{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It has always been a dream of mankind to create artificial intelligence, i.e. non-human entities which are able to perform or outperform human beings. It is not so clear what this means: is it just to calculate quicker? Or to play certain games more successfully by using algorithms? Or to learn playing games even without having certain algorithms or human expert knowledge being programmed? Or to enter the very heart of human creative activities (speaking to each other, writing books, composing music, investing money, etc) and producing work which is indistinguishable from human beings?\n",
    "\n",
    "This reminds us the [Turing test](https://en.wikipedia.org/wiki/Turing_test#Standard_interpretation): can one distinguish machines from human beings doing certain tasks in a blind observation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is not so simple to pass the Turing test as first artificial intelligence communicators show: [ELIZA](https://www.masswerk.at/elizabot/eliza.html). Still it is fun and relaxing to chat a bit with Eliza.\n",
    "\n",
    "If Eliza were the peak of artificial intelligence, would you trust your money, your future pension, your banking environment to her, or would you rather believe that she can be outperformed?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have, however, recently seen some spectacular successes by machine learning techniques in areas like\n",
    "1. Artificial communicators: [Google Duplex](https://www.youtube.com/watch?v=D5VN56jQMWM)\n",
    "2. Artificial Players: [AlphaGo](https://www.youtube.com/watch?v=8dMFJpEGNLQ)\n",
    "3. Artificial Composers: [Schubert's unfinished symphony](https://www.youtube.com/watch?v=GcFkoTUraMM)\n",
    "4. Artificial Writers: [Open AI](https://www.theguardian.com/technology/2019/feb/14/elon-musk-backed-ai-writes-convincing-news-fiction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we definitively come closer to machines passing Turing tests, to machines outperforming human beings in core human activities, maybe also in investing money ... ?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several aspects make this renaissance of artificial intelligence possible: why renaissance? Because artifical intelligence as a scientific discipline has also experienced [AI winters](https://en.wikipedia.org/wiki/AI_winter)\n",
    "1. Computing power has evolved tremendously.\n",
    "2. The mathematical theory of learning has developed many tools.\n",
    "3. Techonology is nowadays very accessible.\n",
    "4. Convincing breakthroughs have been achieved in image recognition, natural languages, games, music, etc.\n",
    "\n",
    "Look for instance at the following simple task of recognizing handwritten digits, which is learned by a tabula rasa machine. Notice the simplicity of the code and its accessibility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local64.hg/app/python/3.6.8-3.fc28.rpm-20190521/usr/lib64/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "#matplotlib inline # Only use this if using iPython\n",
    "image_index = np.random.randint(60000) #7777 # You may select anything up to 60,000\n",
    "print(y_train[image_index]) # The label is printed\n",
    "plt.imshow(x_train[image_index], cmap='Greys')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (60000, 28, 28, 1)\n",
      "Number of images in x_train 60000\n",
      "Number of images in x_test 10000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(60000,)"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reshaping the array to 4-dims so that it can work with the Keras API\n",
    "x_train = x_train.reshape(x_train.shape[0], 28, 28, 1)\n",
    "x_test = x_test.reshape(x_test.shape[0], 28, 28, 1)\n",
    "input_shape = (28, 28, 1)\n",
    "# Making sure that the values are float so that we can get decimal points after division\n",
    "x_train = x_train.astype('float32')\n",
    "x_test = x_test.astype('float32')\n",
    "# Normalizing the RGB codes by dividing it to the max RGB value.\n",
    "x_train /= 255\n",
    "x_test /= 255\n",
    "print('x_train shape:', x_train.shape)\n",
    "print('Number of images in x_train', x_train.shape[0])\n",
    "print('Number of images in x_test', x_test.shape[0])\n",
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing the required Keras modules containing model and layers\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Conv2D, Dropout, Flatten, MaxPooling2D\n",
    "# Creating a Sequential Model and adding the layers\n",
    "model = Sequential()\n",
    "layer1=Conv2D(28, kernel_size=(3,3), input_shape=input_shape)\n",
    "layer1.trainable=True\n",
    "model.add(layer1) # (3,3) for mnist\n",
    "model.add(MaxPooling2D(pool_size=(2, 2))) # (2,2) for mnist\n",
