autoencoders.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using Autoencoders to Learn Most Salient Features from Time Series\n",
    "\n",
    "In this post we examine a simple, if not the simplest, tool in deep learning and see how it can be applied to multi-dimensional financial time series. This is a toy example of how one would apply such model to sequential data such as ones encountered in finance.\n",
    "\n",
    "## Autoencoder\n",
    "\n",
    "Autoencoding is the practice of copying input to output. It has an internal state $h$ to represent the input. Autoencoders is composed of two parts: an encoder $f :{\\mathcal {X}}\\rightarrow {\\mathcal {H}}$ and a decoder $g :{\\mathcal {H}}\\rightarrow {\\mathcal {Y}}$. Autoencoders are designed to be unable to learn to copy perfectly.\n",
    "\n",
    "![autoencoder(keras)](https://blog.keras.io/img/ae/autoencoder_schema.jpg)\n",
    "\n",
    "The hidden dimension should constrained to be smaller than $x$, the input dimension. This way, $h$ is forced to take on useful properties and most salient features of the input space.\n",
    "\n",
    "To train an autoencoder, minimize\n",
    "\n",
    "$\\arg \\min _{f, g}||X-(g \\circ f )X||^{2}$\n",
    "\n",
    "\n",
    "## Recurrent Autoencoder\n",
    "For time series data, recurrent autoencoder is more useful. The encoder and decoder are RNNs such as LSTMs. We encode the input into an undercomplete latent vector $h$ which is then decoded. For the decoder, we can either initialize with the latent vector and use output at time $t-1$ as input for time $t$ or we can use latent vector $h$ as the input at each timestep. These are called conditional and unconditional RNNs. Recurrent autoencoder is a special case of sequence-to-sequence(seq2seq) architecture which is extremely powerful in neural machine translation.\n",
    "\n",
    "![](https://esciencegroup.files.wordpress.com/2016/03/seq2seq.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task\n",
    "\n",
    "Copy a tensor of two sine function that are initialized out of phase.\n",
    "\n",
    "The shape of the tensor is: $(batch\\_size, time\\_step, input\\_dim)$ where $input\\_dim$ = 2.\n",
    "\n",
    "To deal with financial data, simply replace the $input\\_dim$ axis with desired data points.\n",
    "\n",
    "* Bid, Ask, Spread, Volume, RSI. For this setup, the $input\\_dim$ would be 5.\n",
    "* Order book levels. We can rebin the order book such that each tick aggregates more liquidity. An example would be 10 levels that are 1 stddev apart. Then $input\\_dim$ would be 10.\n",
    "\n",
    "Here is an artist's rendering of a recurrent autoencoder."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 288,
   "metadata": {},
   "outputs": [
    {
     "data": {
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IQqEgKSkp5MMPPySHDh0ie/fuJW+++SYZM2YMvbHu2dy9MaKKhSVc6bXjLykpIZmZmeTD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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9657ed2dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xkcd()\n",
    "\n",
    "x1 = np.linspace(-np.pi, np.pi)\n",
    "y1 = np.sin(x1)\n",
    "phi = 3\n",
    "x2 = np.linspace(-np.pi+phi, np.pi+phi)\n",
    "y2 = np.sin(x2)\n",
    "\n",
    "f, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, sharex=True, sharey=True)\n",
    "ax1.plot(x1, y1)\n",
    "ax1.set_title('Recurrent Autoencoder')\n",
    "ax2.plot(x1, y1)\n",
    "ax3.plot(x2, y2)\n",
    "ax4.plot(x2, y2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generator\n",
    "\n",
    "We generate 10 time steps for the random phased sine function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random\n",
    "def gen(batch_size):\n",
    "    seq_length = 10\n",
    "\n",
    "    batch_x = []\n",
    "    batch_y = []\n",
    "    for _ in range(batch_size):\n",
    "        rand = random.random() * 2 * np.pi\n",
    "\n",
    "        sig1 = np.sin(np.linspace(0.0 * np.pi + rand,\n",
