From 88cb7fe23101a92801264782882cb4f693b5d59c Mon Sep 17 00:00:00 2001 From: bushuhui Date: Fri, 8 Apr 2022 17:54:24 +0800 Subject: [PATCH] Improve figure save --- 4_logistic_regression/1-Least_squares.ipynb | 23 +- 4_logistic_regression/2-Logistic_regression.ipynb | 14 +- 4_logistic_regression/isomap_visualize.pdf | Bin 42324 -> 0 bytes .../logistic_confusion_matrix.pdf | Bin 12718 -> 0 bytes 4_logistic_regression/logistic_pred_res.pdf | Bin 57099 -> 0 bytes 4_logistic_regression/logistic_train_data.pdf | Bin 9236 -> 0 bytes 4_logistic_regression/logstic_fuction.pdf | Bin 10251 -> 0 bytes 4_logistic_regression/ls.ipynb | 968 --------------------- 4_logistic_regression/missle_est.pdf | Bin 10752 -> 0 bytes 4_logistic_regression/missle_taj.pdf | Bin 8303 -> 0 bytes 4_logistic_regression/pca_visualize.pdf | Bin 42399 -> 0 bytes .../sklean_isomap_confusion_matrix.pdf | Bin 14233 -> 0 bytes 4_logistic_regression/sklearn_linear_fitting.pdf | Bin 9245 -> 0 bytes 13 files changed, 18 insertions(+), 987 deletions(-) delete mode 100644 4_logistic_regression/isomap_visualize.pdf delete mode 100644 4_logistic_regression/logistic_confusion_matrix.pdf delete mode 100644 4_logistic_regression/logistic_pred_res.pdf delete mode 100644 4_logistic_regression/logistic_train_data.pdf delete mode 100644 4_logistic_regression/logstic_fuction.pdf delete mode 100644 4_logistic_regression/ls.ipynb delete mode 100644 4_logistic_regression/missle_est.pdf delete mode 100644 4_logistic_regression/missle_taj.pdf delete mode 100644 4_logistic_regression/pca_visualize.pdf delete mode 100644 4_logistic_regression/sklean_isomap_confusion_matrix.pdf delete mode 100644 4_logistic_regression/sklearn_linear_fitting.pdf diff --git a/4_logistic_regression/1-Least_squares.ipynb b/4_logistic_regression/1-Least_squares.ipynb index b9d5f25..858831f 100644 --- a/4_logistic_regression/1-Least_squares.ipynb +++ b/4_logistic_regression/1-Least_squares.ipynb @@ -31,7 +31,7 @@ "source": [ "### 1.1 示例\n", "\n", - "假设我们有下面的一些观测数据,我们希望找到他们内在的规律。" + "假设我们有下面的一些观测数据,希望找到它们内在的规律。" ] }, { @@ -82,7 +82,7 @@ "$$\n", "其中$\\mathbf{X}$为自变量,$\\mathbf{Y}$为因变量。\n", "\n", - "我们希望找到一个模型能够解释这些数据,假设使用最简单的线性模型来拟合数据:\n", + "希望找到一个模型能够解释这些数据,假设使用最简单的线性模型来拟合数据:\n", "$$\n", "y = ax + b\n", "$$\n", @@ -190,11 +190,10 @@ "梯度下降法有很多优点,其中最主要的优点是,**在梯度下降法的求解过程中只需求解损失函数的一阶导数,计算的代价比较小,这使得梯度下降法能在很多大规模数据集上得到应用。**\n", "\n", "梯度下降法的含义是通过当前点的梯度方向寻找到新的迭代点。梯度下降法的基本思想可以类比为一个下山的过程。假设这样一个场景:\n", - "* 一个人被困在山上,需要从山上下来(i.e. 找到山的最低点,也就是山谷)。\n", + "* 一个人被困在山上,需要从山上下来,找到山的最低点,也就是山谷;\n", "* 但此时山上的浓雾很大,导致可视度很低。因此,下山的路径就无法全部确定,他必须利用自己周围的信息去找到下山的路径。\n", - "* 这个时候,他就可以利用梯度下降算法来帮助自己下山。\n", - " - 具体来说就是,以他当前的所处的位置为基准,寻找这个位置最陡峭的地方,然后朝着山的高度下降的地方走\n", - " - 然后每走一段距离,都反复采用同一个方法,最后就能成功的抵达山谷。\n", + "* 以他当前的所处的位置为基准,寻找这个位置最陡峭的地方,然后朝着山的高度下降的地方走\n", + "* 每走一段距离,都反复采用同一个方法,最后就能成功的抵达山谷。\n", "\n", "\n", "一般情况下,这座山最陡峭的地方是无法通过肉眼立马观察出来的,而是需要一个工具来测量;同时,这个人此时正好拥有测量出最陡峭方向的能力。所以,此人每走一段距离,都需要一段时间来测量所在位置最陡峭的方向,这是比较耗时的。那么为了在太阳下山之前到达山底,就要尽可能的减少测量方向的次数。这是一个两难的选择,如果测量的频繁,可以保证下山的方向是绝对正确的,但又非常耗时;如果测量的过少,又有偏离轨道的风险。