    "model.add(Flatten()) # Flattening the 2D arrays for fully connected layers\n",
    "layer2 = Dense(128, activation=tf.nn.relu,kernel_initializer='random_uniform')#glorot_uniform is by default\n",
    "layer2.trainable=True#False\n",
    "model.add(layer2)\n",
    "#layer3 = Dense(2*128, activation=tf.nn.relu,kernel_initializer='random_uniform')\n",
    "#layer3.trainable=False\n",
    "#model.add(layer3)\n",
    "model.add(Dropout(0.2))\n",
    "model.add(Dense(10,activation=tf.nn.softmax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_32 (Conv2D)           (None, 26, 26, 28)        280       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_29 (MaxPooling (None, 13, 13, 28)        0         \n",
      "_________________________________________________________________\n",
      "flatten_29 (Flatten)         (None, 4732)              0         \n",
      "_________________________________________________________________\n",
      "dense_86 (Dense)             (None, 128)               605824    \n",
      "_________________________________________________________________\n",
      "dropout_28 (Dropout)         (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_87 (Dense)             (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 607,394\n",
      "Trainable params: 607,394\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 54s - loss: 0.2115 - acc: 0.9365    \n",
      " 9888/10000 [============================>.] - ETA: 0s\n",
      " [0.08093519524633884, 0.9733]\n"
     ]
    }
   ],
   "source": [
    "model.compile(optimizer='adam', \n",
    "              loss='sparse_categorical_crossentropy', \n",
    "              metrics=['accuracy'])\n",
    "for i in range(1):\n",
    "    model.fit(x=x_train,y=y_train, epochs=1)\n",
    "    x = model.evaluate(x_test, y_test)\n",
    "    print('\\n',x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa2c1b7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 3\n",
      "Grand Truth 9\n",
      "0.01\n"
     ]
    }
   ],
   "source": [
    "img_rows=28\n",
    "img_cols=28\n",
    "count = 0\n",
    "for i in range(100):\n",
    "    image_index = np.random.randint(10000)\n",
    "    pred = model.predict(x_test[image_index].reshape(1, img_rows, img_cols, 1))\n",
    "    if pred.argmax() != y_test[image_index]:\n",
    "        plt.imshow(x_test[image_index].reshape(28, 28),cmap='Greys')\n",
    "        plt.show()\n",
    "        print('Prediction',pred.argmax())\n",
    "        print('Grand Truth',y_test[image_index])\n",
    "        count = count + 1\n",
    "        #break\n",
    "print(count/100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "What happened here? It is as simple as fascinating.\n",
    "\n",
    "A parametrized family of functions (a so called neural network) has been constructed. The functions take as input the picture of the handwritten digits (28 times 28 pixels) and produce an output which corresponds to its value. The parameters of the function are trained on 60000 training pictures and then tested on 10000 test pictures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "607394"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.count_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An amazing amount of 607394 parameters is trained ... "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or look at the following task which is less accessible for human beings but more important in investment universes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_trainlr = np.load('x_trainlr.npy')\n",
    "y_trainlr = np.load('y_trainlr.npy')\n",
    "x_testlr = np.load('x_testlr.npy')\n",
    "y_testlr = np.load('y_testlr.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nnGd7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aeb50ae48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae5bf3860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(x_trainlr[3000].reshape(28, 28),cmap='Greys')\n",
    "plt.show()\n",
    "plt.imshow(x_trainlr[33000].reshape(28, 28),cmap='Greys')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Importing the required Keras modules containing model and layers\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Conv2D, Dropout, Flatten, MaxPooling2D\n",
    "# Creating a Sequential Model and adding the layers\n",
    "modellr = Sequential()\n",
    "modellr.add(Conv2D(28, kernel_size=(1,10), input_shape=input_shape)) # (3,3) for mnist\n",
    "modellr.add(MaxPooling2D(pool_size=(1, 7))) # (2,2) for mnist\n",
    "modellr.add(Flatten()) # Flattening the 2D arrays for fully connected layers\n",
    "modellr.add(Dense(128, activation=tf.nn.relu))\n",
    "modellr.add(Dense(128, activation=tf.nn.relu))\n",
    "modellr.add(Dropout(0.1))\n",