    "                                  3.0 * np.pi + rand, seq_length * 2))\n",
    "        sig2 = np.cos(np.linspace(0.0 * np.pi + rand,\n",
    "                                  3.0 * np.pi + rand, seq_length * 2))\n",
    "        x1 = sig1[:seq_length]\n",
    "        y1 = sig1[seq_length:]\n",
    "        x2 = sig2[:seq_length]\n",
    "        y2 = sig2[seq_length:]\n",
    "\n",
    "        x_ = np.array([x1, x2])\n",
    "        y_ = np.array([y1, y2])\n",
    "        x_, y_ = x_.T, y_.T\n",
    "\n",
    "        batch_x.append(x_)\n",
    "        batch_y.append(y_)\n",
    "\n",
    "    batch_x = np.array(batch_x)\n",
    "    batch_y = np.array(batch_y)\n",
    "\n",
    "    return batch_x, batch_x#batch_y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model\n",
    "\n",
    "We use a 2-vector to represent the sine functions. Normally, we use $\\phi \\in \\mathbb{R}$ to represent the phase angle for a trignometric function. The big picture here is to compress the input sine functions into two numbers and then decode them back.\n",
    "\n",
    "We define the architecture and let the neural network do its trick."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4845\n",
      "Epoch 2/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4843\n",
      "Epoch 3/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4840\n",
      "Epoch 4/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4838\n",
      "Epoch 5/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4836\n",
      "Epoch 6/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4834\n",
      "Epoch 7/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4832\n",
      "Epoch 8/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4830\n",
      "Epoch 9/2000\n",
      "100/100 [==============================] - 0s - loss: 0.4828\n",
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    {
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     "text": [
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      "Epoch 1951/2000\n",
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      "Epoch 1952/2000\n",
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      "Epoch 1959/2000\n",
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      "Epoch 1961/2000\n",
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      "Epoch 1963/2000\n",
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      "Epoch 1965/2000\n",
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      "Epoch 1966/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1967/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1968/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1969/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1970/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1971/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1972/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1973/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1974/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1975/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0282\n",
      "Epoch 1976/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1977/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1978/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1979/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1980/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1981/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1982/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1983/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1984/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1985/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1986/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1987/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1988/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1989/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1990/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0281\n",
