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nn-from-scratch.ipynb 503 kB

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  1. {
  2. "cells": [
  3. {
  4. "cell_type": "markdown",
  5. "metadata": {},
  6. "source": [
  7. "# Implementing a Neural Network from Scratch - An Introduction\n",
  8. "\n",
  9. "In this post we will implement a simple 3-layer neural network from scratch. We won't derive all the math that's required, but I will try to give an intuitive explanation of what we are doing and will point to resources to read up on the details.\n",
  10. "\n",
  11. "In this post I'm assuming that you are familiar with basic Calculus and Machine Learning concepts, e.g. you know what classification and regularization is. Ideally you also know a bit about how optimization techniques like gradient descent work. But even if you're not familiar with any of the above this post could still turn out to be interesting ;)\n",
  12. "\n",
  13. "But why implement a Neural Network from scratch at all? Even if you plan on using Neural Network libraries like [PyBrain](http://pybrain.org) in the future, implementing a network from scratch at least once is an extremely valuable exercise. It helps you gain an understanding of how neural networks work, and that is essential to designing effective models.\n",
  14. "\n",
  15. "One thing to note is that the code examples here aren't terribly efficient. They are meant to be easy to understand. In an upcoming post I will explore how to write an efficient Neural Network implementation using [Theano](http://deeplearning.net/software/theano/). "
  16. ]
  17. },
  18. {
  19. "cell_type": "code",
  20. "execution_count": 1,
  21. "metadata": {},
  22. "outputs": [],
  23. "source": [
  24. "# Package imports\n",
  25. "import matplotlib.pyplot as plt\n",
  26. "import numpy as np\n",
  27. "import sklearn\n",
  28. "import sklearn.datasets\n",
  29. "import sklearn.linear_model\n",
  30. "import matplotlib\n",
  31. "\n",
  32. "# Display plots inline and change default figure size\n",
  33. "%matplotlib inline\n",
  34. "matplotlib.rcParams['figure.figsize'] = (10.0, 8.0)"
  35. ]
  36. },
  37. {
  38. "cell_type": "markdown",
  39. "metadata": {},
  40. "source": [
  41. "## Generating a dataset\n",
  42. "\n",
  43. "Let's start by generating a dataset we can play with. Fortunately, [scikit-learn](http://scikit-learn.org/) has some useful dataset generators, so we don't need to write the code ourselves. We will go with the [`make_moons`](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html) function."
  44. ]
  45. },
  46. {
  47. "cell_type": "code",
  48. "execution_count": 2,
  49. "metadata": {},
  50. "outputs": [
  51. {
  52. "data": {
  53. "text/plain": [
  54. "<matplotlib.collections.PathCollection at 0x110609f50>"
  55. ]
  56. },
  57. "execution_count": 2,
  58. "metadata": {},
  59. "output_type": "execute_result"
  60. },
  61. {
  62. "data": {
  63. 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MxMfHxyY5hRD5gxReQogHlpycjKIoeHl53f/gAioyMpLR77zL1t9+w9XZmZd69uTDiR/j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\n2o4DBw4SFRVFVFQUjdA8j7IBNiQ9TCAyMrI8wxUErROJlyC8pLZt24S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sCsqcJRM6Zzmw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3xVKlcjPuFwrjLLshF36gg1atRwUFTFx5jRr1O/Rh9qVeuEi4sb3l4BtG3yAKGhO9m8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\nAABJRU5ErkJggg==\n"
  64. },
  65. "metadata": {},
  66. "output_type": "display_data"
  67. }
  68. ],
  69. "source": [
  70. "# Generate a dataset and plot it\n",
  71. "np.random.seed(0)\n",
  72. "X, y = sklearn.datasets.make_moons(200, noise=0.20)\n",
  73. "plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)"
  74. ]
  75. },
  76. {
  77. "cell_type": "markdown",
  78. "metadata": {},
  79. "source": [
  80. "The dataset we generated has two classes, plotted as red and blue points. You can think of the blue dots as male patients and the red dots as female patients, with the x- and y- axis being medical measurements. \n",
  81. "\n",
  82. "Our goal is to train a Machine Learning classifier that predicts the correct class (male or female) given the x- and y- coordinates. Note that the data is not *linearly separable*, we can't draw a straight line that separates the two classes. This means that linear classifiers, such as Logistic Regression, won't be able to fit the data unless you hand-engineer non-linear features (such as polynomials) that work well for the given dataset.\n",
  83. "\n",
  84. "In fact, that's one of the major advantages of Neural Networks. You don't need to worry about [feature engineering](http://machinelearningmastery.com/discover-feature-engineering-how-to-engineer-features-and-how-to-get-good-at-it/). The hidden layer of a neural network will learn features for you."