    "modellr.add(Dense(2,activation=tf.nn.softmax))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 26s - loss: 0.6345 - acc: 0.6055    \n",
      " 9920/10000 [============================>.] - ETA: 0s\n",
      " [0.5010306933403015, 0.7484]\n",
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 25s - loss: 0.4624 - acc: 0.7751    \n",
      " 9856/10000 [============================>.] - ETA: 0s\n",
      " [0.44502502093315127, 0.7844]\n",
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 27s - loss: 0.3916 - acc: 0.8207    \n",
      " 9984/10000 [============================>.] - ETA: 0s\n",
      " [0.4896464219093323, 0.7689]\n",
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 27s - loss: 0.3188 - acc: 0.8647    \n",
      " 9920/10000 [============================>.] - ETA: 0s\n",
      " [0.525030509185791, 0.7673]\n",
      "Epoch 1/1\n",
      "60000/60000 [==============================] - 26s - loss: 0.2419 - acc: 0.9054    \n",
      "10000/10000 [==============================] - 1s     \n",
      "\n",
      " [0.5767976376533508, 0.7625]\n"
     ]
    }
   ],
   "source": [
    "modellr.compile(optimizer='adam', \n",
    "              loss='sparse_categorical_crossentropy', \n",
    "              metrics=['accuracy'])\n",
    "for i in range(5):\n",
    "    modellr.fit(x=x_trainlr,y=y_trainlr, epochs=1)\n",
    "    x = modellr.evaluate(x_testlr, y_testlr)\n",
    "    print('\\n',x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQFKEH0iK8ANJEX4gKcIPJPV/EcRVcHVvV1QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9ac24c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a7521d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa2b44ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae0c71080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a6a8828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUv8HhDLcETEoC54AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a6ec550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a52bb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a6c0320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a554ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a63b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a292c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa3170e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA0kRfiCp/wPmglgwXeHwGQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa336c0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae0d708d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4adc0f4f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa33664a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae0c16c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa2fb5a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n+KWiDL9UlOGXivo/W02zErqUTYMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa2fb0438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa2bef048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa010a048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9afe7080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKsrwS0X9Pxg76ypkkkjnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9a3e78d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nB5Ii/EBS/w+X/2iXBVzygQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4adc0b2e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 1\n",
      "Grand Truth 0\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAD8CAYAAAC4nHJkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhB9IivADSRF+IKk/AB0FQfuLIW3fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4a9bf2c8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction 0\n",
      "Grand Truth 1\n",
      "0.25\n"
     ]
    }
   ],
   "source": [
    "img_rows=28\n",
    "img_cols=28\n",
    "count = 0\n",
    "for i in range(100):\n",
    "    image_index = np.random.randint(10000)\n",
    "    pred = modellr.predict(x_testlr[image_index].reshape(1, img_rows, img_cols, 1))\n",
    "    if pred.argmax() != y_testlr[image_index]:\n",
    "        plt.imshow(x_testlr[image_index].reshape(28, 28),cmap='Greys')\n",
    "        plt.show()\n",
    "        print('Prediction',pred.argmax())\n",
    "        print('Grand Truth',y_testlr[image_index])\n",
    "        count = count + 1\n",
    "        #break\n",
    "print(count/100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above pictures are just graphical representations (aligned in a matrix) of 28 times 28 randomly or fake randomly drawn numbers 0 or 1. The faking mechanisms is detected by our machine with a success rate of 72 percent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def longestrun(Xrand):\n",
    "    walk = np.cumsum(2*Xrand-1)\n",
    "    y = 1\n",
    "    for i in range(2,20):\n",
    "        for n in range(len(walk)-i):\n",
    "            if abs(walk[n+i]-walk[n])==i:\n",