      "Epoch 1991/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1992/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1993/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1994/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1995/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1996/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1997/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1998/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 1999/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n",
      "Epoch 2000/2000\n",
      "100/100 [==============================] - 0s - loss: 0.0280\n"
     ]
    }
   ],
   "source": [
    "from keras.models import Sequential, Model\n",
    "from keras.layers import LSTM, RepeatVector\n",
    "\n",
    "batch_size = 100\n",
    "X_train, _ = gen(batch_size)\n",
    "\n",
    "m = Sequential()\n",
    "m.add(LSTM(2, input_shape=(10, 2)))\n",
    "m.add(RepeatVector(10))\n",
    "m.add(LSTM(2, return_sequences=True))\n",
    "print m.summary()\n",
    "m.compile(loss='mse', optimizer='adam')\n",
    "history = m.fit(X_train, X_train, nb_epoch=2000, batch_size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "lstm_37 (LSTM)               (None, 2)                 40        \n",
      "_________________________________________________________________\n",
      "repeat_vector_12 (RepeatVect (None, 10, 2)             0         \n",
      "_________________________________________________________________\n",
      "lstm_38 (LSTM)               (None, 10, 2)             40        \n",
      "=================================================================\n",
      "Total params: 80\n",
      "Trainable params: 80\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "m.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this post is a demonstration of the technique, we use the smallest model possible which happens to be the best in this case. The \"best\" dimensionality will be one that results in the highest lossless compression. In practice, it's equal part art and science. In production, there are a plethora of trick to accelerate training and finding the right capacity of the latent vector. Topics include: architectures for dealing with the asynchronus, non-stationary time series, preprocessing techniques such as wavelet transforms and FFT. I might cover these in an upcoming post if there's enough interest."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family [u'xkcd', u'Humor Sans', u'Comic Sans MS'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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vf/0rZsyYASB9Fv6mTZtQU1PT4oWTzu+aIV0hkQBLdzTBFaTjX4QUk6wLzKhR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\nGYIBQ0REhvgPX6yLz6EUOMwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f966a2a7290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(history.history['loss'])\n",
    "plt.ylabel(\"loss\")\n",
    "plt.xlabel(\"epoch\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may think that the neural network suddenly \"got it\" during training but this is just the optimzer escaping a saddle point. In fact, as we demonstrate below, the neural network(at least the decoder) didn't get anything at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fMxYdOnTgk08+4erVqwQHBwNIcxXt27cvlP/dd9/l3XffLbY8i8VS4k5fbm4d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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f966a18fe50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test, _ = gen(1)\n",
    "decoded_imgs = m.predict(X_test)\n",
    "\n",
    "for i in range(2):\n",
    "    plt.plot(range(10), decoded_imgs[0, :, i])\n",
    "    plt.plot(range(10), X_test[0, :, i])\n",
    "plt.title(dos_numeros)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With more training, it would be even closer to input but that is not necessary for this demonstration.\n",
    "\n",