  85. ]
  86. },
  87. {
  88. "cell_type": "markdown",
  89. "metadata": {},
  90. "source": [
  91. "## Logistic Regression\n",
  92. "\n",
  93. "To demonstrate the point let's train a Logistic Regression classifier. It's input will be the x- and y-values and the output the predicted class (0 or 1). To make our life easy we use the Logistic Regression class from `scikit-learn`."
  94. ]
  95. },
  96. {
  97. "cell_type": "code",
  98. "execution_count": 3,
  99. "metadata": {},
  100. "outputs": [
  101. {
  102. "data": {
  103. "text/plain": [
  104. "LogisticRegressionCV(Cs=10, class_weight=None, cv=None, dual=False,\n",
  105. " fit_intercept=True, intercept_scaling=1.0, max_iter=100,\n",
  106. " multi_class='ovr', n_jobs=1, penalty='l2', refit=True,\n",
  107. " scoring=None, solver='lbfgs', tol=0.0001, verbose=0)"
  108. ]
  109. },
  110. "execution_count": 3,
  111. "metadata": {},
  112. "output_type": "execute_result"
  113. }
  114. ],
  115. "source": [
  116. "# Train the logistic regression classifier\n",
  117. "clf = sklearn.linear_model.LogisticRegressionCV()\n",
  118. "clf.fit(X, y)"
  119. ]
  120. },
  121. {
  122. "cell_type": "code",
  123. "execution_count": 4,
  124. "metadata": {},
  125. "outputs": [],
  126. "source": [
  127. "# Helper function to plot a decision boundary.\n",
  128. "# If you don't fully understand this function don't worry, it just generates the contour plot below.\n",
  129. "def plot_decision_boundary(pred_func):\n",
  130. " # Set min and max values and give it some padding\n",
  131. " x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n",
  132. " y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n",
  133. " h = 0.01\n",
  134. " # Generate a grid of points with distance h between them\n",
  135. " xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
  136. " # Predict the function value for the whole gid\n",
  137. " Z = pred_func(np.c_[xx.ravel(), yy.ravel()])\n",
  138. " Z = Z.reshape(xx.shape)\n",
  139. " # Plot the contour and training examples\n",
  140. " plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)\n",
  141. " plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)"
  142. ]
  143. },
  144. {
  145. "cell_type": "code",
  146. "execution_count": 12,
  147. "metadata": {},
  148. "outputs": [
  149. {
  150. "data": {
  151. "text/plain": [
  152. "<matplotlib.text.Text at 0x111951450>"
  153. ]
  154. },
  155. "execution_count": 12,
  156. "metadata": {},
  157. "output_type": "execute_result"
  158. },
  159. {
  160. "data": {
  161. 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Vb+ALhPATosiZyN1li4bViNMfCtHod5Nhc5BktQ+7NqVU/Fn26LzDbp/75Jnw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ZAAAS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\nAQAAeOT/AHlYJGqod0csAAAAAElFTkSuQmCC\n"
  162. },
  163. "metadata": {},
  164. "output_type": "display_data"
  165. }
  166. ],
  167. "source": [
  168. "# Plot the decision boundary\n",
  169. "plot_decision_boundary(lambda x: clf.predict(x))\n",
  170. "plt.title(\"Logistic Regression\")"
  171. ]
  172. },
  173. {
  174. "cell_type": "markdown",
  175. "metadata": {},
  176. "source": [
  177. "The graph shows the decision boundary learned by our Logistic Regression classifier. It separates the data as good as it can using a straight line, but it's unable to capture the \"moon shape\" of our data."