    "                y = i\n",
    "                break\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD8CAYAAAB5Pm/hAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae42c0588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0\n",
      " 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1\n",
      " 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0\n",
      " 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1\n",
      " 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0\n",
      " 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1\n",
      " 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0\n",
      " 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0\n",
      " 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1\n",
      " 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1\n",
      " 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1\n",
      " 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1\n",
      " 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 0 1\n",
      " 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0\n",
      " 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0\n",
      " 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1\n",
      " 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 1\n",
      " 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0\n",
      " 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0\n",
      " 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0\n",
      " 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0\n",
      " 1 0 1 0 0 0 1]\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "def histlongestrun(N,M):\n",
    "    lrts = []\n",
    "    for i in range(M):\n",
    "        draw = np.random.binomial(1,0.5,N*N)\n",
    "        lr = longestrun(draw)\n",
    "        lrts = lrts + [lr]\n",
    "    plt.hist(lrts)\n",
    "    plt.show()\n",
    "histlongestrun(28,500)\n",
    "draw = np.random.binomial(1,0.5,28*28)\n",
    "print(draw)\n",
    "print(longestrun(draw))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "201527"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "modellr.count_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The nature of randomness is very structured and our tabula rasa machine can alreay quite well understand the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can try to predict asset price behavior. We can incode this into a game.\n",
    "\n",
    "We throw two dices five times (two independent sources of randomness). A token is moving according to the results of the dices and according to an *unknown* law (which only depends on the current place). By observing the game for some time one should understand how to predict ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "d=2\n",
    "M=30 \n",
    "\n",
    "def canonical(i,M):\n",
    "    e = np.zeros((M,1))\n",
    "    e[i,0]=1.0\n",
    "    return e\n",
    "\n",
    "def vectorfield2d(state,increment):\n",
    "    return np.array([(5.0*np.sqrt(state[1]**2))**0.7,0.3*state[1]])*increment[0]+np.array([(1.0*np.sqrt(state[1]**2))**0.7,1.0*state[1]])*increment[1]\n",
    "\n",
    "def randomAbeta(d,M):\n",
    "    A = []\n",
    "    beta = []\n",
    "    for i in range(d):\n",
    "        B = np.random.normal(0.0,0.5,size=(M,M))\n",
    "        B = np.random.permutation(B)\n",
    "        A = A + [B]\n",
    "        beta = beta + [canonical(i,M)+np.random.normal(0.0,0.1,size=(M,1))]\n",
    "    return [A,beta]\n",
    "\n",
    "Abeta = randomAbeta(d,M)\n",
    "A = Abeta[0]\n",
    "beta = Abeta[1]\n",
    "\n",
    "def sigmoid(x):\n",
    "    return np.tanh(x)\n",
    "\n",
    "def reservoirfield(state,increment):\n",
    "    value = np.zeros((M,1))\n",
    "    for i in range(d):\n",
    "        value = value + sigmoid(np.matmul(A[i],state) + beta[i])*increment[i]\n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class SDE:\n",
    "    def __init__(self,timehorizon,initialvalue,dimension,dimensionBM,dimensionR,vectorfield,timesteps,):\n",
    "        self.timehorizon = timehorizon\n",
    "        self.initialvalue = initialvalue # np array\n",
    "        self.dimension = dimension\n",
    "        self.dimensionBM = dimensionBM\n",
    "        self.dimensionR = dimensionR\n",
    "        self.vectorfield = vectorfield\n",
    "        self.timesteps = timesteps\n",
    "\n",
    "    def path(self):\n",
    "        BMpath = [np.zeros(self.dimensionBM)]\n",
    "        SDEpath = [np.array([1.0, self.initialvalue])]\n",
    "        \n",
    "        for i in range(self.timesteps):\n",
    "            helper = np.sqrt(self.timehorizon/self.timesteps)*(np.random.randint(-2,4,self.dimensionBM)-3/6)/np.sqrt(19/6)\n",
    "            BMpath = BMpath + [BMpath[-1]+helper]\n",
