {
@@ -54,18 +45,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 梯度下降"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\\begin{aligned}\n",
-    "\\theta_j:&=\\theta_j-\\alpha\\frac{\\partial}{\\partial\\theta_j}J(\\theta) \\\\\n",
-    "\\theta_j:&=\\theta_j-\\alpha\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}\n",
-    "\\end{aligned}\n",
-    "$$"
+    "## 梯度下降\n",
+    "\n",
+    "![](img/gradient.png)"
    ]
   },
   {

ex1-linear regression/ex1-normal-equation.ipynb

@@ -338,18 +338,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 正则方程"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\n",
-    "\\begin{aligned}\n",
-    "\\theta=(X^TX)^{-1}X^TY\n",
-    "\\end{aligned}\n",
-    "$$"
+    "## 正则方程\n",
+    "\n",
+    "![](img/regularization.png)"
    ]
   },
   {

ex1-linear regression/ex1-one-variable.ipynb

@@ -232,18 +232,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 代价函数"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\\begin{aligned}\n",
-    "h_\\theta(x)&= \\theta^Tx=\\theta_0+\\theta_1x_1 \\\\\n",
-    "J(\\theta)&=\\frac{1}{2m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)})^2\n",
-    "\\end{aligned}\n",
-    "$$"
+    "## 代价函数\n",
+    "\n",
+    "![](img/cost.png)"
    ]
   },
   {
@@ -560,18 +551,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 梯度下降"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "$$\\begin{aligned}\n",
-    "\\theta_j:&=\\theta_j-\\alpha\\frac{\\partial}{\\partial\\theta_j}J(\\theta) \\\\\n",
-    "\\theta_j:&=\\theta_j-\\alpha\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}\n",
-    "\\end{aligned}\n",
-    "$$"
+    "## 梯度下降\n",
+    "\n",
+    "![](img/gradient.png)"
    ]
   },
   {

ex2-logistic regression/ex2-logistic regression.ipynb

@@ -260,10 +260,8 @@
    "metadata": {},
    "source": [
     "## sigmoid函数\n",
-    "$$\n",
-    "h_\\theta(x)=g(\\theta^Tx) \\\\\n",
-    "g(z)=\\frac{1}{1+e^{-z}}\n",
-    "$$"
+    "\n",
+    "![](img/sigmoid.png)"
    ]
   },
   {
@@ -307,9 +305,8 @@
    "metadata": {},
    "source": [
     "## 代价函数\n",
-    "$$\n",
-    "J(\\theta) = -\\frac{1}{m}\\sum_{i=1}^{m}[y^{(i)}log(h_\\theta(x^{(i)})) + (1-y^{(i)})log(1-h_\\theta(x^{(i)}))]\n",
-    "$$"
+    "\n",
+    "![](img/cost.png)"
    ]
   },
   {
@@ -432,11 +429,9 @@
    "metadata": {},
    "source": [
     "## 梯度下降\n",
-    "$$\n",
-    "梯度下降：\\frac{\\partial J(\\theta)}{\\partial\\theta_j}=\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}) \\\\\n",
-    "向量计算：\\frac{1}{m}X^T(sigmoid(X\\theta) - y)\\\\\n",
-    "\\theta_j = \\theta_j - \\alpha\\frac{\\partial}{\\partial\\theta_j}J(\\theta)\n",
-    "$$\n",
+    "\n",
+    "![](img/gradient.png)\n",
+    "\n",
     "[偏导的推导过程](https://sanzo.top/#/post/学习笔记/机器学习?id=梯度下降)"
    ]
   },
@@ -710,14 +705,7 @@
    "source": [
     "## 决策边界\n",
     "\n",
-    "\n",
-    "$$\n",
-    "\\begin{aligned}\n",
-    "0&=X\\theta \\\\\n",
-    "0&=\\theta_0X_0 + \\theta_1X_1 + \\theta_2X_2\\\\\n",
-    "x2 &= -(\\frac{\\theta_0}{\\theta_2}x_0+\\frac{\\theta_1}{\\theta_2}x_1) \\\\\n",
-    "\\end{aligned}\n",
-    "$$"
+    "![](img/decision_boundary.png)"
    ]
   },
   {

