diff --git a/.gitignore b/.gitignore index 790125a..32b46f9 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,3 @@ .ipynb_checkpoints .idea -references diff --git a/1_logistic_regression/Least_squares.ipynb b/1_logistic_regression/Least_squares.ipynb index 0de3486..e6996ac 100644 --- a/1_logistic_regression/Least_squares.ipynb +++ b/1_logistic_regression/Least_squares.ipynb @@ -160,7 +160,54 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## How to use iterative method to estimate parameters?\n" + "## 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", + "### 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，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。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。\n", + "\n", + "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：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)。但此时山上的浓雾很大，导致可视度很低。因此，下山的路径就无法确定，他必须利用自己周围的信息去找到下山的路径。这个时候，他就可以利用梯度下降算法来帮助自己下山。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，同理，如果我们的目标是上山，也就是爬到山顶，那么此时应该是朝着最陡峭的方向往上走。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", + "我们同时可以假设这座山最陡峭的地方是无法通过肉眼立马观察出来的，而是需要一个复杂的工具来测量，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，得到了局部最优解。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", + "对于某一个损失函数\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", + "$$\n", + "\\theta^1 = \\theta^0 - \\alpha \\triangledown L(\\theta)\n", + "$$\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$\\alpha$，走完这个段步长，就到达了$\\theta_1$这个点！\n", + "\n", + "下面就这个公式的几个常见的疑问：\n", + "\n", + "* **$\\alpha$是什么含义？**\n", + "$\\alpha$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$\\alpha$来控制每一步走的距离，以保证不要步子跨的太大扯着蛋，哈哈，其实就是不要走太快，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$\\alpha$的选择在梯度下降法中往往是很重要的！$\\alpha$不能太大也不能太小，太小的话，可能导致迟迟走不到最低点，太大的话，会导致错过最低点！\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！我们在前文提到，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": [ + "### Program" ] }, { @@ -4889,7 +4936,10 @@ "source": [ "## How to use batch update method?\n", "\n", - "If some data is outliear, then the " + "If some data is outliear, then only use one data can make the learning inaccuracy and slow.\n", + "\n", + "\n", + "* [梯度下降方法的几种形式](https://blog.csdn.net/u010402786/article/details/51188876)" ] }, { diff --git a/1_logistic_regression/Least_squares.py b/1_logistic_regression/Least_squares.py index 3a7c63c..8e0e7e3 100644 --- a/1_logistic_regression/Least_squares.py +++ b/1_logistic_regression/Least_squares.py @@ -1,3 +1,4 @@ +# -*- coding: utf-8 -*- # --- # jupyter: # jupytext_format_version: '1.2' @@ -113,8 +114,50 @@ plt.legend() plt.show() # - -# ## How to use iterative method to estimate parameters? +# ## 如何使用迭代的方法求出模型参数 # +# 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。 +# +# ### 梯度下降法 +# 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)。 +# +# 梯度下降法有很多优点，其中，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。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：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)。但此时山上的浓雾很大，导致可视度很低。因此，下山的路径就无法确定，他必须利用自己周围的信息去找到下山的路径。这个时候，他就可以利用梯度下降算法来帮助自己下山。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，同理，如果我们的目标是上山，也就是爬到山顶，那么此时应该是朝着最陡峭的方向往上走。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。 +# +# +# 我们同时可以假设这座山最陡峭的地方是无法通过肉眼立马观察出来的，而是需要一个复杂的工具来测量，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！ +# +# +# ![gradient_descent](images/gradient_descent.png) +# +# 如上图所示，得到了局部最优解。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。 +# +# 对于某一个损失函数 +# $$ +# L = \sum_{i=1}^{N} (y_i - a x_i + b)^2 +# $$ +# +# 我们更新的策略是： +# $$ +# \theta^1 = \theta^0 - \alpha \triangledown L(\theta) +# $$ +# 其中$\theta$代表了模型中的参数，例如$a$, $b$ +# +# 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$\alpha$，走完这个段步长，就到达了$\theta_1$这个点！ +# +# 下面就这个公式的几个常见的疑问： +# +# * **$\alpha$是什么含义？** +# $\alpha$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$\alpha$来控制每一步走的距离，以保证不要步子跨的太大扯着蛋，哈哈，其实就是不要走太快，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$\alpha$的选择在梯度下降法中往往是很重要的！$\alpha$不能太大也不能太小，太小的话，可能导致迟迟走不到最低点，太大的话，会导致错过最低点！ +# ![gd_stepsize](images/gd_stepsize.png) +# +# * **为什么要梯度要乘以一个负号？** +# 梯度前加一个负号，就意味着朝着梯度相反的方向前进！我们在前文提到，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 +# +# + +# ### Program # + n_epoch = 3000 # epoch size @@ -183,7 +226,10 @@ plt.show() # ## How to use batch update method? # -# If some data is outliear, then the +# If some data is outliear, then only use one data can make the learning inaccuracy and slow. +# +# +# * [梯度下降方法的几种形式](https://blog.csdn.net/u010402786/article/details/51188876) # ## How to fit polynomial function? # diff --git a/1_logistic_regression/images/gd_stepsize.png b/1_logistic_regression/images/gd_stepsize.png new file mode 100644 index 0000000..8886a50 Binary files /dev/null and b/1_logistic_regression/images/gd_stepsize.png differ diff --git a/1_logistic_regression/images/gradient_descent.png b/1_logistic_regression/images/gradient_descent.png new file mode 100644 index 0000000..ae8e47d Binary files /dev/null and b/1_logistic_regression/images/gradient_descent.png differ diff --git a/README.md b/README.md index d074b61..25dfadb 100644 --- a/README.md +++ b/README.md @@ -2,7 +2,17 @@ 本notebook教程包含了一些使用Python来学习机器学习的教程，通过本教程能够引导学习Python的基础知识和机器学习的背景和实际编程。 +## 内容 +1. [Python基础](0_python/) +2. [numpy & matplotlib](0_numpy_matplotlib_scipy_sympy/) +3. [kMenas](1_kmeans/) +4. [knn](1_knn/) +5. [Logistic Regression](1_logistic_regression/) +6. [Neural Network](nn/) +7. CNN +8. PyTorch -内容 +## 其他参考 * [安装Python环境](InstallPython.md) -* [参考资料等](References.md) \ No newline at end of file +* [参考资料等](References.md) +* [confusion matrix](metric/confusion_matrix.ipynb) \ No newline at end of file diff --git a/nn/images/bp_loss.png b/nn/images/bp_loss.png new file mode 100644 index 0000000..0be87f2 Binary files /dev/null and b/nn/images/bp_loss.png differ diff --git a/nn/images/bp_weight_update.png b/nn/images/bp_weight_update.png new file mode 100644 index 0000000..7e51940 Binary files /dev/null and b/nn/images/bp_weight_update.png differ diff --git a/nn/images/eqn_13_16.png b/nn/images/eqn_13_16.png new file mode 100644 index 0000000..ee5c699 Binary files /dev/null and b/nn/images/eqn_13_16.png differ diff --git a/nn/images/eqn_17_20.png b/nn/images/eqn_17_20.png new file mode 100644 index 0000000..9450644 Binary files /dev/null and b/nn/images/eqn_17_20.png differ diff --git a/nn/images/eqn_21_22.png b/nn/images/eqn_21_22.png new file mode 100644 index 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files /dev/null and b/nn/images/sigmod.jpg differ diff --git a/nn/mlp_bp.ipynb b/nn/mlp_bp.ipynb new file mode 100644 index 0000000..6385ea9 --- /dev/null +++ b/nn/mlp_bp.ipynb @@ -0,0 +1,600 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 多层神经网络和反向传播\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 神经元\n", + "\n", + "神经元和感知器本质上是一样的，只不过我们说感知器的时候，它的激活函数是阶跃函数；而当我们说神经元时，激活函数往往选择为sigmoid函数或tanh函数。