    "            SDEpath = SDEpath + [(SDEpath[-1]+self.vectorfield(SDEpath[-1],helper))]\n",
    "            #np.ones(self.dimensionBM)*self.timehorizon/self.timesteps\n",
    "        return [BMpath, SDEpath]\n",
    "        \n",
    "    def reservoir(self,BMpath):\n",
    "        reservoirpath = [canonical(0,self.dimensionR)*self.initialvalue]\n",
    "        for i in range(self.timesteps):\n",
    "            increment = BMpath[i+1]-BMpath[i]\n",
    "            reservoirpath = reservoirpath + [np.exp(-0.2*self.timehorizon/self.timesteps)*(reservoirpath[-1]+reservoirfield(reservoirpath[-1],increment))]\n",
    "        return reservoirpath    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Game = SDE(1,1.0,2,d,M,vectorfield2d,10000)\n",
    "training = Game.path()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 2)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "BMpath=training[0]\n",
    "Y = training[1]\n",
    "Ydata = np.squeeze(Y)\n",
    "Ydatadiff = np.diff(Ydata,axis=0)\n",
    "Ytrain = np.concatenate((Ydata[:1000],Ydatadiff[:1000:1]),axis=0)\n",
    "np.shape(Ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 30)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=Game.reservoir(BMpath)\n",
    "np.shape(X)\n",
    "Xdata = np.squeeze(X)\n",
    "Xdatadiff = np.diff(Xdata,axis=0)\n",
    "Xtrain=np.concatenate((Xdata[:1000],Xdatadiff[:1000:1]),axis=0)\n",
    "np.shape(Xtrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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sIP+TbsvySnlx65n8bJY7lLI43+pdJmX4tycU9Kv14xafZLmEygrc+eAT460f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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae44fd438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 1.00007742,  1.40555855,  1.29248913, -0.65250517, -0.04872096,\n",
       "        -0.22533942, -1.81449724, -1.00725761,  0.59383689, -0.31728096,\n",
       "         0.45195022,  1.26742775, -0.11309925, -0.23920377,  0.31127225,\n",
       "        -0.86211167,  1.17015998,  0.29360029,  0.60496026, -0.2692004 ,\n",
       "        -0.35098848,  0.61568122, -0.65398973, -0.34246955,  0.26692739,\n",
       "        -0.51020895, -0.16093013, -0.16426014, -0.80049429, -0.32827308],\n",
       "       [ 1.00038069,  0.40529793,  1.41854304,  0.48752566,  0.02400001,\n",
       "         0.89316778,  1.14170356,  0.0119457 ,  0.48049085, -0.05616884,\n",
       "         1.38400335,  0.74703812, -0.19348471,  0.83266988,  0.7840968 ,\n",
       "         0.18658821, -0.1290385 , -0.04406387,  0.69602349,  1.07335673,\n",
       "         0.42368715,  1.02010113, -2.18517691,  0.09225776,  0.8373396 ,\n",
       "        -1.02548373, -0.21731557, -0.36139092, -0.91983584, -0.33026363]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "import pandas as pd\n",
    "lm = linear_model.LinearRegression()\n",
    "modelR = lm.fit(Xtrain,Ytrain)\n",
    "plt.plot(modelR.predict(Xtrain),'r')\n",
    "plt.plot(Ytrain,'b')\n",
    "plt.show()\n",
    "modelR.score(Xtrain,Ytrain)\n",
    "modelR.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "generalization = Game.path()\n",
    "BMpath = generalization[0]\n",
    "Y = generalization[1]\n",
    "Ydata = np.squeeze(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4. 5. 1. 1. 2. 5. 5. 5. 3. 2.]\n",
      "[1. 3. 1. 6. 1. 3. 4. 4. 3. 6.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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GAMUvGZU6n/GV/x3j/+oLXX7Dr7SceuqpXfoZN25cAPH+97+/YvsrrriiyxhKl0siIq64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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4ae3b6feb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=10\n",
    "Z = np.squeeze(BMpath)\n",
    "returns = np.diff(Z,axis=0)*np.sqrt(19/6)*np.sqrt(10000)+3/6+3\n",
    "for i in range(2):\n",
    "    print(returns[0:k,i])\n",
    "\n",
    "X = Game.reservoir(BMpath)\n",
    "Xdata = np.squeeze(X)\n",
    "for i in range(k):\n",
    "    plt.plot(Ydata[0:k+1][:,0],Ydata[0:k+1][:,1],zorder=1,c='r')\n",
    "    plt.scatter(Ydata[0:k+1][:,0],Ydata[0:k+1][:,1],zorder=2,c='b')\n",
    "    plt.annotate(Ydata[k],Ydata[k])\n",
    "    plt.xlim(0.5,1.5)\n",
    "    plt.ylim(0.9,1.1)\n",
    "    plt.axvline(x=1.0)\n",
    "    plt.axhline(y=1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7dyCNAE4FHs9sMx94G+gHLAbmkbvd1PIvilic6qmqqvK7nlaSk749iNqhcP5rcN3utxj4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\nWYpxnS4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aeacc0cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(k):\n",
    "    plt.plot(Ydata[:k+1][:,0],Ydata[:k+1][:,1],zorder=1,c='r')\n",
    "    plt.scatter(Ydata[:k+1][:,0],Ydata[:k+1][:,1],zorder=2,c='b')\n",