所以需要找到一个合适的测量方向的频率,来确保下山的方向不错误,同时又不至于耗时太多!\n", @@ -209,7 +208,7 @@ "L = \\sum_{i=1}^{N} (y_i - a x_i - b)^2\n", "$$\n", "\n", - "我们更新的策略是:\n", + "更新的策略是:\n", "$$\n", "\\theta^1 = \\theta^0 - \\eta \\triangledown L(\\theta)\n", "$$\n", @@ -217,7 +216,7 @@ "\n", "此公式的意义是:$L$是关于$\\theta$的一个函数,我们当前所处的位置为$\\theta_0$点,要从这个点走到L的最小值点,也就是山底。首先我们先确定前进的方向,也就是梯度的反向,然后走一段距离的步长,也就是$\\eta$,走完这个段步长,就到达了$\\theta_1$这个点!\n", "\n", - "更新的策略是:\n", + "最终的更新方程是:\n", "\n", "$$\n", "a^1 = a^0 + 2 \\eta [ y - (ax+b)]*x \\\\\n", @@ -1410,7 +1409,7 @@ "plt.plot(t, y)\n", "plt.xlabel(\"time\")\n", "plt.ylabel(\"height\")\n", - "plt.savefig(\"missle_taj.pdf\")\n", + "plt.savefig(\"fig-res-missle_taj.pdf\")\n", "plt.show()" ] }, @@ -1493,7 +1492,7 @@ "plt.plot(t, y, 'r-', label='Real data')\n", "plt.plot(t, y_est, 'g-x', label='Estimated data')\n", "plt.legend()\n", - "plt.savefig(\"missle_est.pdf\")\n", + "plt.savefig(\"fig-res-missle_est.pdf\")\n", "plt.show()\n" ] }, @@ -1562,7 +1561,7 @@ "plt.plot([x_min, x_max], [y_min, y_max], 'r')\n", "plt.xlabel(\"X\")\n", "plt.ylabel(\"Y\")\n", - "plt.savefig(\"sklearn_linear_fitting.pdf\")\n", + "plt.savefig(\"fig-res-sklearn_linear_fitting.pdf\")\n", "plt.show()" ] }, @@ -1636,7 +1635,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.7.9" } }, "nbformat": 4, diff --git a/4_logistic_regression/2-Logistic_regression.ipynb b/4_logistic_regression/2-Logistic_regression.ipynb index ce3b459..c544710 100644 --- a/4_logistic_regression/2-Logistic_regression.ipynb +++ b/4_logistic_regression/2-Logistic_regression.ipynb @@ -19,7 +19,7 @@ "\n", "一说回归最先想到的是终结者那句:I'll be back\n", "\n", - "regress,re表示back,gress等于go,数值go back to mean value,也就是I'll be back 的意思\n", + "regress中,re表示back,gress等于go,数值go back to mean value,也就是I'll be back 的意思\n", "\n", "在数理统计中,回归是确定多种变量相互依赖的定量关系的方法\n", "\n", @@ -80,7 +80,7 @@ "y=1/(1+np.e**(-X))\n", "plt.plot(X,y,'b-')\n", "plt.title(\"Logistic function\")\n", - "plt.savefig(\"logstic_fuction.pdf\")\n", + "plt.savefig(\"fig-res-logstic_fuction.pdf\")\n", "plt.show()" ] }, @@ -227,7 +227,7 @@ "data, label = sklearn.datasets.make_moons(200, noise=0.30)\n", "\n", "plt.scatter(data[:,0], data[:,1], c=label)\n", - "plt.savefig(\"logistic_train_data.pdf\")\n", + "plt.savefig(\"fig-res-logistic_train_data.pdf\")\n", "plt.title(\"Original Data\")" ] }, @@ -408,7 +408,7 @@ "plt.colorbar()\n", "plt.ylabel('Groundtruth')\n", "plt.xlabel(u'Predict')\n", - "plt.savefig('logistic_confusion_matrix.pdf')\n", + "plt.savefig('fig-res-logistic_confusion_matrix.pdf')\n", "plt.show()" ] }, @@ -567,7 +567,7 @@ "\n", "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()\n", - "plt.savefig(\"pca_visualize.pdf\")\n", + "plt.savefig(\"fig-res-pca_visualize.pdf\")\n", "plt.show()" ] }, @@ -605,7 +605,7 @@ "\n", "plt.scatter(proj[:, 0], proj[:, 1], c=digits.target)\n", "plt.colorbar()\n", - "plt.savefig(\"isomap_visualize.pdf\")\n", + "plt.savefig(\"fig-res-isomap_visualize.pdf\")\n", "plt.show()" ] }, @@ -721,7 +721,7 @@ "plt.colorbar()\n", "plt.ylabel(u'Groundtruth')\n", "plt.xlabel(u'Predict')\n", - "plt.savefig(\"sklean_isomap_confusion_matrix.pdf\")\n", + "plt.savefig(\"fig-res-sklean_isomap_confusion_matrix.pdf\")\n", "plt.show()" ] }, diff --git a/4_logistic_regression/isomap_visualize.pdf b/4_logistic_regression/isomap_visualize.pdf deleted file mode 100644 index 7d92ea622cfeeeb01852f6c2b3c937e013e1b173..0000000000000000000000000000000000000000 GIT binary patch literal 0 KcmV+b0RR6000031 literal 42324 zcmV)ZrK?&cP((&8F)lO;C9K>atGWs?ATS_rVrmLJJRmPnVP|D?ATl5@AW|SNRC#b^ zATL8c;Wgs*lFd$MOFGg=} zbRaVzFd$MOFHm80bY*gGAT=N`AW{l1P;zf$Q)P4@TOcn`L`EPlRAqQ{ATLR6VP|DR 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"cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 最小二乘\n", - "\n", - "## 1. 最小二乘的基本原理\n", - "\n", - "最小二乘法(Least Squares)是一种数学优化技术,它通过最小化误差的平方和找到一组数据的最佳函数匹配, 最小二乘法通常用于曲线拟合、求解模型。很多其他的优化问题也可通过最小化能量或最大化熵用最小二乘形式表达。\n", - "\n", - "![ls_theory](images/least_squares.png)\n", - "\n", - "最小二乘原理的一般形式为:\n", - "$$\n", - "L = \\sum (V_{obv} - V_{target}(\\theta))^2\n", - "$$\n", - "其中\n", - "* $V_{obv}$是观测的多组样本值\n", - "* $V_{target}$是假设拟合函数的输出值\n", - "* $\\theta$为构造模型的参数\n", - "* $L$是目标函数\n", - "\n", - "如果通过调整模型参数$\\theta$,使得$L$下降到最小则表明,拟合函数与观测最为接近,也就是找到了最优的模型。\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 1.1 示例\n", - "\n", - "假设我们有下面的一些观测数据,我们希望找到他们内在的规律。" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "# 生成数据\n", - "data_num = 50\n", - "X = np.random.rand(data_num, 1)*10\n", - "Y = X * 3 + 4 + 4*np.random.randn(data_num,1)\n", - "\n", - "# 画出数据的分布\n", - "plt.scatter(X, Y)\n", - "plt.xlabel(\"X\")\n", - "plt.ylabel(\"Y\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 1.2 数学原理\n", - "有$N$个观测数据为:\n", - "$$\n", - "\\mathbf{X} = \\{x_1, x_2, ..., x_N \\} \\\\\n", - "\\mathbf{Y} = \\{y_1, y_2, ..., y_N \\}\n", - "$$\n", - "其中$\\mathbf{X}$为自变量,$\\mathbf{Y}$为因变量。\n", - "\n", - "我们希望找到一个模型能够解释这些数据,假设使用最简单的线性模型来拟合数据:\n", - "$$\n", - "y = ax + b\n", - "$$\n", - "那么问题就变成求解参数$a$, $b$能够使得模型输出尽可能和观测数据有比较小的误差。\n", - "\n", - "如何构建函数来评估模型输出与观测数据之间的误差是一个关键问题,这里我们使用观测数据与模型输出的平方和来作为评估函数(也被称为损失函数Loss function):\n", - "$$\n", - "L = \\sum_{i=1}^{N} \\{y_i - (a x_i + b)\\}^2 \\\\\n", - "L = \\sum_{i=1}^{N} (y_i - a x_i - b)^2 \n", - "$$\n", - "\n", - "使误差函数最小,那么我们就可以求出模型的参数:\n", - "$$\n", - "\\frac{\\partial L}{\\partial a} = -2 \\sum_{i=1}^{N} (y_i - a x_i - b) x_i \\\\\n", - "\\frac{\\partial L}{\\partial b} = -2 \\sum_{i=1}^{N} (y_i - a x_i - b)\n", - "$$\n", - "\n", - "即当偏微分为0时,误差函数为最小,因此我们可以得到:\n", - "$$\n", - "-2 \\sum_{i=1}^{N} (y_i - a x_i - b) x_i = 0 \\\\\n", - "-2 \\sum_{i=1}^{N} (y_i - a x_i - b) = 0 \\\\\n", - "$$\n", - "\n", - "将上式调整一下顺序可以得到:\n", - "$$\n", - "a \\sum x_i^2 + b \\sum x_i = \\sum y_i x_i \\\\\n", - "a \\sum x_i + b N = \\sum y_i\n", - "$$\n", - "\n", - "上式中$\\sum x_i^2$, $\\sum x_i$, $\\sum y_i$, $\\sum y_i x_i$都是已知的数据,而参数$a$, $b$是我们想要求得未知参数。通过求解二元一次方程组,我们即可求出模型的最优参数。" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 1.3 求解程序" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "a = 3.159836, b = 3.125757\n" - ] - }, - { - "data": { - "image/png": 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W/PGPcOKJCYlt5sxZjBp1Odu27YgsPpEsopICErGIyt26w+OPB+V0DzggWKYu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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N = X.shape[0]\n", - "\n", - "S_X2 = np.sum(X*X)\n", - "S_X = np.sum(X)\n", - "S_XY = np.sum(X*Y)\n", - "S_Y = np.sum(Y)\n", - "\n", - "A1 = np.array([[S_X2, S_X], \n", - " [S_X, N]])\n", - "B1 = np.array([S_XY, S_Y])\n", - "\n", - "# numpy.linalg模块包含线性代数的函数。\n", - "# 使用这个模块,可以计算逆矩阵、求特征值、解线性方程组以及求解行列式等。\n", - "coeff = np.linalg.inv(A1).dot(B1)\n", - "\n", - "print('a = %f, b = %f' % (coeff[0], coeff[1]))\n", - "\n", - "x_min = np.min(X)\n", - "x_max = np.max(X)\n", - "y_min = coeff[0] * x_min + coeff[1]\n", - "y_max = coeff[0] * x_max + coeff[1]\n", - "\n", - "plt.scatter(X, Y, label='original data')\n", - "plt.plot([x_min, x_max], [y_min, y_max], 'r', label='model')\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2. 如何使用迭代的方法求出模型参数\n", - "\n", - "当数据比较多的时候,或者模型比较复杂,无法直接使用解析的方式求出模型参数。因此更为常用的方式是,通过迭代的方式逐步逼近模型的参数。\n", - "\n", - "### 2.1 梯度下降法\n", - "在机器学习算法中,对于很多监督学习模型,需要对原始的模型构建损失函数,接下来便是通过优化算法对损失函数进行优化,以便寻找到最优的参数。在求解机器学习参数的优化算法中,使用较多的是基于梯度下降的优化算法(Gradient Descent, GD)。\n", - "\n", - "梯度下降法有很多优点,其中最主要的优点是,**在梯度下降法的求解过程中只需求解损失函数的一阶导数,计算的代价比较小,这使得梯度下降法能在很多大规模数据集上得到应用。**\n", - "\n", - "梯度下降法的含义是通过当前点的梯度方向寻找到新的迭代点。梯度下降法的基本思想可以类比为一个下山的过程。假设这样一个场景:\n", - "* 一个人被困在山上,需要从山上下来(i.e. 找到山的最低点,也就是山谷)。\n", - "* 但此时山上的浓雾很大,导致可视度很低。因此,下山的路径就无法全部确定,他必须利用自己周围的信息去找到下山的路径。\n", - "* 这个时候,他就可以利用梯度下降算法来帮助自己下山。\n", - " - 具体来说就是,以他当前的所处的位置为基准,寻找这个位置最陡峭的地方,然后朝着山的高度下降的地方走\n", - " - 然后每走一段距离,都反复采用同一个方法,最后就能成功的抵达山谷。\n", - "\n", - "\n", - "一般情况下,这座山最陡峭的地方是无法通过肉眼立马观察出来的,而是需要一个工具来测量;同时,这个人此时正好拥有测量出最陡峭方向的能力。所以,此人每走一段距离,都需要一段时间来测量所在位置最陡峭的方向,这是比较耗时的。那么为了在太阳下山之前到达山底,就要尽可能的减少测量方向的次数。这是一个两难的选择,如果测量的频繁,可以保证下山的方向是绝对正确的,但又非常耗时;如果测量的过少,又有偏离轨道的风险。所以需要找到一个合适的测量方向的频率,来确保下山的方向不错误,同时又不至于耗时太多!\n", - "\n", - "\n", - "![gradient_descent](images/gradient_descent.png)\n", - "\n", - "如上图所示,得到了最优解。$x$,$y$表示的是$\\theta_0$和$\\theta_1$,$z$方向表示的是花费函数,很明显出发点不同,最后到达的收敛点可能不一样。当然如果是碗状的,那么收敛点就应该是一样的。\n", - "\n", - "对于最小二乘的损失函数\n", - "$$\n", - "L = \\sum_{i=1}^{N} (y_i - a x_i - b)^2\n", - "$$\n", - "\n", - "我们更新的策略是:\n", - "$$\n", - "\\theta^1 = \\theta^0 - \\eta \\triangledown L(\\theta)\n", - "$$\n", - "其中$\\theta$代表了模型中的参数,例如$a$, $b$\n", - "\n", - "此公式的意义是:$L$是关于$\\theta$的一个函数,我们当前所处的位置为$\\theta_0$点,要从这个点走到L的最小值点,也就是山底。首先我们先确定前进的方向,也就是梯度的反向,然后走一段距离的步长,也就是$\\eta$,走完这个段步长,就到达了$\\theta_1$这个点!\n", - "\n", - "更新的策略是:\n", - "\n", - "$$\n", - "a^1 = a^0 + 2 \\eta [ y - (ax+b)]*x \\\\\n", - "b^1 = b^0 + 2 \\eta [ y - (ax+b)] \n", - "$$\n", - "\n", - "下面就这个公式的几个常见的疑问:\n", - "\n", - "* **$\\eta$是什么含义?**\n", - "$\\eta$在梯度下降算法中被称作为学习率或者步长,意味着我们可以通过$\\eta$来控制每一步走的距离,以保证不要步子跨的太大,错过了最低点。同时也要保证不要走的太慢,导致太阳下山了,还没有走到山下。所以$\\eta$的选择在梯度下降法中往往是很重要的。\n", - "![gd_stepsize](images/gd_stepsize.png)\n", - "\n", - "* **为什么要梯度要乘以一个负号?