    "Just for fun, we can visualize the latent 2-vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cv9+/9DdjjLG2RcfOdKWUOCoqKlBaWhpzV8zzzjsPBw4cQFVVVavzhUIh/OY3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\nlQq/+MUv8Oabbya1bpvNBgB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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f966a2a7110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "encoder = Model(m.layers[0].input, m.layers[0].output)\n",
    "encoded_imgs = encoder.predict(X_test)\n",
    "for i in range(len(encoded_imgs)):\n",
    "    plt.imshow(encoded_imgs[i].reshape((1, 2)))\n",
    "    plt.gray()\n",
    "plt.title(encoded_imgs[i])\n",
    "dos_numeros = encoded_imgs[i]\n",
    "plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m.save('m.h5')\n",
    "encoder.save('enc.h5')\n",
    "decoder.save('dec.h5')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualization\n",
    "\n",
    "The model successfully compressed 20 points to 2 points. It learned the most salient features from data. However in this case, the model is useless in that it has successfully learned $g(f(x)) = x$ *everywhere*. Autoencoder are designed to copy imperfectly. Like all neural networks, autoencoders exploit the idea that data concentrates around a lower-dimensional manifold or a set of manifolds. The goal is to learn a function that behaves correctly on the data points from this manifold and exhibit unusual behavior everywhere off this manifold. In this case, we found a 2-D manifold tangent to the 20-D space. Here we discuss some visualization techniques.\n",
    "\n",
    "Below we demonstrate what the manifold looks like when it is projected back to 20D with an animation. Ideally this shows how the decoder works."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = Input(shape=(2,))\n",
    "decoded = m.layers[1](x)\n",
    "decoded = m.layers[2](decoded)\n",
    "decoder = Model(x, decoded)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML\n",
    "from numpy import random\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "x = range(10)\n",
    "\n",
    "arr = decoder.predict(np.array([[-3.3, 0]]))\n",
    "linea, = ax.plot(x, arr[0, :, 0])\n",
    "lineb, = ax.plot(x, arr[0, :, 1])\n",
    "ax.set_ylim(-1, 1)\n",
    "ax.set_xlim(-0.1, 10.1)\n",
    "\n",
    "def animate(i):\n",
    "    ax.set_title(\"{0:.2f}, 0\".format(-3.3+i/30.))\n",
    "    arr = decoder.predict(np.array([[-3.3+i/30., 0]]))\n",
    "    linea.set_ydata(arr[0, :, 0])\n",
    "    lineb.set_ydata(arr[0, :, 1])\n",
    "    return line,\n",
    "\n",
    "\n",
    "# Init only required for blitting to give a clean slate.\n",
    "def init():\n",
    "    line.set_ydata(np.ma.array(x, mask=True))\n",
    "    return line,\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, np.arange(1, 200), init_func=init,\n",
    "                              interval=25, blit=True)\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "x = range(10)\n",
    "\n",
    "arr = decoder.predict(np.array([[-3.3, -3.3]]))\n",
    "linea, = ax.plot(x, arr[0, :, 0])\n",
    "lineb, = ax.plot(x, arr[0, :, 1])\n",
    "ax.set_ylim(-1, 1)\n",
    "ax.set_xlim(-0.1, 10.1)\n",
    "\n",
    "def animate(i):\n",
    "    ax.set_title(\"{0:.2f}, {0:.2f}\".format(-3.3+i/30.))\n",
    "    arr = decoder.predict(np.array([[-3.3+i/30., -3.3+i/30.]]))\n",
    "    linea.set_ydata(arr[0, :, 0])\n",
    "    lineb.set_ydata(arr[0, :, 1])\n",
    "    return line,\n",
    "\n",
    "\n",
    "# Init only required for blitting to give a clean slate.\n",
    "def init():\n",
    "    line.set_ydata(np.ma.array(x, mask=True))\n",
    "    return line,\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, np.arange(1, 200), init_func=init,\n",