    "    plt.plot(modelR.predict(Xdata[:k+1])[:,0],modelR.predict(Xdata[:k+1])[:,1],zorder=1,c='g')\n",
    "    plt.scatter(modelR.predict(Xdata[:k+1])[:,0],modelR.predict(Xdata[:k+1])[:,1],zorder=2,c='y')\n",
    "    plt.xlim(0.5,1.5)\n",
    "    plt.ylim(0.9,1.1)\n",
    "    plt.axvline(x=1.0)\n",
    "    plt.axhline(y=1.0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here training was much quicker since we encode information of the training set so well that actually only a regression was necessary to *store* the observations' information. Such a market simulator is of course useful ... "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is common to all three examples?\n",
    "\n",
    "1. Learning from actual observations.\n",
    "2. Before learning some general knowledge of the problem ('rules of the game') but no particularities are known.\n",
    "3. Learning is accessible.\n",
    "\n",
    "It is the goal of this lecture to explain in detail the mathematical ideas behind these phenomena and to show concrete applications to finance and economics as alluded above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Possible Applications in Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To provide ideas which applications we do have in mind. Instead of using established numerical algorithms one can *learn* solutions from observations.\n",
    "\n",
    "1. Deep Hedging (B&uuml;hler-Gonon-Teichmann-Wood 2017)\n",
    "2. Deep Calibration (Cuchiero-Teichmann et al. 2016-17-18)\n",
    "3. Deep Simulation (Cuchiero-Gonon-Grigoryeva-Ortega 2019)\n",
    "\n",
    "What is Hedging? Solutions of non-linear, non-standard optimization problems.\n",
    "\n",
    "What is Calibration? Model selection given certain market data.\n",
    "\n",
    "What is simulation? Prediction of time series.\n",
    "\n",
    "All tasks of tremendous importance in every day finance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universal Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neural networks appeard in the 1943 seminal work by [Warren McCulloch](https://de.wikipedia.org/wiki/Warren_McCulloch) and [Walter Pitts](https://de.wikipedia.org/wiki/Warren_McCulloch) inspired by certain functionalities of the human brain aiming for artificial intelligence (AI). Essentially neural networks are concatenations of affine functions with standard non-linearities, the essential feature is *one-dimensionality* of involved maps (except the sum), which is related to\n",
    "\n",
    ">[Arnold](https://en.wikipedia.org/wiki/Vladimir_Arnold)-[Kolmogorov](https://en.wikipedia.org/wiki/Andrey_Kolmogorov) representation theorem (around 1960): functions on the unit cube can be represented by sums and uni-variate functions ([Hilbert's](https://en.wikipedia.org/wiki/David_Hilbert) thirteenth problem), i.e. for evey non-linear function of $d$ real variables one can finitely many functions of one real variable such that\n",
    "$$\n",
    "F(x_1,\\ldots,x_d) = \\sum_{i=0}^{2d} \\phi_i \\big(\\sum_{j=1}^d\\psi_{ij} (x_j) \\big)\n",
    "$$\n",
    "holds true.\n",
    "\n",
    "but also to\n",
    "\n",
    ">the [Radon](https://en.wikipedia.org/wiki/Johann_Radon) transform (used in computer tomography) where a multivariate density is approximated by its lower dimensional projections.\n",
    "\n",
    "At the end of the eighties it was proved by George Cybenko in 'Approximation by superposition of sigmoidal functions' and by Kurt Hornik, Maxwell Stinchcombe and Halbert White in 'Multilayer feedforward networks are universal approximator' that neural networks with only *one* hidden layer approximate certain generic classes of functions. We shall prove this theorem first and consider certain instances of it in the sequel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is a neural network precisely? We shall consider a very general definition here.\n",
    "\n",
    "Let $X$ be a compact space, i.e. a compact topological Hausdorff space, and let ${(f_i)}_i$ be a family of real valued continuous functions on $X$ which generates the Borel $\\sigma$-algebra and is closed under addition.\n",
    "\n",
    "Notice that on compact spaces we can consider the space of continuous functions $ C(X) $ with the supremum norm. This provides us with a Banach space and *every* positive linear functional on this Banach space (every element of the dual space can be written as difference of positive and negative linear functionals) can be represented by a unique regular Borel measure $\\mu$ on $X$, i.e.\n",
    "$$\n",
    "\\mu(U) = \\sup \\{ \\mu(K) | \\,  \\text{ for } K \\subset U \\text{ compact }\\}\n",
    "$$\n",
    "for all open $U \\subset X $ and\n",
    "$$\n",
    "\\mu(E) = \\inf \\{ \\mu(U) | \\,  \\text{ for }  E \\subset U \\text{ open }\\}\n",
    "$$\n",