  178. ]
  179. },
  180. {
  181. "cell_type": "markdown",
  182. "metadata": {},
  183. "source": [
  184. "## Training a Neural Network"
  185. ]
  186. },
  187. {
  188. "cell_type": "markdown",
  189. "metadata": {},
  190. "source": [
  191. "Let's now build a 3-layer neural network with one input layer, one hidden layer, and one output layer. The number of nodes in the input layer is determined by the dimensionality of our data, 2. Similarly, the number of nodes in the output layer is determined by the number of classes we have, also 2. (Because we only have 2 classes we could actually get away with only one output node predicting 0 or 1, but having 2 makes it easier to extend the network to more classes later on). The input to the network will be x- and y- coordinates and its output will be two probabilities, one for class 0 (\"female\") and one for class 1 (\"male\"). It looks something like this:\n",
  192. "\n",
  193. "<img src='./nn-3-layer-network.png' style='width: 50%'/>"
  194. ]
  195. },
  196. {
  197. "cell_type": "markdown",
  198. "metadata": {},
  199. "source": [
  200. "We can choose the dimensionality (the number of nodes) of the hidden layer. The more nodes we put into the hidden layer the more complex functions we will be able fit. But higher dimensionality comes at a cost. First, more computation is required to make predictions and learn the network parameters. A bigger number of parameters also means we become more prone to overfitting our data. \n",
  201. "\n",
  202. "How to choose the size of the hidden layer? While there are some general guidelines and recommendations, it always depends on your specific problem and is more of an art than a science. We will play with the number of nodes in the hidden layer later on and see how it affects our output."
  203. ]
  204. },
  205. {
  206. "cell_type": "markdown",
  207. "metadata": {},
  208. "source": [
  209. "We also need to pick an *activation function* for our hidden layer. The activation function transforms the inputs of the layer into its outputs. A nonlinear activation function is what allows us to fit nonlinear hypotheses. Common chocies for activation functions are [tanh](https://reference.wolfram.com/language/ref/Tanh.html), the [sigmoid function](https://en.wikipedia.org/wiki/Sigmoid_function), or [ReLUs](https://en.wikipedia.org/wiki/Rectifier_neural_networks). We will use `tanh`, which performs quite well in many scenarios. A nice property of these functions is that their derivate can be computed using the original function value. For example, the derivative of $\\tanh x$ is $1-\\tanh^2 x$. This is useful because it allows us to compute $\\tanh x$ once and re-use its value later on to get the derivative."
  210. ]
  211. },
  212. {
  213. "cell_type": "markdown",
  214. "metadata": {},
  215. "source": [
  216. "Because we want our network to output probabilities the activation function for the output layer will be the [softmax](https://en.wikipedia.org/wiki/Softmax_function), which is simply a way to convert raw scores to probabilities. If you're familiar with the logistic function you can think of softmax as its generalization to multiple classes."