如下图所示：\n", + "![neuron](images/neuron.gif)\n", + "\n", + "计算一个神经元的输出的方法和计算一个感知器的输出是一样的。假设神经元的输入是向量$\\vec{x}$，权重向量是$\\vec{w}$(偏置项是$w_0$)，激活函数是sigmoid函数，则其输出y：\n", + "$$\n", + "y = sigmod(\\vec{w}^T \\cdot \\vec{x})\n", + "$$\n", + "\n", + "sigmoid函数的定义如下：\n", + "$$\n", + "sigmod(x) = \\frac{1}{1+e^{-x}}\n", + "$$\n", + "将其带入前面的式子，得到\n", + "$$\n", + "y = \\frac{1}{1+e^{-\\vec{w}^T \\cdot \\vec{x}}}\n", + "$$\n", + "\n", + "sigmoid函数是一个非线性函数，值域是(0,1)。函数图像如下图所示\n", + "![sigmod_function](images/sigmod.jpg)\n", + "\n", + "sigmoid函数的导数是：\n", + "$$\n", + "y = sigmod(x) \\ \\ \\ \\ \\ \\ (1) \\\\\n", + "y' = y(1-y)\n", + "$$\n", + "可以看到，sigmoid函数的导数非常有趣，它可以用sigmoid函数自身来表示。这样，一旦计算出sigmoid函数的值，计算它的导数的值就非常方便。\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 神经网络是啥?\n", + "\n", + "![nn1](images/nn1.jpeg)\n", + "\n", + "神经网络其实就是按照一定规则连接起来的多个神经元。上图展示了一个全连接(full connected, FC)神经网络，通过观察上面的图，我们可以发现它的规则包括：\n", + "\n", + "* 神经元按照层来布局。最左边的层叫做输入层，负责接收输入数据；最右边的层叫输出层，我们可以从这层获取神经网络输出数据。输入层和输出层之间的层叫做隐藏层，因为它们对于外部来说是不可见的。\n", + "* 同一层的神经元之间没有连接。\n", + "* 第N层的每个神经元和第N-1层的所有神经元相连(这就是full connected的含义)，第N-1层神经元的输出就是第N层神经元的输入。\n", + "* 每个连接都有一个权值。\n", + "\n", + "上面这些规则定义了全连接神经网络的结构。事实上还存在很多其它结构的神经网络，比如卷积神经网络(CNN)、循环神经网络(RNN)，他们都具有不同的连接规则。\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 计算神经网络的输出\n", + "\n", + "神经网络实际上就是一个输入向量$\\vec{x}$到输出向量$\\vec{y}$的函数，即：\n", + "\n", + "$$\n", + "\\vec{y} = f_{network}(\\vec{x})\n", + "$$\n", + "根据输入计算神经网络的输出，需要首先将输入向量$\\vec{x}$的每个元素的值$x_i$赋给神经网络的输入层的对应神经元，然后根据式1依次向前计算每一层的每个神经元的值，直到最后一层输出层的所有神经元的值计算完毕。最后，将输出层每个神经元的值串在一起就得到了输出向量$\\vec{y}$。\n", + "\n", + "接下来举一个例子来说明这个过程，我们先给神经网络的每个单元写上编号。\n", + "\n", + "![nn2](images/nn2.png)\n", + "\n", + "如上图，输入层有三个节点，我们将其依次编号为1、2、3；隐藏层的4个节点，编号依次为4、5、6、7；最后输出层的两个节点编号为8、9。因为我们这个神经网络是全连接网络，所以可以看到每个节点都和上一层的所有节点有连接。比如，我们可以看到隐藏层的节点4，它和输入层的三个节点1、2、3之间都有连接，其连接上的权重分别为$w_{41}$,$w_{42}$,$w_{43}$。那么，我们怎样计算节点4的输出值$a_4$呢？\n", + "\n", + "\n", + "为了计算节点4的输出值，我们必须先得到其所有上游节点（也就是节点1、2、3）的输出值。节点1、2、3是输入层的节点，所以，他们的输出值就是输入向量$\\vec{x}$本身。按照上图画出的对应关系，可以看到节点1、2、3的输出值分别是$x_1$,$x_2$,$x_3$。我们要求输入向量的维度和输入层神经元个数相同，而输入向量的某个元素对应到哪个输入节点是可以自由决定的，你偏非要把$x_1$赋值给节点2也是完全没有问题的，但这样除了把自己弄晕之外，并没有什么价值。\n", + "\n", + "一旦我们有了节点1、2、3的输出值，我们就可以根据式1计算节点4的输出值$a_4$：\n", + "![eqn_3_4](images/eqn_3_4.png)\n", + "\n", + "上式的$w_{4b}$是节点4的偏置项，图中没有画出来。而$w_{41}$,$w_{42}$,$w_{43}$分别为节点1、2、3到节点4连接的权重，在给权重$w_{ji}$编号时，我们把目标节点的编号$j$放在前面，把源节点的编号$i$放在后面。\n", + "\n", + "同样，我们可以继续计算出节点5、6、7的输出值$a_5$,$a_6$,$a_7$。这样，隐藏层的4个节点的输出值就计算完成了，我们就可以接着计算输出层的节点8的输出值$y_1$：\n", + "![eqn_5_6](images/eqn_5_6.png)\n", + "\n", + "同理，我们还可以计算出$y_2$的值。这样输出层所有节点的输出值计算完毕，我们就得到了在输入向量$\\vec{x} = (x_1, x_2, x_3)^T$时，神经网络的输出向量$\\vec{y} = (y_1, y_2)^T$。这里我们也看到，输出向量的维度和输出层神经元个数相同。\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 神经网络的矩阵表示\n", + "\n", + "神经网络的计算如果用矩阵来表示会很方便（当然逼格也更高），我们先来看看隐藏层的矩阵表示。\n", + "\n", + "首先我们把隐藏层4个节点的计算依次排列出来：\n", + "![eqn_hidden_units](images/eqn_hidden_units.png)\n", + "\n", + "接着，定义网络的输入向量$\\vec{x}$和隐藏层每个节点的权重向量$\\vec{w}$。令\n", + "\n", + "![eqn_7_12](images/eqn_7_12.png)\n", + "\n", + "代入到前面的一组式子，得到：\n", + "\n", + "![eqn_13_16](images/eqn_13_16.png)\n", + "\n", + "现在，我们把上述计算$a_4$, $a_5$,$a_6$,$a_7$的四个式子写到一个矩阵里面，每个式子作为矩阵的一行，就可以利用矩阵来表示它们的计算了。令\n", + "![eqn_matrix1](images/eqn_matrix1.png)\n", + "\n", + "带入前面的一组式子，得到\n", + "![formular_2](images/formular_2.png)\n", + "\n", + "在式2中，$f$是激活函数，在本例中是$sigmod$函数；$W$是某一层的权重矩阵；$\\vec{x}$是某层的输入向量；$\\vec{a}$是某层的输出向量。式2说明神经网络的每一层的作用实际上就是先将输入向量左乘一个数组进行线性变换，得到一个新的向量，然后再对这个向量逐元素应用一个激活函数。\n", + "\n", + "每一层的算法都是一样的。比如，对于包含一个输入层，一个输出层和三个隐藏层的神经网络，我们假设其权重矩阵分别为$W_1$,$W_2$,$W_3$,$W_4$，每个隐藏层的输出分别是$\\vec{a}_1$,$\\vec{a}_2$,$\\vec{a}_3$，神经网络的输入为$\\vec{x}$，神经网络的输出为$\\vec{y}$，如下图所示：\n", + "![nn_parameters_demo](images/nn_parameters_demo.png)\n", + "\n", + "则每一层的输出向量的计算可以表示为：\n", + "![eqn_17_20](images/eqn_17_20.png)\n", + "\n", + "\n", + "这就是神经网络输出值的矩阵计算方法。\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 神经网络的训练 - 反向传播算法\n", + "\n", + "现在，我们需要知道一个神经网络的每个连接上的权值是如何得到的。我们可以说神经网络是一个模型，那么这些权值就是模型的参数，也就是模型要学习的东西。然而，一个神经网络的连接方式、网络的层数、每层的节点数这些参数，则不是学习出来的，而是人为事先设置的。对于这些人为设置的参数，我们称之为超参数(Hyper-Parameters)。\n", + "\n", + "反向传播算法其实就是链式求导法则的应用。然而，这个如此简单且显而易见的方法，却是在Roseblatt提出感知器算法将近30年之后才被发明和普及的。对此，Bengio这样回应道：\n", + "\n", + "> 很多看似显而易见的想法只有在事后才变得显而易见。\n", + "\n", + "按照机器学习的通用套路，我们先确定神经网络的目标函数，然后用随机梯度下降优化算法去求目标函数最小值时的参数值。\n", + "\n", + "我们取网络所有输出层节点的误差平方和作为目标函数：\n", + "![bp_loss](images/bp_loss.png)\n", + "\n", + "其中，$E_d$表示是样本$d$的误差。\n", + "\n", + "然后，使用随机梯度下降算法对目标函数进行优化：\n", + "![bp_weight_update](images/bp_weight_update.png)\n", + "\n", + "随机梯度下降算法也就是需要求出误差$E_d$对于每个权重$w_{ji}$的偏导数（也就是梯度），怎么求呢？\n", + "![nn3](images/nn3.png)\n", + "\n", + "观察上图，我们发现权重$w_{ji}$仅能通过影响节点$j$的输入值影响网络的其它部分，设$net_j$是节点$j$的加权输入，即\n", + "![eqn_21_22](images/eqn_21_22.png)\n", + "\n", + "$E_d$是$net_j$的函数，而$net_j$是$w_{ji}$的函数。根据链式求导法则，可以得到：\n", + "\n", + "![eqn_23_25](images/eqn_23_25.png)\n", + "\n", + "\n", + "上式中，$x_{ji}$是节点传递给节点$j$的输入值，也就是节点$i$的输出值。\n", + "\n", + "对于的$\\frac{\\partial E_d}{\\partial net_j}$推导，需要区分输出层和隐藏层两种情况。\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 输出层权值训练\n", + "\n", + "![nn3](images/nn3.png)\n", + "\n", + "对于输出层来说，$net_j$仅能通过节点$j$的输出值$y_j$来影响网络其它部分，也就是说$E_d$是$y_j$的函数，而$y_j$是$net_j$的函数，其中$y_j = sigmod(net_j)$。所以我们可以再次使用链式求导法则：\n", + "![eqn_26](images/eqn_26.png)\n", + "\n", + "考虑上式第一项:\n", + "![eqn_27_29](images/eqn_27_29.png)\n", + "\n", + "\n", + "考虑上式第二项：\n", + "![eqn_30_31](images/eqn_30_31.png)\n", + "\n", + "将第一项和第二项带入，得到：\n", + "![eqn_ed_net_j.png](images/eqn_ed_net_j.png)\n", + "\n", + "如果令$\\delta_j = - \\frac{\\partial E_d}{\\partial net_j}$，也就是一个节点的误差项$\\delta$是网络误差对这个节点输入的偏导数的相反数。带入上式，得到：\n", + "![eqn_delta_j.png](images/eqn_delta_j.png)\n", + "\n", + "将上述推导带入随机梯度下降公式，得到：\n", + "![eqn_32_34.png](images/eqn_32_34.png)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 隐藏层权值训练\n", + "\n", + "现在我们要推导出隐藏层的$\\frac{\\partial E_d}{\\partial net_j}$。