    "                              interval=25, blit=True)\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see from the animation above. The neural network is not using phase angle as the latent space. Instead, it is using a complex interaction between these two numbers caused by the gradient of LSTM during the training process. As $x \\rightarrow \\infty$, the image under $y = g(h) \\rightarrow 0$. This is understood as the decoder does not learn the underlying trig function but merely approximated a manifold of the high dimensional space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us visualize the latent space in its entirety. For higher dimensional latent space we may encounter in financial data, we can use PCA and tSNE but these are beyond the scope of this post."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eeiu++tWvwmazycvGjRuHvXv3YseOHRBC4OKLLy7r0nfplF+Xy1Vu8YmIhhyl\nYmef7lXl8XgwZ86cbv9mNpu7PeVLp9N1uQakVOFwGAB6HE8hIqKulIqdqrzZk9TcYuIgIiqeUrFT\nlYmjvb0dADp1gxERUe+Uip2qTBx+vx8A4Ha7K1wSIiL1UCp2qjJx+Hw+AEBdXV2FS0JEpB5KxU5V\nJo5QKASTycRbjhARlUCp2KnKxBGJRHgNBxFRiZSKnapMHG1tbfB4PJUuBhGRqigVO1WZOAKBQJfb\nuhMRUe+Uip2qTBzt7e08FZeIqERKxU5VJo5YLMY74xIRlUip2KnKxOH3+znGQURUIqVipyoTRygU\nYuIgIiqRUrFTdYkjk8kgmUxyLg4iohIoGTtVlzh4Z1wiotIpGTtVlzh4g0MiotIpGTtVlzikqWi7\nm+uDiIi6p2TsZOIgIhoChnTi4BgHEVHphvQYB+cbJyIqnZKxU3WJg4PjRESlG9KD41Jziy0OIqLi\nKRk7VZc4otEoAPACQCKiEigZO1WXOCKRCLRaLaxWa6WLQkSkGkrGTtUljkAgAJfLBa1WdUUnIqoY\nJWOn6qJvPB5na4OIqERKxk7VJY5MJgODwVDpYhARqYqSsZOJg4hoCBjSiSObzUKv11e6GEREqqJk\n7FRd4mCLg4iodEO6xZFOp2E0GitdDCIiVVEydqoucbCrioiodEO6qyqXy0Gn01W6GEREqqJk7FRd\n4hBC8OI/IqISKRk7VRmBNRpNpYtARKQ6SsVOVSYOIUSli0BEpDpKxU4mDiKiIWLIJg6dTodcLlfp\nYhARqYqSsVN1iUOv1zNxEBGVSMnYqbrEYTQakUqlKl0MIiJVUTJ2qi5xWCwWJBKJSheDiEhVlIyd\nqkscNptNnnSdiIiKo2TsVF3isFqtbHEQEZVIydhZduI4fPgwrrvuOlRXV2P8+PFYv359wW2uvvpq\nzJgxo9PjySefLOl9DQYD0ul0ucUmIhqSlIydZd3xKhKJYPbs2Zg0aRI2b96Md999F7feeiuEELjx\nxht73G7nzp2YPXs2ZsyYIS8bP358Se9tNBqZOIiISqRk7CwrcWzYsAGBQADPPfcc7HY7Jk2ahL17\n92LVqlW9Jg4AmD17Nm6//fayCgv89cMLIXjrESKiIikZO8vqqnrrrbcwc+ZM2O12edn8+fOxZ88e\nxGKxXrc9evQoNm3ahD179pR1FaPJZIIQAtlstuRtiYiGKiVjZ1mJ49ChQ2hsbOy0bNiwYcjlcjh8\n+HCv2/4KNXRjAAAW30lEQVTsZz/Dt771LVxwwQUYPXo0du7c2e16K1asgEaj6fR46aWX4HA4AJzs\nLiMiouIoGTvLShzJZBJWq7XTMul5MpnscbtNmzYhGAziiy++wNGjR1FdXY3rr78e+Xy+qPf1+/3w\ner0AgGAwWE7RiYiGJCVjZ6+J4y9/+Qvsdrv8uPfeewEATqcToVCo07rSc5fL1ePrnX/++XLf2hln\nnIFVq1bhyJEj2LFjR1GFDQaDcLvdAIBAIFDUNkREBEVjZ6+D4/X19Xj//ffl5x6PBwBw4YUXYuvW\nrZ3W/eijj+BwODBq1Kii31z6INFotMvfVqxYgRUrVnRZvm3bNgBAOBwu+n2IiIY6p9MJQJnY2WuL\nw2Aw4Nxzz5Uf9fX1AIC5c+di165d+OijjwCcvFXvc889hzlz5shTEx47dgz//d//LXddxePxToPh\nQgg8/fTTsNlsuPjii4susM1mAwBePU5EVAIlY2dZp+POnz8f8+fPx6xZs/Dtb38b77zzDnbs2IG3\n335bXmfbtm248cYbcfz4cTQ0NGDLli247777MGvWLFitVuzYsQPbt2/HT3/6U1RVVRX93kpmTSKi\noWLAWhw9bqTV4pVXXsHq1atx7NgxTJkyBYcPH8a4cePkdSZOnIhVq1bJI/nTp0/H4sWLYTAYEAqF\n8Ld/+7fYt28fli5dWtJ7SwM8bW1t5RSdiGhIUjJ2aoTKptMTQsBqteLOO+/ET37yk0oXh4hIFZSM\nnaq7yaFGo0FDQwNOnDhR6aIQEamGkrFTdYkDOHk21qmnAxMRUe+Uip2qTBxVVVUcHCciKpFSsVO1\niaO7az+IiKhnSsVOVSYOr9cLn89X6WIQEamKUrFTlYmjvr4ePp+vrLvrEhENVUrFTlUmjrq6OuRy\nOfj9/koXhYhINZSKnapNHADQ2tpa4ZIQEamHUrFTlYlDmkCq0KRRRET0V0rFTlUmDuneVpzMiYio\neErFTiYOIqIhYkgnDmm2Qd5anYioeErFTlUmDilr8iJAIqLiKRU7VZk4pFu1M3EQERVPqdipysRh\nsVgAnJxVkIiIiqNU7FRl4tBqtTCbzRzjICIqgVKxU5WJAzg5yJNIJCpdDCIiVVEidqo2cdjtdl4A\nSERUIiVip2oTh81mY+IgIiqRErFTtYnDYDAgk8lUuhhERKqiROxUbeIwGo1Ip9OVLgYRkaooETtV\nmzjY4iAiKt2QbnHodDrkcrlKF4OISFWUiJ2qTRxarZYzABIRlUiJ2KnaxJHP56HRaCpdDCIiVVEi\ndqo2ceRyOeh0ukoXg4hIVZSInapNHNlsFnq9vtLFICJSFSVip2oTRyqVgslkqnQxiIhURYnYqdrE\nkUwmYTabK10MIiJVUSJ2qjZxxONxeTYrIiIqjhKxk4mDiGgIGdKJI51Ow2g0VroYRESqokTsVG3i\n4OA4EVHphuzgeDabRSaTYVcVEVEJlIqdqkwc0rSHNputwiUhIlIPpWKnKhNHIBAAALjd7gqXhIhI\nPZSKnapOHNXV1RUuCRGReigVO1WZOCKRCACgqqqqwiUhIlIPpWKnKhNHOBwGADidzgqXhIhIPZSK\nnapMHMFgEADHOIiISqFU7FRl4ojFYgAAu91e4ZIQEamHUrFTlYkjkUgAACwWS4VLQkSkHkrFzrJv\nyh4MBrF7924cPnwYTU1NmDNnTlHbffrpp3jmmWeQTqfxta99DRMmTCj5vcPhMHQ6HS8AJCIqgVKx\ns6wWx65du+DxeDB//nzcc889WLduXVHbPf/88xgzZgwOHz6MQCCAiy66CKtXry75/aPRKBwOB6eO\nJSIqgVKxs6zEcfbZZ2Pnzp2IRqOYPHlyUdvkcjncc889+N73vocNGzbgN7/5DX7+859j+fLl8rnF\nxQqHw3C5XOUUnYhoyPrpT38Kn8/X59fRCCFEX15g1qxZGD16NJ5++ule1/vggw8wYcIE7N+/H+ef\nfz6Ak91dNTU1ePHFF3HFFVeU9L5qnnNcCIFwOAy/349wOIz29naEw2EEg0H4/X5Eo1GkUimk02mk\n02lkMhnE43G0t7cjkUggnU4jm80il8t1el2NRgOdTge9Xg+j0QiDwQC9Xg+DwQCDwQCr1QqPx4Oq\nqio4HA44nU7YbDa4XC44nU6YzWaYzWbYbDY4nU4YDIYK1VD/ymazCIVCiMViaG9vRyQSkes2kUgg\nmUwiFoshGo0iHo/Lj3Q6jVQqhWQyiUwmg2w2Kz/y+Tzy+Tykn5N0RCfVe8e6NZlMMBgMsNvtcDqd\ncDqdqKqqQlVVlfz/2tpaOJ1O1baqo9EoAoEA2tvb5Uc8Hkc0GkU0GpXrV/q/VKfJZBKpVAqZTAbp\ndLrTPq7RaOR922g0wmKxwOFwyI+O9edyueByueT/u93u02J/TqVSOH78OILBIAKBAFpaWuT9N5lM\nyvtqKpWS92lpX83lcsjn8xg/fjwef/zxPpVjwCbt3rFjBwBgzJgx8jK3242Ghgbs2LGjS+JYsWIF\nHnzwwS6vk8/nsWTJEhw4cAAWiwUulwsej0cOhBaLBXa7HW63W96JPB4PPB4PbDabYvOU5/N5JBIJ\nRKNRRCIRxONxRCIRRCIRxGIxtLS0oKWlBSdOnIDf75f/FgwG0dzcjGQy2evrazQa+Qci/UhsNhss\nFgtMJhN0Oh10Oh00Gg00Gg2EEMjlckilUshms3LCkW5qJiWfUCiEfD5f1Gc0m81wuVzwer2w2+2w\n2WzweDyorq6Wf5C1tbXwer2w2WzyD1f6wVosFsUDXzqdRmtrKwKBgBx0/H4//H6/HIBisRiCwSAi\nkQjC4TCi0agcvGKxGNra2oquA+DkQKLFYoHRaITJZILZbJaTsvTQarXyAzh5cCDtIy0tLXJCisfj\ncpBMp9O9vq/RaERtbS1qampQW1uLhoYG1NXVoa6uDlarFS6XC9XV1XC73aiurobL5YLdbpfL0FdC\nCKRSKfmgRQr+0kFPc3MzTpw4If974sQJBAIB+bsohslkgt1uh8VigV6vh9lslhOr0WiU93Hg5MFi\nMpmUD6iSyaT8+5MGfXtjtVpht9vhcDjkOvV6vfB4PLBaraipqUF1dbW8rzudTrjdbjkJKVGvQgik\n02nE43HEYjFEIhG0trYiGAzKz6XPJB1MNjc3o7W1FT6fD62trb2+vjR+YTKZ5HjRcV/V6XSIx+N9\n/hwDljiCwSCqqqq6BG6Px4NQKFTUa5jNZnknSiaTCIVC+PDDDxEKhRCNRrscgXfHYDDAZDLBaDTC\narXKR4Mmk0muWK1Wi3w+j1wuJ//AM5mMHHikH38hOp0OtbW1qK2thcPhQENDA8aOHYv6+no0NDSg\nurpaPup3Op3weDxwu91yPfXH0WY+n5eP/EKhENrb2xEKhRAOh5FMJpFMJuUWkHTUGAgE5KPz/fv3\nIxAIIBKJIJVKFfz8NptNTnxScJBaQFqtVk6A0o8yl8shl8vJyU8qUzqdRiwWKyogSUFVOpp3OByo\nq6uDzWaDw+GQvxObzSYvk35k0kMKMGazWbFAfKpMJoNIJIJQKCQHjHA4jHA4jJaWFvh8Pvh8PrS1\ntaG5uRkHDhyAz+dDJpPp8TU1Go2ctKXgazAY5H1cCsRarRYajUZuKaXTaSQSCTmgSUerhToktFot\namtrMWzYMDQ0NGDcuHHweDwYNmwYvF4vrFarXM9Wq1Vu7drtdtjtdsVaAblcrtOBQigUkus1FAoh\nGAzKcSIajcLn8+HPf/4zdu7ciVAoVDCYSvVqs9nkepXiiBSYpR6QjvtwKpVCKpVCIpGQW7nFdPLo\n9Xr5IKyurg5NTU2YPn06Ghsb0djYKB8w1NXVwel0ynHMYDAMSCu118QRCARw//33y88vueQSXH/9\n9WW9kdFolHfEjh8sHo8XPalIVVUVhBBYvXp1l8oRQiAejyORSMhHnOFwGJFIBG1tbQgGg/IRk9QN\nJDXrpOax1JwTQkCv13c68pG6FqSjI+mHIDWTpSPuqqoq2O121NTUwOv1DrquBq1WK3+OhoYG3Hvv\nvXKyuvvuu0t6rXg8Dp/PJ9etFPQ6BsJYLCYHJelIW3pIyVmqcwDyUabUJSF18RiNRtjtdng8HvnI\nUApAbrcbNTU1sNls/Rroi9Hx+y4UIAwGA7xeL7xeb9Gvn8/n5a4JqbtCanF1rH+pi0I66JH2camu\npYfUWpJa61LSlPZvaV+Xnkv7udfrlRNwf9a3VquV67G3+tTpdHC73WVf2JbP59HW1ia3ljp2H4dC\nIQQCAflAS9p/pQMaqWUvtWI77sMmkwkmk0k+mLHb7TCbzXLskOrS4/HAbrfLibU/WuvAX7v4Y7FY\nn67l6HWMIxQK4bHHHpOfT506FZdffnmndYod43jttdcwf/58tLa2yjfYyuVycLvd+MlPfoJvfvOb\nxRdao4HJZILb7UZzc3PR21FXpQQ6Koz1qSzWp7KkcVCz2Vx0d2J3em1xuFwuPPLII2W/eEdTp06F\nVqvF5s2bcdNNNwEA3n33XUSjUUyfPr3k10ulUjhx4oQiZSMiGipyuZw8L0e5yhrjyOfzePbZZwEA\nLS0t0Gg0+N3vfge73Y6rrroKAPDCCy/g9ttvx6FDh1BfXw+n04lbb70V999/P4YNGwa73Y677roL\nc+fOxbnnntunD0FERAOnrNNxc7kcLr744i7LGxsb8fLLLwMA/vCHP+D+++/Ha6+9hpqaGgAn+8Qf\neugh/PrXv0Ymk8Ett9yCf/qnfyqpjxdg81VJrEtlsT6VxfpUllL12efrOCqBO5NyWJfKYn0qi/Wp\nLKXqU5U3OSQiosoZsOs4lPTjH/+40kU4bbAulcX6VBbrU1lK1acqu6qIiKhy2FVFREQlYeIgIqKS\nDOoxjkpOFnU6isfj+M1vfoPDhw9jypQpuO6663q9w7Df78fzzz/fZfkVV1yBYcOG9WdRB61sNov/\n+I//wK5duzB27FjcdtttMJvNBbfbtWsXnnvuOVgsFtx+++0YMWJE/xdWBU6cOIE1a9YgGAziyiuv\nxOzZs3td/+DBg9i6dWuX5YsWLVLt3bKVEo/H8cEHH+DDDz+E2+3G1VdfXdR2bW1teOqpp9Da2or5\n8+dj3rx5hW93IgapnTt3CgDCYDAIo9Eobr/99qK2+8///E+h1+vFddddJ/7hH/5B6PV68cQTT/Rz\naQe/5uZmcdZZZ4nx48eLe++9VzQ0NIhZs2aJVCrV4zYffPCBACAmT54sZs6cKT/27t07gCUfPOLx\nuLjooovE8OHDxfe//30xduxYMWrUKNHW1tbrditXrhQGg0EsWrRIfPWrXxUGg0G89NJLA1Tqwevt\nt98WVqtVfOUrXxF33XWXsFgsYsmSJb1u89RTTwmj0dhpf5w5c2av+/FQkEqlhE6nExqNRlitVnHB\nBRcUtd2ePXtEVVWVmDNnjli8eLGw2+3i7//+7wtuN2gTh9/vFzt37hTJZFLMnDmzqMSRzWZFfX29\nuO++++Rlv/zlL4XZbBZ+v78/izvo3XXXXWLUqFEimUwKIYQ4duyYMJlM4t/+7d963EZKHC0tLQNU\nysHt5z//uXA4HKK1tVUIcTKRnHnmmWL58uU9btPc3CwMBoN45pln5GVLliwRw4cPF/l8vt/LPJhd\nfPHF4rrrrpPr4dVXXxUAxIEDB3rc5qmnnhIjRowYqCKqRjabFVu3bhWRSETcfffdRSeOSy+9VFx2\n2WXyd7B9+3YBQLzzzju9bjdoxzg8Hg8uuOACmEymorc5cOAATpw4gZtvvlledsMNNyCTyeCtt97q\nj2KqxpYtW3D99dfL9Tls2DBceuml2LJlS4VLph5btmzB/Pnz5Zt0WiwWXHPNNb3W4datW6HRaHDt\ntdfKy2655RYcPXoUH3/8cb+XebAKhUJ4//33ccstt8jdIvPmzUNtbS3++Mc/Vrh06qPT6TBz5kw4\nHI6it0kmk9i6dStuvvlm+TuYMmUKRo4cWTAuDNrEUY5Ck0UNVZFIBB999FGXe4KNHTu2qHqZPHky\nPB4P5syZg/Xr1w/ZK3h37NjRbR3u2bOnxzkyduzYgeHDh3e6hfXYsWPlvw1Vu3btAoBO9anT6dDU\n1FSwXo4fP44zzzwTtbW1uPrqq7F9+