  217. ]
  218. },
  219. {
  220. "cell_type": "markdown",
  221. "metadata": {},
  222. "source": [
  223. "### How our network makes predictions\n",
  224. "\n",
  225. "Our network makes predictions using *forward propagation*, which is just a bunch of matrix multiplications and the application of the activation function(s) we defined above. If $x$ is the 2-dimensional input to our network then we calculate our prediction $\\hat{y}$ (also two-dimensional) as follows:"
  226. ]
  227. },
  228. {
  229. "cell_type": "markdown",
  230. "metadata": {},
  231. "source": [
  232. "$$\n",
  233. "\\begin{aligned}\n",
  234. "z_1 & = xW_1 + b_1 \\\\\n",
  235. "a_1 & = \\tanh(z_1) \\\\\n",
  236. "z_2 & = a_1W_2 + b_2 \\\\\n",
  237. "a_2 & = \\hat{y} = \\mathrm{softmax}(z_2)\n",
  238. "\\end{aligned}\n",
  239. "$$"
  240. ]
  241. },
  242. {
  243. "cell_type": "markdown",
  244. "metadata": {},
  245. "source": [
  246. "$z_i$ is the weighted sum of inputs of layer $i$ (bias included) and $a_i$ is the output of layer $i$ after applying the activation function. $W_1, b_1, W_2, b_2$ are parameters of our network, which we need to learn from our training data. You can think of them as matrices transforming data between layers of the network. Looking at the matrix multiplications above we can figure out the dimensionality of these matrices. If we use 500 nodes for our hidden layer then $W_1 \\in \\mathbb{R}^{2\\times500}$, $b_1 \\in \\mathbb{R}^{500}$, $W_2 \\in \\mathbb{R}^{500\\times2}$, $b_2 \\in \\mathbb{R}^{2}$. Now you see why we have more parameters if we increase the size of the hidden layer."
  247. ]
  248. },
  249. {
  250. "cell_type": "markdown",
  251. "metadata": {},
  252. "source": [
  253. "### Learning the Parameters\n",
  254. "\n",
  255. "Learning the parameters for our network means finding parameters ($W_1, b_1, W_2, b_2$) that minimize the error on our training data. But how do we define the error? We call the function that measures our error the *loss function*. A common choice with the softmax output is the [cross-entropy loss](https://en.wikipedia.org/wiki/Cross_entropy#Cross-entropy_error_function_and_logistic_regression). If we have $N$ training examples and $C$ classes then the loss for our prediction $\\hat{y}$ with respect to the true labels $y$ is given by:\n",
  256. "\n",
  257. "$$\n",
  258. "\\begin{aligned}\n",
  259. "L(y,\\hat{y}) = - \\frac{1}{N} \\sum_{n \\in N} \\sum_{i \\in C} y_{n,i} \\log\\hat{y}_{n,i}\n",
  260. "\\end{aligned}\n",
  261. "$$\n",
  262. "\n"
  263. ]
  264. },
  265. {
  266. "cell_type": "markdown",
  267. "metadata": {},
  268. "source": [
  269. "The formula looks complicated, but all it really does is sum over our training examples and add to the loss if we predicted the incorrect class. So, the further away $y$ (the correct labels) and $\\hat{y}$ (our predictions) are, the greater our loss will be. "
  270. ]
  271. },
  272. {
  273. "cell_type": "markdown",
  274. "metadata": {},
  275. "source": [
  276. "Remember that our goal is to find the parameters that minimize our loss function. We can use [gradient descent](http://cs231n.github.io/optimization-1/) to find its minimum. I will implement the most vanilla version of gradient descent, also called batch gradient descent with a fixed learning rate. Variations such as SGD (stochastic gradient descent) or minibatch gradient descent typically perform better in practice. So if you are serious you'll want to use one of these, and ideally you would also [decay the learning rate over time](http://cs231n.github.io/neural-networks-3/#anneal).\n",