\n", + "\n", + "![nn3](images/nn3.png)\n", + "\n", + "首先，我们需要定义节点$j$的所有直接下游节点的集合$Downstream(j)$。例如，对于节点4来说，它的直接下游节点是节点8、节点9。可以看到$net_j$只能通过影响$Downstream(j)$再影响$E_d$。设$net_k$是节点$j$的下游节点的输入，则$E_d$是$net_k$的函数，而$net_k$是$net_j$的函数。因为$net_k$有多个，我们应用全导数公式，可以做出如下推导：\n", + "![eqn_35_40](images/eqn_35_40.png)\n", + "\n", + "因为$\\delta_j = - \\frac{\\partial E_d}{\\partial net_j}$，带入上式得到：\n", + "![eqn_delta_hidden.png](images/eqn_delta_hidden.png)\n", + "\n", + "\n", + "至此，我们已经推导出了反向传播算法。需要注意的是，我们刚刚推导出的训练规则是根据激活函数是sigmoid函数、平方和误差、全连接网络、随机梯度下降优化算法。如果激活函数不同、误差计算方式不同、网络连接结构不同、优化算法不同，则具体的训练规则也会不一样。但是无论怎样，训练规则的推导方式都是一样的，应用链式求导法则进行推导即可。\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 具体解释\n", + "\n", + "我们假设每个训练样本为$(\\vec{x}, \\vec{t})$，其中向量$\\vec{x}$是训练样本的特征，而$\\vec{t}$是样本的目标值。\n", + "\n", + "![nn3](images/nn3.png)\n", + "\n", + "首先，我们根据上一节介绍的算法，用样本的特征$\\vec{x}$，计算出神经网络中每个隐藏层节点的输出$a_i$，以及输出层每个节点的输出$y_i$。\n", + "\n", + "然后，我们按照下面的方法计算出每个节点的误差项$\\delta_i$：\n", + "\n", + "* **对于输出层节点$i$**\n", + "![formular_3.png](images/formular_3.png)\n", + "其中，$\\delta_i$是节点$i$的误差项，$y_i$是节点$i$的输出值，$t_i$是样本对应于节点$i$的目标值。举个例子，根据上图，对于输出层节点8来说，它的输出值是$y_1$，而样本的目标值是$t_1$，带入上面的公式得到节点8的误差项应该是：\n", + "![forumlar_delta8.png](images/forumlar_delta8.png)\n", + "\n", + "* **对于隐藏层节点**\n", + "![formular_4.png](images/formular_4.png)\n", + "\n", + "其中，$a_i$是节点$i$的输出值，$w_{ki}$是节点$i$到它的下一层节点$k$的连接的权重，$\\delta_k$是节点$i$的下一层节点$k$的误差项。例如，对于隐藏层节点4来说，计算方法如下：\n", + "![forumlar_delta4.png](images/forumlar_delta4.png)\n", + "\n", + "\n", + "最后，更新每个连接上的权值：\n", + "![formular_5.png](images/formular_5.png)\n", + "\n", + "其中，$w_{ji}$是节点$i$到节点$j$的权重，$\\eta$是一个成为学习速率的常数，$\\delta_j$是节点$j$的误差项，$x_{ji}$是节点$i$传递给节点$j$的输入。例如，权重$w_{84}$的更新方法如下：\n", + "![eqn_w84_update.png](images/eqn_w84_update.png)\n", + "\n", + "类似的，权重$w_{41}$的更新方法如下：\n", + "![eqn_w41_update.png](images/eqn_w41_update.png)\n", + "\n", + "\n", + "偏置项的输入值永远为1。例如，节点4的偏置项$w_{4b}$应该按照下面的方法计算：\n", + "![eqn_w4b_update.png](images/eqn_w4b_update.png)\n", + "\n", + "我们已经介绍了神经网络每个节点误差项的计算和权重更新方法。显然，计算一个节点的误差项，需要先计算每个与其相连的下一层节点的误差项。这就要求误差项的计算顺序必须是从输出层开始，然后反向依次计算每个隐藏层的误差项，直到与输入层相连的那个隐藏层。这就是反向传播算法的名字的含义。当所有节点的误差项计算完毕后，我们就可以根据式5来更新所有的权重。\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Program" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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0.51466915]\n", + " [0.69730956 0.41614571]\n", + " [0.63243373 0.55370584]\n", + " [0.67098643 0.49947521]\n", + " [0.68511739 0.44534543]\n", + " [0.65313156 0.51375309]\n", + " [0.63300568 0.56124219]\n", + " [0.63605962 0.539493 ]\n", + " [0.64836686 0.51628529]\n", + " [0.62139293 0.58008798]\n", + " [0.64932898 0.51333776]\n", + " [0.6235741 0.56673449]\n", + " [0.67305114 0.47308517]\n", + " [0.65700846 0.50320471]\n", + " [0.68682776 0.44420681]\n", + " [0.65349271 0.53822609]\n", + " [0.64658026 0.53509776]\n", + " [0.63130791 0.54998535]\n", + " [0.62871243 0.55143978]\n", + " [0.67641457 0.46208977]\n", + " [0.68083831 0.4618562 ]\n", + " [0.67051156 0.48964901]\n", + " [0.67839015 0.46427427]\n", + " [0.64545239 0.51292276]\n", + " [0.6606294 0.52549281]\n", + " [0.64222193 0.53932354]\n", + " [0.65220627 0.50861605]\n", + " [0.63349683 0.54876668]\n", + " [0.62113983 0.58530881]\n", + " [0.61760612 0.58478278]\n", + " [0.62154618 0.57528528]\n", + " [0.66276585 0.49998043]\n", + " [0.64789962 0.52213533]\n", + " [0.69171714 0.43236179]\n", + " [0.61884282 0.59008273]\n", + " [0.66202646 0.48904737]\n", + " [0.68505323 0.44422315]\n", + " [0.69703152 0.41719461]\n", + " [0.65463078 0.51385956]\n", + " [0.62727924 0.56710318]\n", + " [0.68234907 0.45343016]\n", + " [0.62152597 0.57502776]\n", + " [0.69106941 0.43467972]\n", + " [0.6577279 0.50070683]\n", + " [0.62167217 0.58763578]\n", + " [0.6319471 0.56142611]\n", + " [0.66526845 0.48615861]\n", + " [0.69239083 0.43076428]\n", + " [0.6302144 0.56671889]\n", + " [0.68269858 0.45823332]\n", + " [0.69473345 0.42048606]\n", + " [0.66914479 0.49183979]\n", + " [0.62590343 0.57079016]\n", + " [0.67882189 0.45883859]\n", + " [0.69099277 0.43617846]\n", + " [0.69857324 0.4111444 ]\n", + " [0.6257689 0.57580567]\n", + " [0.64428699 0.51370314]\n", + " [0.62812104 0.5542497 ]\n", + " [0.64162491 0.52666474]\n", + " [0.66370428 0.48858184]\n", + " [0.68245629 0.45374376]\n", + " [0.6439251 0.54817104]\n", + " [0.63229486 0.54634744]\n", + " [0.63368004 0.54360187]\n", + " [0.62920379 0.56252525]\n", + " [0.68802781 0.44443285]\n", + " [0.63367224 0.54096919]\n", + " [0.66908967 0.50101927]\n", + " [0.69333237 0.43288566]\n", + " [0.66294924 0.5164213 ]\n", + " [0.62071028 0.58516989]\n", + " [0.63089179 0.55649663]\n", + " [0.6960798 0.41867759]\n", + " [0.63428896 0.54164095]\n", + " [0.62316292 0.56879113]\n", + " [0.63333752 0.54240036]\n", + " [0.62334574 0.57923263]\n", + " [0.65510668 0.51380363]\n", + " [0.65758931 0.50857068]\n", + " [0.64630815 0.52118855]\n", + " [0.62065332 0.5763107 ]\n", + " [0.67037756 0.49168361]\n", + " [0.66297331 0.4903177 ]\n", + " [0.62110186 0.58268245]\n", + " [0.68025074 0.46575819]]\n" + ] + } + ], + "source": [ + "# generate the NN model\n", + "class NN_Model:\n", + " epsilon = 0.01 # learning rate\n", + " n_epoch = 1000 # iterative number\n", + " \n", + "nn = NN_Model()\n", + "nn.n_input_dim = X.shape[1] # input size\n", + "nn.n_output_dim = 2 # output node size\n", + "nn.n_hide_dim = 3 # hidden node size\n", + "\n", + "# initial weight array\n", + "nn.W1 = np.random.randn(nn.n_input_dim, nn.n_hide_dim) / np.sqrt(nn.n_input_dim)\n", + "nn.b1 = np.zeros((1, nn.n_hide_dim))\n", + "nn.W2 = np.random.randn(nn.n_hide_dim, nn.n_output_dim) / np.sqrt(nn.n_hide_dim)\n", + "nn.b2 = np.zeros((1, nn.n_output_dim))\n", + "\n", + "# defin sigmod & its derivate function\n", + "def sigmod(X):\n", + " return 1.0/(1+np.exp(-X))\n", + "\n", + "def sigmod_derivative(X):\n", + " f = sigmod(X)\n", + " return f*(1-f)\n", + "\n", + "# network forward calculation\n", + "def forward(n, X):\n", + " n.z1 = sigmod(X.dot(n.W1) + n.b1)\n", + " n.z2 = sigmod(n.z1.dot(n.W2) + n.b2)\n", + " return n\n", + "\n", + "# use random weight to perdict\n", + "forward(nn, X)\n", + "y = nn.z2[:, 0]>nn.z2[:,1]\n", + "y_pred = np.zeros(nn.z2.shape[0])\n", + "y_pred[np.where(nn.z2[:,0] 很多看似显而易见的想法只有在事后才变得显而易见。 +# +# 按照机器学习的通用套路，我们先确定神经网络的目标函数，然后用随机梯度下降优化算法去求目标函数最小值时的参数值。 +# +# 我们取网络所有输出层节点的误差平方和作为目标函数： +# ![bp_loss](images/bp_loss.png) +# +# 其中，$E_d$表示是样本$d$的误差。 +# +# 然后，使用随机梯度下降算法对目标函数进行优化： +# ![bp_weight_update](images/bp_weight_update.png) +# +# 随机梯度下降算法也就是需要求出误差$E_d$对于每个权重$w_{ji}$的偏导数（也就是梯度），怎么求呢？ +# ![nn3](images/nn3.png) +# +# 观察上图，我们发现权重$w_{ji}$仅能通过影响节点$j$的输入值影响网络的其它部分，设$net_j$是节点$j$的加权输入，即 +# ![eqn_21_22](images/eqn_21_22.png) +# +# $E_d$是$net_j$的函数，而$net_j$是$w_{ji}$的函数。根据链式求导法则，可以得到： +# +# ![eqn_23_25](images/eqn_23_25.png) +# +# +# 上式中，$x_{ji}$是节点传递给节点$j$的输入值，也就是节点$i$的输出值。 +# +# 对于的$\frac{\partial E_d}{\partial net_j}$推导，需要区分输出层和隐藏层两种情况。 +# +# + +# ### 输出层权值训练 +# +# ![nn3](images/nn3.png) +# +# 对于输出层来说，$net_j$仅能通过节点$j$的输出值$y_j$来影响网络其它部分，也就是说$E_d$是$y_j$的函数，而$y_j$是$net_j$的函数，其中$y_j = sigmod(net_j)$。所以我们可以再次使用链式求导法则： +# ![eqn_26](images/eqn_26.png) +# +# 考虑上式第一项: +# ![eqn_27_29](images/eqn_27_29.png) +# +# +# 考虑上式第二项： +# ![eqn_30_31](images/eqn_30_31.png) +# +# 将第一项和第二项带入，得到： +# ![eqn_ed_net_j.png](images/eqn_ed_net_j.png) +# +# 如果令$\delta_j = - \frac{\partial E_d}{\partial net_j}$，也就是一个节点的误差项$\delta$是网络误差对这个节点输入的偏导数的相反数。带入上式，得到： +# ![eqn_delta_j.png](images/eqn_delta_j.png) +# +# 将上述推导带入随机梯度下降公式，得到： +# ![eqn_32_34.png](images/eqn_32_34.png) +# + +# ### 隐藏层权值训练 +# +# 现在我们要推导出隐藏层的$\frac{\partial E_d}{\partial net_j}$。 +# +# ![nn3](images/nn3.png) +# +# 首先，我们需要定义节点$j$的所有直接下游节点的集合$Downstream(j)$。例如，对于节点4来说，它的直接下游节点是节点8、节点9。可以看到$net_j$只能通过影响$Downstream(j)$再影响$E_d$。设$net_k$是节点$j$的下游节点的输入，则$E_d$是$net_k$的函数，而$net_k$是$net_j$的函数。因为$net_k$有多个，我们应用全导数公式，可以做出如下推导： +# ![eqn_35_40](images/eqn_35_40.png) +# +# 因为$\delta_j = - \frac{\partial E_d}{\partial net_j}$，带入上式得到： +# ![eqn_delta_hidden.png](images/eqn_delta_hidden.png) +# +# +# 至此，我们已经推导出了反向传播算法。需要注意的是，我们刚刚推导出的训练规则是根据激活函数是sigmoid函数、平方和误差、全连接网络、随机梯度下降优化算法。如果激活函数不同、误差计算方式不同、网络连接结构不同、优化算法不同，则具体的训练规则也会不一样。但是无论怎样，训练规则的推导方式都是一样的，应用链式求导法则进行推导即可。 +# + +# ### 具体解释 +# +# 我们假设每个训练样本为$(\vec{x}, \vec{t})$，其中向量$\vec{x}$是训练样本的特征，而$\vec{t}$是样本的目标值。 +# +# ![nn3](images/nn3.png) +# +# 首先，我们根据上一节介绍的算法，用样本的特征$\vec{x}$，计算出神经网络中每个隐藏层节点的输出$a_i$，以及输出层每个节点的输出$y_i$。 +# +# 然后，我们按照下面的方法计算出每个节点的误差项$\delta_i$： +# +# * **对于输出层节点$i$** +# ![formular_3.png](images/formular_3.png) +# 其中，$\delta_i$是节点$i$的误差项，$y_i$是节点$i$的输出值，$t_i$是样本对应于节点$i$的目标值。举个例子，根据上图，对于输出层节点8来说，它的输出值是$y_1$，而样本的目标值是$t_1$，带入上面的公式得到节点8的误差项应该是： +# ![forumlar_delta8.png](images/forumlar_delta8.png) +# +# * **对于隐藏层节点** +# ![formular_4.png](images/formular_4.png) +# +# 其中，$a_i$是节点$i$的输出值，$w_{ki}$是节点$i$到它的下一层节点$k$的连接的权重，$\delta_k$是节点$i$的下一层节点$k$的误差项。例如，对于隐藏层节点4来说，计算方法如下： +# ![forumlar_delta4.png](images/forumlar_delta4.png) +# +# +# 最后，更新每个连接上的权值： +# ![formular_5.png](images/formular_5.png) +# +# 其中，$w_{ji}$是节点$i$到节点$j$的权重，$\eta$是一个成为学习速率的常数，$\delta_j$是节点$j$的误差项，$x_{ji}$是节点$i$传递给节点$j$的输入。例如，权重$w_{84}$的更新方法如下： +# ![eqn_w84_update.png](images/eqn_w84_update.png) +# +# 类似的，权重$w_{41}$的更新方法如下： +# ![eqn_w41_update.png](images/eqn_w41_update.png) +# +# +# 偏置项的输入值永远为1。例如，节点4的偏置项$w_{4b}$应该按照下面的方法计算： +# ![eqn_w4b_update.png](images/eqn_w4b_update.png) +# +# 我们已经介绍了神经网络每个节点误差项的计算和权重更新方法。显然，计算一个节点的误差项，需要先计算每个与其相连的下一层节点的误差项。这就要求误差项的计算顺序必须是从输出层开始，然后反向依次计算每个隐藏层的误差项，直到与输入层相连的那个隐藏层。这就是反向传播算法的名字的含义。当所有节点的误差项计算完毕后，我们就可以根据式5来更新所有的权重。 +# +# + +# ## Program + +# + +% matplotlib inline + +import numpy as np +from sklearn import datasets, linear_model +import matplotlib.pyplot as plt + +# generate sample data +np.random.seed(0) +X, y = datasets.make_moons(200, noise=0.20) + +# plot data +plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral) +plt.show() + +# + +# generate the NN model +class NN_Model: + epsilon = 0.01 # learning rate + n_epoch = 1000 # iterative number + +nn = NN_Model() +nn.n_input_dim = X.shape[1] # input size +nn.n_output_dim = 2 # output node size +nn.n_hide_dim = 3 # hidden node size + +# initial weight array +nn.W1 = np.random.randn(nn.n_input_dim, nn.n_hide_dim) / np.sqrt(nn.n_input_dim) +nn.b1 = np.zeros((1, nn.n_hide_dim)) +nn.W2 = np.random.randn(nn.n_hide_dim, nn.n_output_dim) / np.sqrt(nn.n_hide_dim) +nn.b2 = np.zeros((1, nn.n_output_dim)) + +# defin sigmod & its derivate function +def sigmod(X): + return 1.0/(1+np.exp(-X)) + +def sigmod_derivative(X): + f = sigmod(X) + return f*(1-f) + +# network forward calculation +def forward(n, X): + n.z1 = sigmod(X.dot(n.W1) + n.b1) + n.z2 = sigmod(n.z1.dot(n.W2) + n.b2) + return n + +# use random weight to perdict +forward(nn, X) +y = nn.z2[:, 0]>nn.z2[:,1] +y_pred = np.zeros(nn.z2.shape[0]) +y_pred[np.where(nn.z2[:,0]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "plt.scatter(X_train, y_train)\n", + "plt.scatter(X_test, y_test)\n", + "plt.xlabel('Data')\n", + "plt.ylabel('Target');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Linear regression\n", + "=================\n", + "Create linear regression object, which we use later to apply linear regression on data" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn import linear_model\n", + "import numpy as np\n", + "regr = linear_model.LinearRegression()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fit the model using the training set" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "regr.fit(X_train, y_train);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We found the coefficients and the bias (the intercept)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[988.07836941]\n", + "150.80798145969447\n" + ] + } + ], + "source": [ + "print(regr.coef_)\n", + "print(regr.intercept_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we calculate the mean square error on the test set" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Training error: 3960.4058766864073\n", + "Test error: 3811.1989929980004\n" + ] + } + ], + "source": [ + "# The mean square error\n", + "print(\"Training error: \", np.mean((regr.predict(X_train) - y_train) ** 2))\n", + "print(\"Test error: \", np.mean((regr.predict(X_test) - y_test) ** 2))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting data and linear model\n", + "==============================\n", + "Now we want to plot the train data and teachers (marked as dots). \n", + "\n", + "With line we represents the data and predictions (linear model that we found):\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,'Target')" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Visualises dots, where each dot represent a data exaple and corresponding teacher\n", + "plt.scatter(X_train, y_train, color='black')\n", + "# Plots