    "for all Borel sets $E$. We shall refer to such measures as Radon measures. This is called [Riesz-Markov-Kakutani representation theorem](https://en.wikipedia.org/wiki/Riesz%E2%80%93Markov%E2%80%93Kakutani_representation_theorem) or short Riesz representation theorem.\n",
    "\n",
    "Let $ \\phi : \\mathbb{R} \\to \\mathbb{R} $ be a sigmoidal activation function, i.e. a function with $ \\phi(t) \\to 1 $ for $ t \\to  \\infty $ and $ \\phi(t) \\to 0 $ as $ t \\to -\\infty$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">A neural network $ g $ is a linear combination of functions of type $ \\phi \\circ (f_i + \\beta_i) $ for some number $\\beta_i $, i.e\n",
    "$$\n",
    "g(x) = \\sum_{i=1}^N  \\alpha_i \\phi(f_i(x)+ \\beta_i) \n",
    "$$\n",
    ">for $ x \\in X $.\n",
    ">We say that the neural network has $N$ hidden nodes and one hidden layer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We shall also need a second definition. A locally bounded measurable function $ \\phi $ is called *discriminatory* if every (signed) Radon measure $ \\mu $ on $ X $ with\n",
    "$$\n",
    "\\int_X \\phi(f_i(x) + \\beta_i) \\mu(dx) = 0 \n",
    "$$\n",
    "for all $ i $ and for all $\\beta_i $ it holds that the signed Radon measure $ \\mu $ vanishes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily prove the following statement:\n",
    "\n",
    "<b>Lemma:</b> Every bounded measurable sigmoidal function is discrimatory.\n",
    "\n",
    "Let $ \\phi $ a be a sigmoidal activation function and let $ \\mu $ be a signed Radon measure such that\n",
    "$$\n",
    "\\int_X \\phi(f_i(x) + \\beta_i) \\mu(dx) = 0 \n",
    "$$\n",
    "for all $ i $ and $\\beta_i $, then -- by assumption $ \\phi(n f_i(x) + n \\theta_i + \\xi) $ approximates\n",
    "$$\n",
    "1_{\\{f_i + \\theta > 0 \\}} +  \\phi(\\xi) 1_{\\{f_i + \\theta = 0 \\}}\n",
    "$$\n",
    "as the integers $ n \\to \\infty $ for all $ x \\in X$. By Lebesgue's dominated convergence theorem the signed measure $ \\mu $ satisfies therefore (notice that $\\xi$ is arbitrary!)\n",
    "$$\n",
    "\\int_X 1_{\\{f_i + \\theta_i > 0\\}} (x) \\mu(dx) = 0 \n",
    "$$\n",
    "for all $ i $ and for all $ \\theta_i $. Hence the signed Radon measure $ \\mu $ vanishes on all sets of the form $ f_i + \\theta_i > 0 $. \n",
    "\n",
    "By linear combinations and dominated convergence one obtains that\n",
    "$$\n",
    "\\int_X h(f_i(x))\\mu(dx) = 0\n",
    "$$\n",
    "for all continuous functions $h:\\mathbb{R} \\to \\mathbb{R}$, since a continuous function $ h $ can be approximated pointwise by step functions.\n",
    "\n",
    "Take now $ h(x) = \\sin(x) $ or $ h(x) = \\cos(x) $, then we obtain that actually\n",
    "$$\n",
    "\\int_X \\exp( \\sum f_i(x) k_i ) \\mu(dx) = 0\n",
    "$$\n",
    "for all integers $ k_i \\in \\mathbb{Z} $. Hence actually thec closure of the linear space generated by $ h(f_i) $ for all $ i $ and for all continuous functions $ h $ contains an algebra, e.g.\n",
    "$$\n",
    "\\int_X f_{i_1}(x) \\cdots f_{i_k}(x) \\mu(dx) = 0\n",
    "$$\n",
    "for all $i_1,\\ldots,i_k$. This, however, means that the measure $ \\mu $ vanishes, since the algebra generated by the point separating function family $ (f_i) $ is dense due to the Stone-Weierstrass theorem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By the [Hahn](https://en.wikipedia.org/wiki/Hans_Hahn_&#40;mathematician&#41;)-[Banach](https://en.wikipedia.org/wiki/Stefan_Banach) theorem and the [Riesz](https://en.wikipedia.org/wiki/Frigyes_Riesz) representation theorem it is now clear that neural networks generated with a fixed continuous bounded sigmoidal function $ \\phi $ are dense in all continuous functions.\n",
    "\n",
    "<b>Theorem: The set of one layer neural networks is dense in $C(X)$.</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the closure of the set of all neural networks in $C(X)$ and take a contiuous linear functional $ l $ on $ C(X) $ which vanishes on it: its existence is guaranteed by the Hahn-Banach theorem. This linear functional can be represented by a Radon measure $ \\mu $. Since $ l $ vanishes on all neural networks it holds in particular that\n",
    "$$\n",
    "\\int_X \\phi(f_i(x) + \\beta_i) \\mu(dx) = 0 \n",
    "$$\n",
    "for all $ i $ and for all $\\beta_i $. But $ \\phi $ is discrimatory, hence $ \\mu = 0 $ and therefore the closure of the space of neural networks has to be $ C(X) $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several remarks due:\n",
    "\n",
    "1. Sigmoidal functions are discrimatory, but they are not the only ones. By Norbert Wiener's famous Tauberian theorem every function $ \\phi \\in L^1(\\mathbb{R}) $ such that $ \\int_{\\mathbb{R}} \\phi(t) dt \\neq 0 $ has the property that the closure of $ \\phi(a.+b) $ for all real $ a , b $ is dense in $L^1(\\mathbb{R}) $ (see Walter Rudin's book on functional analysis). Other classes can be described too.\n",