  277. "\n",
  278. "As an input, gradient descent needs the gradients (vector of derivatives) of the loss function with respect to our parameters: $\\frac{\\partial{L}}{\\partial{W_1}}$, $\\frac{\\partial{L}}{\\partial{b_1}}$, $\\frac{\\partial{L}}{\\partial{W_2}}$, $\\frac{\\partial{L}}{\\partial{b_2}}$. To calculate these gradients we use the famous *backpropagation algorithm*, which is a way to efficiently calculate the gradients starting from the output. I won't go into detail how backpropagation works, but there are many excellent explanations ([here](http://colah.github.io/posts/2015-08-Backprop/) or [here](http://cs231n.github.io/optimization-2/)) floating around the web.\n",
  279. "\n",
  280. "Applying the backpropagation formula we find the following (trust me on this):"
  281. ]
  282. },
  283. {
  284. "cell_type": "markdown",
  285. "metadata": {},
  286. "source": [
  287. "$$\n",
  288. "\\begin{aligned}\n",
  289. "& \\delta_3 = \\hat{y} - y \\\\\n",
  290. "& \\delta_2 = (1 - \\tanh^2z_1) \\circ \\delta_3W_2^T \\\\\n",
  291. "& \\frac{\\partial{L}}{\\partial{W_2}} = a_1^T \\delta_3 \\\\\n",
  292. "& \\frac{\\partial{L}}{\\partial{b_2}} = \\delta_3\\\\\n",
  293. "& \\frac{\\partial{L}}{\\partial{W_1}} = x^T \\delta_2\\\\\n",
  294. "& \\frac{\\partial{L}}{\\partial{b_1}} = \\delta_2 \\\\\n",
  295. "\\end{aligned}\n",
  296. "$$"
  297. ]
  298. },
  299. {
  300. "cell_type": "markdown",
  301. "metadata": {},
  302. "source": [
  303. "### Implementation\n",
  304. "\n",
  305. "Now we are ready for our implementation. We start by defining some useful variables and parameters for gradient descent:"
  306. ]
  307. },
  308. {
  309. "cell_type": "code",
  310. "execution_count": 15,
  311. "metadata": {},
  312. "outputs": [],
  313. "source": [
  314. "num_examples = len(X) # training set size\n",
  315. "nn_input_dim = 2 # input layer dimensionality\n",
  316. "nn_output_dim = 2 # output layer dimensionality\n",
  317. "\n",
  318. "# Gradient descent parameters (I picked these by hand)\n",
  319. "epsilon = 0.01 # learning rate for gradient descent\n",
  320. "reg_lambda = 0.01 # regularization strength"
  321. ]
  322. },
  323. {
  324. "cell_type": "markdown",
  325. "metadata": {},
  326. "source": [
  327. "First let's implement the loss function we defined above. We use this to evaluate how well our model is doing:"
  328. ]
  329. },
  330. {
  331. "cell_type": "code",
  332. "execution_count": 7,
  333. "metadata": {},
  334. "outputs": [],
  335. "source": [
  336. "# Helper function to evaluate the total loss on the dataset\n",
  337. "def calculate_loss(model):\n",
  338. " W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']\n",
  339. " # Forward propagation to calculate our predictions\n",
  340. " z1 = X.dot(W1) + b1\n",
  341. " a1 = np.tanh(z1)\n",
  342. " z2 = a1.dot(W2) + b2\n",
  343. " exp_scores = np.exp(z2)\n",
  344. " probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)\n",
  345. " # Calculating the loss\n",
  346. " corect_logprobs = -np.log(probs[range(num_examples), y])\n",
  347. " data_loss = np.sum(corect_logprobs)\n",
  348. " # Add regulatization term to loss (optional)\n",
  349. " data_loss += reg_lambda/2 * (np.sum(np.square(W1)) + np.sum(np.square(W2)))\n",
  350. " return 1./num_examples * data_loss"
  351. ]
  352. },
  353. {
  354. "cell_type": "markdown",
  355. "metadata": {},
  356. "source": [
  357. "We also implement a helper function to calculate the output of the network. It does forward propagation as defined above and returns the class with the highest probability."