the linear model\n", + "plt.plot(X_train, regr.predict(X_train), color='blue', linewidth=3);\n", + "plt.xlabel('Data')\n", + "plt.ylabel('Target')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We do similar with test data, and show that linear model is valid for a test set:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Visualises dots, where each dot represent a data example and corresponding teacher\n", + "plt.scatter(X_test, y_test, color='black')\n", + "# Plots the linear model\n", + "plt.plot(X_test, regr.predict(X_test), color='blue', linewidth=3);\n", + "plt.xlabel('Data')\n", + "plt.ylabel('Target');" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/references/logistic_regression_demo/3b - Linear regression 2D.ipynb b/references/logistic_regression_demo/3b - Linear regression 2D.ipynb new file mode 100644 index 0000000..0cec971 --- /dev/null +++ b/references/logistic_regression_demo/3b - Linear regression 2D.ipynb @@ -0,0 +1,433 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Loading data\n", + "=====================================================\n", + "We will work with \"Parkinsons Telemonitoring\" dataset of the University of Oxford. The original study used a range of linear regression methods to predict the clinician's Parkinson's disease symptom score on the UPDRS scale\n", + "\n", + "We load the dataset \"Parkinsons Telemonitoring\" using the numpy loadtxt function.\n", + "\n", + "The columns are separated by ',' delimiter, which we pass to the loadtxt function." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# matplotlib inline\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "data = np.loadtxt(\"data/artifical_lin.txt\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We want to work now with 2-dim data, in order to plot it in 3d space. Therefore we select 2 columns (attributes) from total of 12 columns. \n", + "\n", + "In this example we will select attributes \"Clinician's motor UPDRS score\" and \"Clinician's total UPDRS score\", which are 4th and 5th columns. " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.00747581 0.43208362]\n", + " [0.49910584 0.20943748]\n", + " [0.11935362 0.59634898]\n", + " [0.47691878 0.91091956]\n", + " [0.73039367 0.88576849]\n", + " [0.96646013 0.75029941]\n", + " [0.0254202 0.74285026]\n", + " [0.17781366 0.59303845]\n", + " [0.44925923 0.89314114]\n", + " [0.08370431 0.26143735]]\n", + "[1.45054918 1.1025327 1.33827336 2.6022192 2.2101526 2.6110778\n", + " 1.71069895 2.23335293 3.10281928 0.86406978]\n" + ] + } + ], + "source": [ + "X = data[:, :-1]\n", + "y = data[:, -1]\n", + "print(X[:10, :])\n", + "print(y[:10])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We shuffle examples:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(500, 2)\n", + "(500,)\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/bushuhui/.virtualenv/fintech/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n", + " return f(*args, **kwds)\n", + "/home/bushuhui/.virtualenv/fintech/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n", + " return f(*args, **kwds)\n", + "/home/bushuhui/.virtualenv/fintech/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n", + " return f(*args, **kwds)\n" + ] + } + ], + "source": [ + "from sklearn.utils import shuffle\n", + "X, y = shuffle(X, y, random_state=1)\n", + "print(X.shape)\n", + "print(y.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we split the data into train and test set:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "train_set_size = 250 \n", + "(250, 2)\n", + "(250, 2)\n" + ] + } + ], + "source": [ + "train_set_size = int(X.shape[0] / 2)\n", + "print(\"train_set_size = %d \" % train_set_size)\n", + "\n", + "X_train = X[:train_set_size, :] # selects first train_set_size rows (examples) for train set\n", + "X_test = X[train_set_size:, :] # selects from row train_set_size until the last one for test set\n", + "print(X_train.shape)\n", + "print(X_test.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we split the targets into train and test set in similar way as we splitted data:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(250,)\n", + "(250,)\n" + ] + } + ], + "source": [ + "y_train = y[:train_set_size] # selects first 15 rows (targets) for train set\n", + "y_test = y[train_set_size:] # selects from row 250 until the last one for test set\n", + "print(y_train.shape)\n", + "print(y_test.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's look at the data in the 3d plot. There is some linear relationship in the data:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = Axes3D(fig)\n", + "ax.scatter3D(X_train[:500, 0], X_train[:500, 1], y_train[:500])\n", + "ax.view_init(6,-20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Linear regression\n", + "=================\n", + "Create linear regression object, which we use later to apply linear regression on data" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/bushuhui/.virtualenv/fintech/lib/python3.5/importlib/_bootstrap.py:222: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n", + " return f(*args, **kwds)\n" + ] + } + ], + "source": [ + "from sklearn import linear_model\n", + "regr = linear_model.LinearRegression()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fit the model using the training set" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "regr.fit(X_train, y_train);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We found the coefficients and the bias (the intercept)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.08241879 2.96344602]\n", + "0.09703581706766884\n" + ] + } + ], + "source": [ + "print(regr.coef_)\n", + "print(regr.intercept_)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we calculate the mean square error on the test set" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Training error: 0.1527714636459691\n", + "Test error: 0.16965042383819598\n" + ] + } + ], + "source": [ + "# The mean square error\n", + "print(\"Training error: \", np.mean((regr.predict(X_train) - y_train) ** 2))\n", + "print(\"Test error: \", np.mean((regr.predict(X_test) - y_test) ** 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting data and linear model\n", + "==============================\n", + "Now we want to plot the train data and teachers in 3d plot (marked as dots). \n", + "\n", + "With plane we represents the data and predictions (linear model that we found).