ex2-logistic regression/ex2-regularized logistic regression.ipynb

@@ -254,32 +254,7 @@
    "source": [
     "## 特征映射\n",
     "\n",
-    "$$\n",
-    "mapFeature(x)=\n",
-    "\\begin{bmatrix}\n",
-    "x_1^0x_2^0 \\\\\n",
-    "x_1^1x_2^0 \\\\\n",
-    "x_1^0x_2^1 \\\\\n",
-    "x_1^2x_2^0 \\\\\n",
-    "x_1^1x_2^1 \\\\\n",
-    "x_1^0x_2^2 \\\\\n",
-    "\\vdots \\\\\n",
-    "x_1^1x_2^5 \\\\\n",
-    "x_1^0x_2^6 \\\\\n",
-    "\\end{bmatrix}\n",
-    "=\n",
-    "\\begin{bmatrix}\n",
-    "1 \\\\\n",
-    "x_1 \\\\\n",
-    "x_2 \\\\\n",
-    "x_1^2 \\\\\n",
-    "x_1^1x_2^1 \\\\\n",
-    "x_2^2 \\\\\n",
-    "\\vdots \\\\\n",
-    "x_1^1x_2^5 \\\\\n",
-    "x_2^6 \\\\\n",
-    "\\end{bmatrix}\n",
-    "$$"
+    "![](img/feature_map.png)"
    ]
   },
   {
@@ -826,9 +801,8 @@
    "metadata": {},
    "source": [
     "## 正则化代价函数\n",
-    "$$\n",
-    "J(\\theta) = -\\frac{1}{m}\\sum_{i=1}^{m}[y^{(i)}log(h_\\theta(x^{(i)})) + (1-y^{(i)})log(1-h_\\theta(x^{(i)}))] + \\frac{\\lambda}{2m}\\sum_{j=1}^{n}\\theta_j^2\n",
-    "$$"
+    "\n",
+    "![](img/regularized_cost.png)"
    ]
   },
   {
@@ -933,15 +907,7 @@
    "source": [
     "## 正则化梯度\n",
     "\n",
-    "$$\n",
-    "\\frac{\\partial J(\\theta)}{\\partial\\theta_j}=\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j \\\\\n",
-    "\\begin{aligned}\n",
-    "  & Repeat\\ until\\ convergence \\{ \\\\ \n",
-    "  & \\theta_0 := \\theta_0 - \\alpha \\frac{1}{m} \\sum_{i=1}^{m}\\left(h_\\theta(x^{(i)}) - y^{(i)}\\right) x_0^{(i)} \\\\\n",
-    "  & \\theta_j := \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^{m}\\left(h_\\theta(x^{(i)}) - y^{(i)}\\right) x_j^{(i)} + \\frac{\\lambda}{m}\\theta_j \\\\\n",
-    "\\}\n",
-    "\\end{aligned}\n",
-    "$$"
+    "![](img/regularized_gradient.png)"
    ]
   },
   {

ex3-neural network/ex3-neural network.ipynb

@@ -215,9 +215,7 @@
    "metadata": {},
    "source": [
     "## 代价函数\n",
-    "$$\n",
-    "J(\\theta) = -\\frac{1}{m}\\sum_{i=1}^{m}[y^{(i)}log(h_\\theta(x^{(i)})) + (1-y^{(i)})log(1-h_\\theta(x^{(i)}))] + \\frac{\\lambda}{2m}\\sum_{j=1}^{n}\\theta_j^2\n",
-    "$$"
+    "![](img/cost.png)"
    ]
   },
   {
@@ -248,15 +246,7 @@
    "metadata": {},
    "source": [
     "## 梯度函数\n",
-    "$$\n",
-    "\\frac{\\partial J(\\theta)}{\\partial\\theta_j}=\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}) + \\frac{\\lambda}{m}\\theta_j \\\\\n",
-    "\\begin{aligned}\n",
-    "  & Repeat\\ until\\ convergence \\{ \\\\ \n",
-    "  & \\theta_0 := \\theta_0 - \\alpha \\frac{1}{m} \\sum_{i=1}^{m}\\left(h_\\theta(x^{(i)}) - y^{(i)}\\right) x_0^{(i)} \\\\\n",
-    "  & \\theta_j := \\theta_j - \\alpha \\frac{1}{m} \\sum_{i=1}^{m}\\left(h_\\theta(x^{(i)}) - y^{(i)}\\right) x_j^{(i)} + \\frac{\\lambda}{m}\\theta_j \\\\\n",
-    "\\}\n",
-    "\\end{aligned}\n",
-    "$$"
+    "![](img/gradient.png)\n"
    ]
   },
   {
@@ -775,7 +765,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.7"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,