**\n", - "梯度前加一个负号,就意味着朝着梯度相反的方向前进!梯度的方向实际就是函数在此点上升最快的方向,而我们需要朝着下降最快的方向走,自然就是负的梯度的方向,所以此处需要加上负号。\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 2.2 示例代码" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "epoch 0: loss = 706.814761, a = 3.405291, b = 1.325704\n", - "epoch 100: loss = 673.646148, a = 3.147842, b = 2.914551\n", - "epoch 200: loss = 670.748958, a = 3.189792, b = 3.074196\n", - "epoch 300: loss = 691.807179, a = 3.272848, b = 3.110038\n", - "epoch 400: loss = 669.919974, a = 3.158443, b = 3.088828\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import random\n", - "\n", - "n_epoch = 500 # epoch size\n", - "a, b = 1, 1 # initial parameters\n", - "epsilon = 0.001 # learning rate\n", - "\n", - "for i in range(n_epoch):\n", - " data_idx = list(range(N))\n", - " random.shuffle(data_idx)\n", - " \n", - " for j in data_idx:\n", - " a = a + epsilon*2*(Y[j] - a*X[j] - b)*X[j]\n", - " b = b + epsilon*2*(Y[j] - a*X[j] - b)\n", - "\n", - " L = 0\n", - " for j in range(N):\n", - " L = L + (Y[j]-a*X[j]-b)**2\n", - " \n", - " if i % 100 == 0:\n", - " print(\"epoch %4d: loss = %f, a = %f, b = %f\" % (i, L, a, b))\n", - " \n", - "x_min = np.min(X)\n", - "x_max = np.max(X)\n", - "y_min = a * x_min + b\n", - "y_max = a * x_max + b\n", - "\n", - "plt.scatter(X, Y, label='original data')\n", - "plt.plot([x_min, x_max], [y_min, y_max], 'r', label='model')\n", - "plt.legend()\n", - "plt.savefig(\"gd_res.pdf\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 3. 如何可视化迭代过程" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "fig_name = gd_res_00.pdf\n" - ] - }, - { - "data": { - "image/png": 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dXDZpWW5/ltsOan/Sst7+WjQisEfa2SOrsv6PI8vtz3LbQe1PWtbbX4tGBPZP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\n2EVEckaBXUQkZxTYRURy5v8DAE7DK6iiAnUAAAAASUVORK5CYII=\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "fig_name = gd_res_01.pdf\n" - ] - }, - { - "data": { - "image/png": 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XkU+lk9g1QSnL2lsMbMmSJznssCPbXSSs0Jb7bWho4N3nnuPARx+l129/G3S3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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "fig_name = gd_res_03.pdf\n" - ] - }, - { - "data": { - "image/png": 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pTErsOdL+Jmdn/c379euXUsLOV3fDIe+8w/0fLGEqpzOFcQznD9zHegarfFGk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\nxbZAUIGBAAAAAElFTkSuQmCC\n", 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AnkPJ1IJ/HfxXAHV0dUNQXi7EtrTAPfcEbQA++gjmzQsCfJ8+uTuniGSNUjF5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\nJUaBXUSkxCiwi4iUGAV2EZES8/8BApOLbpDRQNgAAAAASUVORK5CYII=\n", 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SkehoKCYLetryrCX/fcOGfnz+eQNlZTsBH2w00ZqRPPmWgl0NDUHBrgMOSKjN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\n", 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MA/Y2s7fN7CxgDDDMzF4Fjgpfd0ptVW08//yCpAbVtAwEWrx4cXQjK92DxS8G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\nNqBBAAAAAElFTkSuQmCC\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "fig_name = gd_res_08.pdf\n" - ] - }, - { - "data": { - "image/png": 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ttmA3o//5H5g9W0FdJF8luvt1so+gqcI2deojHon08qKigR6J9PJ77rnPI5Fe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\npMD8f5ABORzDBhiUAAAAAElFTkSuQmCC\n", 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FHHLIr1m+fO6G16uqhjJr1nhqamo2vD/Izd8PHA0UKEe/ahWce24wQp84Eb7/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\nFNhFRCqMAruISIVRYBcRqTD/H5DpuXGdvOrcAAAAAElFTkSuQmCC\n", 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XKUkpl2LMbAYQBzY3s9eACcCVwB1mdgKwHDgyF0GWgtajNoIee1PTcp55ZhEj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\nyowSu4hImVFiFxEpM/8PxYvW7eAdwHsAAAAASUVORK5CYII=\n", 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KVLj7CjMbAMxz973bOLakW+wlM2rjscegshJOOgl+85tg0pGI5E0uWuwWPprM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\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "fig_name = gd_res_13.pdf\n" - ] - }, - { - "data": { - "image/png": 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ms6sg1tR+5RU48UQ45BC2/OdiHqmry6lEmq2FukQyJR6PE4/H23WN9vbY3wXK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\nAABJRU5ErkJggg==\n", - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "fig_name = gd_res_14.pdf\n" - ] - }, - { - "data": { - "image/png": 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eL280N6d2w/vZ0urdwMqVcN558K9/weTJMHhwpiMSkVaIp9xxEvAqsK2ZfWpm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\n+25p+SbxVgAAAABJRU5ErkJggg==\n", 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "import matplotlib.animation as animation\n", - "import random\n", - "\n", - "\n", - "n_epoch = 300 # epoch size\n", - "a, b = 1, 1 # initial parameters\n", - "epsilon = 0.0001 # learning rate\n", - "\n", - "fig = plt.figure()\n", - "\n", - "# 生成数据\n", - "data_num = 50\n", - "X = np.random.rand(data_num, 1)*10\n", - "Y = X * 3 + 4 + 4*np.random.randn(data_num,1)\n", - "\n", - "N = np.shape(X)[0]\n", - "\n", - "k = 0\n", - "for i in range(n_epoch):\n", - " data_idx = list(range(N))\n", - " random.shuffle(data_idx)\n", - " \n", - " for j in data_idx[:10]:\n", - " a = a + epsilon*2*(Y[j] - a*X[j] - b)*X[j]\n", - " b = b + epsilon*2*(Y[j] - a*X[j] - b)\n", - "\n", - "\n", - " \n", - " if i<80 and i % 5 == 0:\n", - " x_min = np.min(X)\n", - " x_max = np.max(X)\n", - " y_min = a * x_min + b\n", - " y_max = a * x_max + b\n", - "\n", - " plt.clf()\n", - " plt.cla()\n", - " plt.scatter(X, Y, label='original data')\n", - " plt.plot([x_min, x_max], [y_min, y_max], 'r', label='model')\n", - " plt.title(\"Iteration [%03d]\" % i)\n", - " #plt.legend()\n", - " fname = \"gd_res_%02d.pdf\" % k\n", - " print(\"fig_name = %s\" % fname)\n", - " plt.savefig(fname)\n", - " k = k + 1\n", - " plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import matplotlib.animation as animation\n", - "\n", - "n_epoch = 300 # epoch size\n", - "a, b = 