\n", + "\n", + "We first scatter the 3d points using mplot3d:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = Axes3D(fig)\n", + "\n", + "\n", + "ax.scatter3D(X_train[:500, 0], X_train[:500, 1], y_train[:500]) # plots 3d points, 500 is number of points which are visualized\n", + "\n", + "# here we create plane which we want to plot, using the train data and predictions (you don't need to understand it)\n", + "range_x = np.linspace(X_train[:, 0].min(), X_train[:, 0].max(), num=10)\n", + "range_y = np.linspace(X_train[:, 1].min(), X_train[:, 1].max(), num=10)\n", + "xx, yy = np.meshgrid(range_x, range_y)\n", + "zz = np.vstack([xx.ravel(), yy.ravel()]).T\n", + "pred = regr.predict(zz)\n", + "pred = pred.reshape(10, 10)\n", + "\n", + "ax.plot_surface(xx, yy, pred, alpha=.1) # plots the plane\n", + "ax.view_init(6,-20)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we plot the data and the plane in similar way for test data:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from mpl_toolkits.mplot3d import Axes3D\n", + "fig = plt.figure()\n", + "ax = Axes3D(fig)\n", + "ax.scatter3D(X_test[:500, 0], X_test[:500, 1], y_test[:500]) # plots 3d points 500 is number of points which are visualized\n", + "\n", + "# here we create plane which we want to plot, using the train data and predictions (you don't need to understand it)\n", + "range_x = np.linspace(X_test[:, 0].min(), X_test[:, 0].max(), num=10)\n", + "range_y = np.linspace(X_test[:, 1].min(), X_test[:, 1].max(), num=10)\n", + "xx, yy = np.meshgrid(range_x, range_y)\n", + "zz = np.vstack([xx.ravel(), yy.ravel()]).T\n", + "pred = regr.predict(zz)\n", + "pred = pred.reshape(10, 10)\n", + "\n", + "ax.plot_surface(xx, yy, pred, alpha=.1) # plots the plane\n", + "ax.view_init(6,-20)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Playing with this Notebook\n", + "==========================\n", + "\n", + "Do linear regression on dataset named 'artifical_lin\".\n", + "\n", + "Try to see what happens with the error, if you change the sizes of train set and test set. \n", + "\n", + "Add noise to the data, and fit the model again. How does the error changes when you add more noise?\n", + "\n", + "You add noise using normal distribution, with mean 0 and width 0.4 (you can vary this parameters).\n", + "noise = np.random.normal(0,0.4, (train_set_size,2))\n", + "\n", + "Add noise to data:\n", + "X = X + noise\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": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/references/logistic_regression_demo/4 - Logistic Regression.ipynb b/references/logistic_regression_demo/4 - Logistic Regression.ipynb new file mode 100644 index 0000000..3f8d950 --- /dev/null +++ b/references/logistic_regression_demo/4 - Logistic Regression.ipynb @@ -0,0 +1,658 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Logistic Regression\n", + "===================" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we generate some data to train to train with." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.datasets import make_blobs\n", + "X, y = make_blobs(centers=2) # generate dataset consisting of two Gaussian clusters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Take a look at how large the data is and what the labels look like:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X.shape: (100, 2)\n", + "y: [1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0\n", + " 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0\n", + " 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0]\n" + ] + } + ], + "source": [ + "print \"X.shape:\", X.shape \n", + "print \"y: \", y " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As the data is two-dimensional, we can easily visualize it:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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TM/licfEx/OrVqzPu6fFsiHTnp6GuJLR0Z+jgx6hXr16J9m/K66/y6DN/J8H/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\niB1TyIuI2DGFvIiIHVPIi4jYsf8DukTFtk9nJv0AAAAASUVORK5CYII=\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.prism()\n", + "plt.scatter(X[:, 0], X[:, 1], c=y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Import logistic regression from scikit-learn and generate a classification object." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "logreg = LogisticRegression()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Split the dataset into a training set and a test set." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "X_train = X[:50]\n", + "y_train = y[:50]\n", + "X_test = X[50:]\n", + "y_test = y[50:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To get an idea of how hard the task is, let us visualize the data again, this time only labeling the training points.\n", + "\n", + "The test points are plottet as white triangles.\n", + "Can we see which class the test points belong to?" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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PVaJ+/fpVOteVK1ciKyurSm3QU2hlhX4F6ahboudSdna2eHfkW8LK2lLMmjVL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\nkCcikjCGPBGRhDHkiYgkjCFPRCRh/wec8kSBPkpGngAAAABJRU5ErkJggg==\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.prism()\n", + "plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train)\n", + "plt.scatter(X_test[:, 0], X_test[:, 1], c='white', marker='^')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That doesn't look too hard.\n", + "\n", + "Now let's fit the logistic regression model to the training data, to see if we can do it automatically:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", + " intercept_scaling=1, penalty='l2', random_state=None, tol=0.0001)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "logreg.fit(X_train, y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, we have a look at how logistic regression did on the training set.\n", + "\n", + "We do this by now setting colors using the predicted class." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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mKCiIK6+8klq1alGmTBmuv/561q/czNM936BJ9TYsWrCI0pFhvDD6eYwxPPX4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\nNlLoiojY6P8B89y1HqfLjHwAAAAASUVORK5CYII=\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from utility import plot_decision_boundary\n", + "y_pred_train = logreg.predict(X_train)\n", + "plt.scatter(X_train[:, 0], X_train[:, 1], c=y_pred_train)\n", + "plot_decision_boundary(logreg, X)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "That looks pretty good. It is not always that easy to inspect the result visually,\n", + "so we can also use the logistic regression object to calculate a core for us:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy on training set: 1.0\n" + ] + } + ], + "source": [ + "print \"Accuracy on training set:\", logreg.score(X_train, y_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1.0 means an accuracy of 100%, just as it looked like.\n", + "\n", + "Now let us have a look at how the algorithm generalizes to the test data." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy on test set: 1.0\n" + ] + }, + { + "data": { + "image/png": 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IwORlIivdxak9qezbt59adWtQf1kKxarBlv/a+L9K/Xl90Bt06daZbaUWcPw7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\nQ1cppdzo/wEzbZF7AN/ugwAAAABJRU5ErkJggg==\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "y_pred_test = logreg.predict(X_test)\n", + "plt.scatter(X_test[:, 0], X_test[:, 1], c=y_pred_test, marker='^')\n", + "plt.scatter(X_train[:, 0], X_train[:, 1], c=y_pred_train)\n", + "plot_decision_boundary(logreg, X)\n", + "print \"Accuracy on test set:\", logreg.score(X_test, y_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also take a look at the coefficients, but they probably don't tell you much." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[ 0.42842754, -0.62076837]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "logreg.coef_" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "MNIST DIGITS\n", + "-------------\n", + "Let's go back to the MNIST example of before.\n", + "This dataset is a bit more exciting since it is much higher dimensional and not as easy to separate.\n", + "First we load the data again" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.datasets import fetch_mldata\n", + "mnist = fetch_mldata(\"MNIST original\")\n", + "X_digits, y_digits = mnist.data, mnist.target" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember what the dataset looks like:\n", + "\n", + "- 70000 examples, 784 dimensional\n", + "- ten classes, 0-9\n", + "- each 784 vector is a 28 * 28 digit" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X_digits.shape: (70000, 784)\n", + "Unique entries of y_digits: [ 0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n" + ] + } + ], + "source": [ + "print \"X_digits.shape:\", X_digits.shape\n", + "print \"Unique entries of y_digits:\", np.unique(y_digits)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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z584NZzsDeuihh5T1BQsWKOuvvvrqcLZD/0+VP860IxKEgScShIEnEoSBJxKEgScShIEn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\nEwnCwBMJwsATCcLAEwnyf5Vj4wB6AR6qAAAAAElFTkSuQmCC\n" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(y_digits[0])\n", + "plt.rc(\"image\", cmap=\"binary\")\n", + "plt.matshow(X_digits[0].reshape(28, 28))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We could try to learn all ten classes with logistic regression, but let us keep with two classes for the moment.\n", + "We will use two classes that are quite hard to distinguish: seven and nine.\n", + "\n", + "To create a dataset only consisting of the classes zero and one, we need a new numpy trick!\n", + "\n", + "We can not only slice our data using ranges, like ``X[5:10]``, we can also select elements using conditions, like so:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "zeros.shape: (6903, 784)\n", + "ones.shape: (7877, 784)\n" + ] + } + ], + "source": [ + "zeros = X_digits[y_digits==0] # select all the rows of X where y is zero (i.e. the zeros)\n", + "ones = X_digits[y_digits==1] # select all the rows of X where y is one (i.e. the ones)\n", + "print \"zeros.shape: \", zeros.shape\n", + "print \"ones.shape: \", ones.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Lets have a quick look to see that we did it right." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.matshow(ones[0].reshape(28, 28)) # change the 0 to another number to see some more zeros. Or try looking at some ones." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we generate some new data set.\n", + "\n", + "For the training labels y, we write as many 0's as the ``zeros`` array is long, the asame for ``ones``." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X_new.shape: (14780, 784)\n", + "y_new.shape: (14780,)\n", + "y_new: [0 0 0 ..., 1 1 1]\n" + ] + } + ], + "source": [ + "X_new = np.vstack([zeros, ones]) # this \"stacks\" sevens and nines vertically\n", + "print \"X_new.shape: \", X_new.shape\n", + "y_new = np.hstack([np.repeat(0, zeros.shape[0]), np.repeat(1, ones.shape[0])])\n", + "print \"y_new.shape: \", y_new.shape\n", + "print \"y_new: \", y_new" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we shuffle them around and create a training and test dataset." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.utils import shuffle\n", + "X_new, y_new = shuffle(X_new, y_new)\n", + "X_mnist_train = X_new[:5000]\n", + "y_mnist_train = y_new[:5000]\n", + "X_mnist_test = X_new[5000:]\n", + "y_mnist_test = y_new[5000:]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let us learn a logistic regression model." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n", + " intercept_scaling=1, penalty='l2', random_state=None, tol=0.0001)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "logreg.fit(X_mnist_train, y_mnist_train)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "... and visualize the coefficients.\n", + "\n", + "We can see that the middle is dark, corresponding to high positive values for where\n", + "a 1 would be. Around it is a lighter circle, corresponding to the position of a 0." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.matshow(logreg.coef_.reshape(28, 28))\n", + "plt.colorbar()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, let as look at the accuracy on training and test set:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Accuracy training set: 1.0\n", + "Accuracy test set: 0.998466257669\n" + ] + } + ], + "source": [ + "print \"Accuracy training set:\", logreg.score(X_mnist_train, y_mnist_train)\n", + "print \"Accuracy test set:\", logreg.score(X_mnist_test, y_mnist_test)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Playing around with this notebook\n", + "=================================\n", + "1. What would be the accuracy of a completely random predictor on the first dataset?