/Z+Levpav/+/Uin052+A41GU1RcGNSD46VSYrKo01E4HAaA\nLvO0ezweBIPBHrerqqrCI488gsmTJyOdTuPFF1/EjTfeiGQyidtuu60/izwohUKhbuswl8shFot1\nOxdEMBjsslyaxXEo75PSftddffZWL1/60pewevVqnHfeefD7/XjyyScxZ84cvP/++zwJpkRSPZ/6\nHbjdbnz22We9blvxxDHYJotSuzfffBPPPfec/Hzx4sXweDwA0GXWwng83mtX4IgRI7B8+XL5+WWX\nXYZQKIQnnnhiSCYOo9HYbR0C6LEepX2yI2mK36GyT3ZH+uzd1WdvEwxdcskluOSSS+TnCxYswHnn\nnYcnn3wSa9as6Z/CnqZ6+g4SiUTBIYKKd1VptVp5TnBp7t9yNTU1IZPJwO/3y8tyuRxaWlrQ1NSk\nRHEHPZPJ1Kk+9Xo9ampq4HK5cPz48U7rNjc3l1wv06ZNw6FDh5QssmqMHj262zo844wzetxvm5qa\n0Nzc3Kl7r6WlRf7bUCV99r7uk0ajERdeeOGQ3Sf7YvTo0QDK+w4q3uIYzJNFqdGUKVMwZcqULsun\nTZuGzZs348477wRwck6VLVu24Otf/3pJr79z506MHDlSkbKqzYwZM/Daa691atH+4Q9/6HXfmjFj\nBvx+P3bv3o0LLrgAwMnZMA0GAy666KIBKfdgNHr0aNTU1GDz5s248MILAQDHjh3DgQMHsHLlyqJf\nJ5vNYu/evd3u89S7hoYGnHPOOdi8eTPmzp0L4GT31XvvvYc77rij9437dA5YP8rlcmLt2rVi7dq1\nYvTo0WLWrFli7dq14sUXX5TX+f3vfy+cTqdobm6Wl912223irLPOEn/605/Ejh07xIQJE8TcuXOH\n/KmPr776qtBqtWL16tXi008/FXfccYewWq3is88+k9f5xje+IWbNmiU//8UvfiHWrFkj3n//fbFt\n2zaxdOlSAUD88pe/rMAnqLyDBw8Kk8kkvve974kjR46If/7nfxZarVZs3bpVXmflypXijDPOkJ/n\n83kxbdo0ceGFF4pdu3aJLVu2iDPOOEN85zvfqcRHGFQefPBB4Xa7xX/913+JAwcOiLlz54qmpqZO\n12RMmDBBLF26VH6+bNkysWHDBrF7926xefNmccUVVwidTifee++9SnyEQeXll18Wa9euFfPmzRMj\nRoyQ42c6nRZCCHHo0CHhdDrF5s2b5W1Wr14t7Ha7WL9+vfi///s/cfnll4szzzxTtLe39/pegzZx\nZLNZMWnSpC6Pyy+/XF7ntddeE5MmTRI+n09e1t7eLpYvXy7cbrew2+3iO9/5TsELtIaK3//+9+Lc\nc8+VL6A69Vzt+++/X9x0003y86eeekqMHTtWmEwmYTQaxbRp08TTTz89pJPwm2++KaZMmSKMRqP4\n8pe/LF555ZVOf//Xf/1XMXPmzE7LWlpaxKJFi4TVahVer1f88Ic/FIlEYiCLPShls1nx2GOPiYaG\nBmE2m8UNN9wgPv/8807rXHHFFeKRRx6Rny9ZskScddZZQqfTCbvdLhYsWCD++Mc/DnTRB6Xrrruu\n25gZi8WEEEIcOXJETJo0Sbz11lvyNvl8XvzLv/yLOPPMM4XJZBILFy4UH3/8ccH34t1xiYioJBUf\nHCciInVh4iAiopIwcRARUUmYOIiIqCRMHEREVBImDiIiKgkTBxERlYSJg4iISsLEQUREJfl/3cWH\nnME347QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f966a650310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test, _ = gen(1000)\n",
    "latent_vec = encoder.predict(X_test)\n",
    "plt.scatter(latent_vec[:, 0], latent_vec[:, 1])\n",
    "plt.xlim(-1,1)\n",
    "plt.ylim(-1,1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This circle you see above is the image under the encoder $f(x)$ in the latent space $H$. As you may have guessed from the beginning, since the trig map projects cartesian coordinate to a polar coordinate. The encoded vector is a linear subspace. A circle in polar coordinate has the equation $r = a$. I hope this is a good enough punchline for those who didn't hypothesize this result.\n",
    "\n",
    "With PCA, any high-dimensional space can be projected into several linear subspaces using the Gram-Schmidt algorithm in linear algebra."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Potential Use Cases\n",
    "\n",
    "### Anomaly detection\n",
    "\n",
    "Regulators can identify illegal trading strategies by building an unsupervised deep learning algorithm.\n",
    "\n",
    "Implementation: as shown above.\n",
    "\n",
    "### Pattern Search\n",
    "\n",
    "Given an example trading pattern, quickly identify similar patterns in a multi-dimensional sequence of data.\n",
    "\n",
    "Implementation:\n",
    "\n",
    "* Train a stacked recurrent autoencoder on a set of desired pattern(s).\n",
    "\n",
    "* Then for all historical data, use the encoder(!) to produce a fixed length vector.\n",
    "\n",
    "* Compare this vector with a distance metric.\n",
    "\n",
    "It is basically a fuzzy hash function. This I have not tried since calculating the hash for all sequence requires serious compute only available to big instituional players. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Anomaly Detection\n",
    "\n",
    "As you can see, autoencoding is an *extremely powerful* technique in data visualization and exploration. But there are more depth to autoencoding besides creating pretty graphs. One application is anomaly detection.\n",
    "\n",