  358. ]
  359. },
  360. {
  361. "cell_type": "code",
  362. "execution_count": 8,
  363. "metadata": {},
  364. "outputs": [],
  365. "source": [
  366. "# Helper function to predict an output (0 or 1)\n",
  367. "def predict(model, x):\n",
  368. " W1, b1, W2, b2 = model['W1'], model['b1'], model['W2'], model['b2']\n",
  369. " # Forward propagation\n",
  370. " z1 = x.dot(W1) + b1\n",
  371. " a1 = np.tanh(z1)\n",
  372. " z2 = a1.dot(W2) + b2\n",
  373. " exp_scores = np.exp(z2)\n",
  374. " probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)\n",
  375. " return np.argmax(probs, axis=1)"
  376. ]
  377. },
  378. {
  379. "cell_type": "markdown",
  380. "metadata": {},
  381. "source": [
  382. "Finally, here comes the function to train our Neural Network. It implements batch gradient descent using the backpropagation derivates we found above."
  383. ]
  384. },
  385. {
  386. "cell_type": "code",
  387. "execution_count": 16,
  388. "metadata": {},
  389. "outputs": [],
  390. "source": [
  391. "# This function learns parameters for the neural network and returns the model.\n",
  392. "# - nn_hdim: Number of nodes in the hidden layer\n",
  393. "# - num_passes: Number of passes through the training data for gradient descent\n",
  394. "# - print_loss: If True, print the loss every 1000 iterations\n",
  395. "def build_model(nn_hdim, num_passes=20000, print_loss=False):\n",
  396. " \n",
  397. " # Initialize the parameters to random values. We need to learn these.\n",
  398. " np.random.seed(0)\n",
  399. " W1 = np.random.randn(nn_input_dim, nn_hdim) / np.sqrt(nn_input_dim)\n",
  400. " b1 = np.zeros((1, nn_hdim))\n",
  401. " W2 = np.random.randn(nn_hdim, nn_output_dim) / np.sqrt(nn_hdim)\n",
  402. " b2 = np.zeros((1, nn_output_dim))\n",
  403. "\n",
  404. " # This is what we return at the end\n",
  405. " model = {}\n",
  406. " \n",
  407. " # Gradient descent. For each batch...\n",
  408. " for i in range(0, num_passes):\n",
  409. "\n",
  410. " # Forward propagation\n",
  411. " z1 = X.dot(W1) + b1\n",
  412. " a1 = np.tanh(z1)\n",
  413. " z2 = a1.dot(W2) + b2\n",
  414. " exp_scores = np.exp(z2)\n",
  415. " probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)\n",
  416. "\n",
  417. " # Backpropagation\n",
  418. " delta3 = probs\n",
  419. " delta3[range(num_examples), y] -= 1\n",
  420. " dW2 = (a1.T).dot(delta3)\n",
  421. " db2 = np.sum(delta3, axis=0, keepdims=True)\n",
  422. " delta2 = delta3.dot(W2.T) * (1 - np.power(a1, 2))\n",
  423. " dW1 = np.dot(X.T, delta2)\n",
  424. " db1 = np.sum(delta2, axis=0)\n",
  425. "\n",
  426. " # Add regularization terms (b1 and b2 don't have regularization terms)\n",
  427. " dW2 += reg_lambda * W2\n",
  428. " dW1 += reg_lambda * W1\n",
  429. "\n",
  430. " # Gradient descent parameter update\n",
  431. " W1 += -epsilon * dW1\n",
  432. " b1 += -epsilon * db1\n",
  433. " W2 += -epsilon * dW2\n",
  434. " b2 += -epsilon * db2\n",
  435. " \n",
  436. " # Assign new parameters to the model\n",
  437. " model = { 'W1': W1, 'b1': b1, 'W2': W2, 'b2': b2}\n",
  438. " \n",
  439. " # Optionally print the loss.\n",
  440. " # This is expensive because it uses the whole dataset, so we don't want to do it too often.\n",
  441. " if print_loss and i % 1000 == 0:\n",