1, 1 # initial parameters\n", - "epsilon = 0.0001 # learning rate\n", - "\n", - "fig = plt.figure()\n", - "imgs = []\n", - "\n", - "for i in range(n_epoch):\n", - " data_idx = list(range(N))\n", - " random.shuffle(data_idx)\n", - " \n", - " for j in data_idx[:10]:\n", - " a = a + epsilon*2*(Y[j] - a*X[j] - b)*X[j]\n", - " b = b + epsilon*2*(Y[j] - a*X[j] - b)\n", - "\n", - " j = 0\n", - " if i<80 and i % 5 == 0:\n", - " x_min = np.min(X)\n", - " x_max = np.max(X)\n", - " y_min = a * x_min + b\n", - " y_max = a * x_max + b\n", - "\n", - " img = plt.scatter(X, Y, label='original data')\n", - " img = plt.plot([x_min, x_max], [y_min, y_max], 'r', label='model')\n", - " imgs.append(img)\n", - " \n", - "ani = animation.ArtistAnimation(fig, imgs)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 4. 如何使用批次更新的方法?\n", - "\n", - "如果有一些数据包含比较大的错误(异常数据),因此每次更新仅仅使用一个数据会导致不精确,同时每次仅仅使用一个数据来计算更新也导致计算效率比较低。\n", - "\n", - "\n", - "* [梯度下降方法的几种形式](https://blog.csdn.net/u010402786/article/details/51188876)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 5. 如何拟合多项式函数?\n", - "\n", - "需要设计一个弹道导弹防御系统,通过观测导弹的飞行路径,预测未来导弹的飞行轨迹,从而完成摧毁的任务。按照物理学,可以得知模型为:\n", - "$$\n", - "y = at^2 + bt + c\n", - "$$\n", - "我们需要求解三个模型参数$a, b, c$。\n", - "\n", - "损失函数的定义为:\n", - "$$\n", - "L = \\sum_{i=1}^N (y_i - at_i^2 - bt_i - c)^2\n", - "$$\n" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "\n", - "pa = -20\n", - "pb = 90\n", - "pc = 800\n", - "\n", - "t = np.linspace(0, 10) \n", - "y = pa*t**2 + pb*t + pc + np.random.randn(np.size(t))*15\n", - "\n", - "\n", - "plt.plot(t, y)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 5.1 如何得到更新项?\n", - "\n", - "$$\n", - "L = \\sum_{i=1}^N (y_i - at_i^2 - bt_i - c)^2\n", - "$$\n", - "\n", - "\\begin{eqnarray}\n", - "\\frac{\\partial L}{\\partial a} & = & - 2\\sum_{i=1}^N (y_i - at_i^2 - bt_i -c) t_i^2 \\\\\n", - "\\frac{\\partial L}{\\partial b} & = & - 2\\sum_{i=1}^N (y_i - at_i^2 - bt_i -c) t_i \\\\\n", - "\\frac{\\partial L}{\\partial c} & = & - 2\\sum_{i=1}^N (y_i - at_i^2 - bt_i -c)\n", - "\\end{eqnarray}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### 5.2 程序" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "epoch 0: loss = 2.45413e+07, a = -3.07866, b = 6.90614, c = 4.30938\n", - "epoch 500: loss = 1.14068e+06, a = -28.6118, b = 222.36, c = 434.835\n", - "epoch 1000: loss = 399358, a = -23.4814, b = 153.657, c = 605.164\n", - "epoch 1500: loss = 165221, a = -20.5589, b = 114.526, c = 702.159\n", - "epoch 2000: loss = 92877.7, a = -18.8947, b = 92.2414, c = 757.394\n", - "epoch 2500: loss = 71458.8, a = -17.9469, b = 79.5512, c = 788.849\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "n_epoch = 3000 # epoch size\n", - "a, b, c = 1.0, 1.0, 1.0 # initial parameters\n", - "epsilon = 0.0001 # learning rate\n", - "\n", - "N = np.size(t)\n", - "\n", - "for i in range(n_epoch):\n", - " for j in range(N):\n", - " a = a + epsilon*2*(y[j] - a*t[j]**2 - b*t[j] - c)*t[j]**2\n", - " b = b + epsilon*2*(y[j] - a*t[j]**2 - b*t[j] - c)*t[j]\n", - " c = c + epsilon*2*(y[j] - a*t[j]**2 - b*t[j] - c)\n", - "\n", - " L = 0\n", - " for j in range(N):\n", - " L = L + (y[j] - a*t[j]**2 - b*t[j] - c)**2\n", - " \n", - " if i % 500 == 0:\n", - " print(\"epoch %4d: loss = %10g, a = %10g, b = %10g, c = %10g\" % (i, L, a, b, c))\n", - " \n", - " \n", - "y_est = a*t**2 + b*t + c \n", - "\n", - "\n", - "plt.plot(t, y, 'r-', label='Real data')\n", - "plt.plot(t, y_est, 'g-x', label='Estimated data')\n", - "plt.legend()\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 6. 如何使用sklearn求解线性问题?\n" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "X: (100, 1)\n", - "Y: (100, 1)\n", - "a = 2.743186, b = 4.076122\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "%matplotlib inline\n", - "\n", - "from sklearn import linear_model\n", - "import numpy as np\n", - "\n", - "# load data\n", - "# generate data\n", - "data_num = 100\n", - "X = np.random.rand(data_num, 1)*10\n", - "Y = X * 3 + 4 + 8*np.random.randn(data_num,1)\n", - "\n", - "print(\"X: \", X.shape)\n", - "print(\"Y: \", Y.shape)\n", - "\n", - "# create regression model\n", - "regr = linear_model.LinearRegression()\n", - "regr.fit(X, Y)\n", - "\n", - "a, b = np.squeeze(regr.coef_), np.squeeze(regr.intercept_)\n", - "\n", - "print(\"a = %f, b = %f\" % (a, b))\n", - "\n", - "x_min = np.min(X)\n", - "x_max = np.max(X)\n", - "y_min = a * x_min + b\n", - "y_max = a * x_max + b\n", - "\n", - "plt.scatter(X, Y)\n", - "plt.plot([x_min, x_max], [y_min, y_max], 'r')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 7. 如何使用sklearn拟合多项式函数?" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([800., 90., -20.])" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Fitting polynomial functions\n", - "\n", - "from sklearn.preprocessing import PolynomialFeatures\n", - "from sklearn.linear_model import LinearRegression\n", - "from sklearn.pipeline import Pipeline\n", - "\n", - "t = np.array([2, 4, 6, 8])\n", - "\n", - "pa = -20\n", - "pb = 90\n", - "pc = 800\n", - "\n", - "y = pa*t**2 + pb*t + pc\n", - "\n", - "model = Pipeline([('poly', PolynomialFeatures(degree=2)),\n", - " ('linear', LinearRegression(fit_intercept=False))])\n", - "model = model.fit(t[:, np.newaxis], y)\n", - "model.named_steps['linear'].coef_\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 参考资料\n", - "* [梯度下降法](https://blog.csdn.net/u010402786/article/details/51188876)\n", - "* [如何理解最小二乘法?](https://blog.csdn.net/ccnt_2012/article/details/81127117)\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.5.4" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/4_logistic_regression/missle_est.pdf b/4_logistic_regression/missle_est.pdf deleted file mode 100644 index 52f8dc230967ef8429bf20700788279b5af20f05..0000000000000000000000000000000000000000 GIT binary patch literal 0 KcmV+b0RR6000031 literal 10752 zcmV+bD*x3bP((&8F)lO;C9K>atGWs?ATS_rVrmLJJRmPnVP|D?ATl5@AW|SNRC#b^ zATL8MmA zHXtw{QVK6na&Kc(Wpp50ATLlvMj$U#Wq5QTFG+1-XJtYlFG+1-XJtbmFG+1-XJtts 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