    "\n",
    "2. The argument can be generalized to $ L^p $ spaces on measure spaces, to $ B^\\rho $ spaces on weithed spaces, to $ C^k $ spaces in manifolds. The essential ingredients are an additively closed, *point separating* set of functions $ f_i $ on the corresponding space and a weak topology on the respective Banach space which allows for dominated convergence and, of course, a discrimatory function for the respective linear functionals.\n",
    "\n",
    "3. We can iterate the argument: take now the additively closed, point separating family of functions the set of neural networks with one hidden layer (written with respect to some family $ f_i $ itself, then we obtain neural networks with *two* hidden layers. We have therefore actually proved that neural networks with finitely many hidden layers are dense in $C(X)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Deep neural networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neural networks with one hidden layer are called *shallow*, with more than one *deep*. The number of nodes in the hidden layer can vary as well as the discrimatory function.\n",
    "\n",
    "Before we talk about the most important question how to actually train a network, i.e. determine the network which approximates well a given function on a trainings set, we try to understand first what we can in principle expect.\n",
    "\n",
    "What shall give a series of arguments why deep neural networks represent so well non-linear functions following the famous article [Provable approximations for deep neural networks](https://arxiv.org/pdf/1509.07385.pdf) by Uri Shaham, Alexander Cloninger and Ronald R. Coifman."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main statement of the article is in fact amazing:\n",
    "\n",
    "<b>$L^2$ functions with sparse wavelet expansion on $d$ dimensional manifolds $\\Gamma \\subset \\mathbb{R}^m$ can be approximated by depth $3$ sparsely connected neural networks with $N$ units up to order $ 1/N $. Constants mainly depend on $ d $ and only weakly on $m$. </b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">Classical work by Barron suggests actually such a relationship by functional analytic arguments. However constants there grow with dimension $m$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most important insight is the following construction:\n",
    "\n",
    "Take a rectifier activation function $ r(x) = \\max(x,0) $ and define a trapezoid shaped function\n",
    "$$\n",
    "t(x) = r(x+3) - r(x+1) - r(x-1) + r(x-3)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
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838cmXc0jFcDMSLQs5kfvHldpWwkp+KvMM53poJRNd+tKZciWtr24TzduloqC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\nEkyYszgXGAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aa35b2198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def r(x):\n",
    "    return np.max([x,0])\n",
    "\n",
    "def t(x):\n",
    "    return r(x+3)-r(x+1)-r(x-1)+r(x-3)\n",
    "\n",
    "x = np.linspace(-5,5,1000)\n",
    "y = np.array([t(z) for z in x])\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we define the scaling function\n",
    "$$\n",
    "\\phi(x_1,\\ldots,x_d) = C_d r \\big (\\sum_{i=1}^d t(x_i) - 2(d-1) \\big)\n",
    "$$\n",
    "which is already neural network of depth $2$ with a constant chosen such that $ \\int \\phi(x) dx = 1 $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function $ \\phi $ is used to define wavelets and so called frames, which serve to expand the non-linear function $ f $, via $ S_{-1} := 0 $.\n",
    "$$\n",
    "S_k(x,b) := 2^k \\phi (2^{k/d}(x-b))\n",
    "$$\n",
    "for $ k \\in \\mathbb{N} $, the 'father' wavelet, and\n",
    "$$\n",
    "D_k(x,b) := S_k(x,b) - S_{k-1}(x,b)\n",
    "$$\n",
    "as well as $ \\psi_k(x) := 2^{-k/2} D_k(x,b) $, the 'mother' wavelet.\n",
    "\n",
    "Then $ \\{ \\psi_k(.,b) \\} $ for $ k \\in \\mathbb{Z} $ and $ b \\in 2^{-k} \\mathbb{Z}^d $ is a frame in $ L^2(\\mathbb{R}^d) $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Let $ f $ be a compactly supported function on $ \\mathbb{R}^d $ with bounded gradient, then for every $ K \\in \\mathbb{N} $ there is a linear combination $ f_K $ of frame elements up to order $ K $ such\n",
    "$$\n",
    "\\big|f(x) - f_K(x) \\big| = O\\big(2^{-2K/d}\\big) \\, .\n",
    "$$\n",
    "</b>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whence one can approximate the function $ f $ by neural networks of depth $2$ build by rectifier units."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can apparently be extended to manifolds by localizing to charts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}