  442. " print(\"Loss after iteration %i: %f\" %(i, calculate_loss(model)))\n",
  443. " \n",
  444. " return model"
  445. ]
  446. },
  447. {
  448. "cell_type": "markdown",
  449. "metadata": {},
  450. "source": [
  451. "### A network with a hidden layer of size 3\n",
  452. "\n",
  453. "Let's see what happens if we train a network with a hidden layer size of 3.\n"
  454. ]
  455. },
  456. {
  457. "cell_type": "code",
  458. "execution_count": 17,
  459. "metadata": {},
  460. "outputs": [
  461. {
  462. "name": "stdout",
  463. "output_type": "stream",
  464. "text": [
  465. "Loss after iteration 0: 0.432387\n",
  466. "Loss after iteration 1000: 0.068947\n",
  467. "Loss after iteration 2000: 0.068936\n",
  468. "Loss after iteration 3000: 0.071218\n",
  469. "Loss after iteration 4000: 0.071253\n",
  470. "Loss after iteration 5000: 0.071278\n",
  471. "Loss after iteration 6000: 0.071293\n",
  472. "Loss after iteration 7000: 0.071303\n",
  473. "Loss after iteration 8000: 0.071308\n",
  474. "Loss after iteration 9000: 0.071312\n",
  475. "Loss after iteration 10000: 0.071314\n",
  476. "Loss after iteration 11000: 0.071315\n",
  477. "Loss after iteration 12000: 0.071315\n",
  478. "Loss after iteration 13000: 0.071316\n",
  479. "Loss after iteration 14000: 0.071316\n",
  480. "Loss after iteration 15000: 0.071316\n",
  481. "Loss after iteration 16000: 0.071316\n",
  482. "Loss after iteration 17000: 0.071316\n",
  483. "Loss after iteration 18000: 0.071316\n",
  484. "Loss after iteration 19000: 0.071316\n"
  485. ]
  486. },
  487. {
  488. "data": {
  489. "text/plain": [
  490. "<matplotlib.text.Text at 0x11b636bd0>"
  491. ]
  492. },
  493. "execution_count": 17,
  494. "metadata": {},
  495. "output_type": "execute_result"
  496. },
  497. {
  498. "data": {
  499. 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ppZQKE02slFJKKaXCRBMrpZRSSqkw0cRKKaWUUipMNLFSSik1qugdgSqWaWKllFJq1Fj0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\n8p9INLG+1a1xNAAAAABJRU5ErkJggg==\n"
  500. },
  501. "metadata": {},
  502. "output_type": "display_data"
  503. }
  504. ],
  505. "source": [
  506. "# Build a model with a 3-dimensional hidden layer\n",
  507. "model = build_model(3, print_loss=True)\n",
  508. "\n",
  509. "# Plot the decision boundary\n",
  510. "plot_decision_boundary(lambda x: predict(model, x))\n",
  511. "plt.title(\"Decision Boundary for hidden layer size 3\")"
  512. ]
  513. },
  514. {
  515. "cell_type": "markdown",
  516. "metadata": {},
  517. "source": [
  518. "Yay! This looks pretty good. Our neural networks was able to find a decision boundary that successfully separates the classes."
  519. ]
  520. },
  521. {
  522. "cell_type": "markdown",
  523. "metadata": {},
  524. "source": [
  525. "# Varying the hidden layer size\n",
  526. "\n",
  527. "In the example above we picked a hidden layer size of 3. Let's now get a sense of how varying the hidden layer size affects the result.\n"
  528. ]
  529. },
  530. {
  531. "cell_type": "code",
  532. "execution_count": 14,
  533. "metadata": {},
  534. "outputs": [
  535. {
  536. "data": {

机器学习越来越多应用到飞行器、机器人等领域,其目的是利用计算机实现类似人类的智能,从而实现装备的智能化与无人化。本课程旨在引导学生掌握机器学习的基本知识、典型方法与技术,通过具体的应用案例激发学生对该学科的兴趣,鼓励学生能够从人工智能的角度来分析、解决飞行器、机器人所面临的问题和挑战。本课程主要内容包括Python编程基础,机器学习模型,无监督学习、监督学习、深度学习基础知识与实现,并学习如何利用机器学习解决实际问题,从而全面提升自我的《综合能力》。