\n", + "\n", + "2. Can you still pick out the class yourself if you set the ``cluster_std`` to ``10`` in ``make_blobs``? Can logistic regression do it?\n", + "\n", + "3. Try to separate some other digit classes from MNIST. Which are hard, which are not?\n", + "\n", + "4. Visualize the classes 0 and 1 using PCA down to two dimensions. Use a scatter plot as above. Would you expect they can be separated with a linear classifier?" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": "3.5.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/references/logistic_regression_demo/data/artifical_lin.txt b/references/logistic_regression_demo/data/artifical_lin.txt new file mode 100644 index 0000000..fc158e3 --- /dev/null +++ b/references/logistic_regression_demo/data/artifical_lin.txt @@ -0,0 +1,500 @@ +7.475811838082768723e-03 4.320836189610323119e-01 1.450549175723391038e+00 +4.991058415580543750e-01 2.094374801667562291e-01 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os.path.join(os.environ["HOME"], "Desktop", "Tutorial") +# It's a good idea to put it on a known, fixed port +c.NotebookApp.port = 9999 +#c.NotebookApp.password = u'sha1:60e7d2645fb4:97064d28bad2a4a12950055c830d9637b652c9ec' diff --git a/references/logistic_regression_demo/utility.py b/references/logistic_regression_demo/utility.py new file mode 100644 index 0000000..213a11f --- /dev/null +++ b/references/logistic_regression_demo/utility.py @@ -0,0 +1,25 @@ +import numpy as np +import matplotlib.pyplot as plt + + +def plot_decision_boundary(clf, X): + w = clf.coef_.ravel() + a = -w[0] / w[1] + xx = np.linspace(np.min(X[:, 0]), np.max(X[:, 0])) + yy = a * xx - clf.intercept_ / w[1] + plt.plot(xx, yy) + plt.xticks(()) + plt.yticks(()) + +def plotEllipse(pos,P,edge='k',face='none',line_width='.1'): + from numpy.linalg import svd + from matplotlib.patches import Ellipse + import math + from numpy import pi + from matplotlib.pyplot import gca + U, s , Vh = svd(P) + orient = math.atan2(U[1,0],U[0,0])*180/pi + ellipsePlot = Ellipse(xy=pos, width=2.0*math.sqrt(s[0]), height=2.0*math.sqrt(s[1]), angle=orient,facecolor=face, edgecolor=edge, lw=line_width) + ax = gca() + ax.add_patch(ellipsePlot); + return ellipsePlot diff --git a/references/nn/.nn_2.py.kate-swp b/references/nn/.nn_2.py.kate-swp new file mode 100644 index 0000000..f37ba8f Binary files /dev/null and b/references/nn/.nn_2.py.kate-swp differ diff --git a/nn/nn-from-scratch b/references/nn/nn-from-scratch similarity index 100% rename from nn/nn-from-scratch rename to references/nn/nn-from-scratch diff --git a/references/nn/nn_1.py b/references/nn/nn_1.py new file mode 100644 index 0000000..7487ee4 --- /dev/null +++ b/references/nn/nn_1.py @@ -0,0 +1,98 @@ +# +# BP demo code +# +# reference: +# https://www.2cto.com/kf/201612/543750.html +# + +import numpy as np +from sklearn import datasets, linear_model +import matplotlib.pyplot as plt + + +class Config: + nn_input_dim = 2 + nn_output_dim = 2 + epsilon = 0.01 + reg_lambda = 0.01 + + +def generate_data(): + np.random.seed(0) + X, y = datasets.make_moons(200, noise=0.20) + return X, y + + +def visualize(X, y, model): + plot_decision_boundary(lambda x:predict(model,x), X, y) + plt.title("Logistic Regression") + + +def plot_decision_boundary(pred_func, X, y): + x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5 + y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5 + h = 0.01 + xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) + Z = pred_func(np.c_[xx.ravel(), yy.ravel()]) + Z = Z.reshape(xx.shape) + plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) + plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral) + plt.show() + +def predict(model, x): + W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2'] + z1 = x.dot(W1) + b1 + a1 = np.tanh(z1) + z2 = a1.dot(W2) + b2 + exp_scores = np.exp(z2) + probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) + return np.argmax(probs, axis=1) + + +def build_model(X, y, nn_hdim, num_passes=20000, print_loss=False): + num_examples = len(X) + np.random.seed(0) + W1 = np.random.randn(Config.nn_input_dim, nn_hdim) / np.sqrt(Config.nn_input_dim) + b1 = np.zeros((1, nn_hdim)) + W2 = np.random.randn(nn_hdim, Config.nn_output_dim) / np.sqrt(nn_hdim) + b2 = np.zeros((1, Config.nn_output_dim)) + + model = {} + + for i in range(0, num_passes): + + z1 = X.dot(W1) + b1 + a1 = np.tanh(z1) + z2 = a1.dot(W2) + b2 + exp_scores = np.exp(z2) + probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True) + + delta3 = probs + delta3[range(num_examples), y] -= 1 + dW2 = (a1.T).dot(delta3) + db2 = np.sum(delta3, axis=0, keepdims=True) + delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2)) + dW1 = np.dot(X.T, delta2) + db1 = np.sum(delta2, axis=0) + + dW2 += Config.reg_lambda * W2 + dW1 += Config.reg_lambda * W1 + + W1 += -Config.epsilon * dW1 + b1 += -Config.epsilon * db1 + W2 += -Config.epsilon * dW2 + b2 += -Config.epsilon * db2 + + model = {'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2} + + return model + + +def main(): + X, y = generate_data() + model = build_model(X, y, 3) + visualize(X, y, model) + + +if __name__ == "__main__": + main() diff --git a/references/nn/nn_2.py b/references/nn/nn_2.py new file mode 100644 index 0000000..7bedb8c --- /dev/null +++ b/references/nn/nn_2.py @@ -0,0 +1,15 @@ + +import numpy as np +from sklearn import datasets, linear_model +import matplotlib.pyplot as plt + + +class nn: + epsilon = 0.01 + + +def generate_data(): + np.random.seed(0) + X, y = datasets.make_moons(200, noise=0.20) + return X, y + diff --git a/supervised_learning/Recognizing hand-written digits - SVM.ipynb b/references/supervised_learning/Recognizing hand-written digits - SVM.ipynb similarity index 100% rename from supervised_learning/Recognizing hand-written digits - SVM.ipynb rename to references/supervised_learning/Recognizing hand-written digits - SVM.ipynb diff --git a/supervised_learning/supervised learning.ipynb b/references/supervised_learning/supervised learning.ipynb similarity index 100% rename from supervised_learning/supervised learning.ipynb rename to references/supervised_learning/supervised learning.ipynb