    "In data mining, anomaly detection (or outlier detection) is the identification of observations that do not conform to an expected pattern in a dataset. The ability to train a neural network in unsupervised manner allows autoencoders to shine in this area. Auto encoders provide a very powerful alternative to traditional methods for signal reconstruction and anomaly detection in time series.\n",
    "\n",
    "Training an autoencoder is conceptually simple:\n",
    "\n",
    "1. Train with training set $\\mathcal{X}_{train}$ with regularization.\n",
    "2. Evaluate on $\\mathcal{X}_{eval}$ and determine the capacity of the autoencoder.\n",
    "3. When we believe it's good enough after inspecting error visualization, choose a threshold of error(such as $2\\sigma$) to determine whether the data point is an anomaly or not. Of course, since we are dealing with time series, this threshold should be chosen on a rolling basis (sliding window).\n",
    "\n",
    "In financial time series(and other series), we often want to detect regime shifts, i.e. know before the price shifts abruptly. In my experiements, this is particularly effective in detecting iceberg orders which is a single large order divided into severel smaller ones for the purpose of hiding the actual order quantity. Detecting iceberg orders using ordinary machine learning methods is difficult, but obvious upon human inspection.\n",
    "\n",
    "In the next part we will simulate how anomaly detection may work. First let us plot the mean square error of the autoencoder output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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g4cKFRTW9dDpd0R+aEEL6qlJiZ1FdUtXV1fj5z3+eNb/rbTmvvfZa6cJjorvv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\nh0EIIcQu1GEQQgixyz+g9kahjBp7ZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f965ca194d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test, _ = gen(1)\n",
    "decoded_imgs = m.predict(X_test)\n",
    "\n",
    "for i in range(2):\n",
    "    plt.plot(range(10), np.square(np.abs(X_test[0, :, i] - decoded_imgs[0, :, i])), label=\"MSE\")\n",
    "\n",
    "plt.ylim(-1,1)\n",
    "plt.xlim(0,10)\n",
    "plt.title(dos_numeros)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's change one data point in the generator. This signifies a regime shift."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 314,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VStq4VxG8XiQSCdM6T8OgMrAtbRs/nf6pCu+kZlIRtjPoHEZBQQEgOozrBUEQ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f965702b0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_test, _ = gen(1)\n",
    "X_test[0, 4, 0] = X_test[0, 4, 0] + 0.5\n",
    "decoded_imgs = m.predict(X_test)\n",
    "\n",
    "for i in range(2):\n",
    "    plt.plot(decoded_imgs[0, :, i])\n",
    "    plt.plot(X_test[0, :, i])\n",
    "\n",
    "plt.ylim(-1,1)\n",
    "plt.xlim(0,10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 315,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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srvImhKCoqAhnzpyBy+VCaWkpSkpKYLFY4HA44PP5xIWKgUAAbrcbLpdLHF8J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\nWAghhJQVFRZCCCFl9T83pEUb8DBsXwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f9656b67210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(2):\n",
    "    mse = np.square(np.abs(X_test[0, :, i] - decoded_imgs[0, :, i]))\n",
    "    anomaly = np.argmax(mse)\n",
    "    if mse[anomaly] > 0.4:\n",
    "        plt.title(\"Anomaly detected in series {} at time step: {}\".format(i, anomaly))\n",
    "    plt.plot(range(10), mse, label=\"MSE\")\n",
    "\n",
    "plt.ylim(-1,1)\n",
    "plt.xlim(0,10)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Note on MSE\n",
    "\n",
    "Also, assume the financial series is normalized to be a zero-centered signal, MSE would be a mal-adapted measure. Because if the an outlier is near 0, then the MSE will likely be less than the MSE of the original signal(centered at 0). So it is imperative to devise a more sophisticated loss function by adding a moving average to the MSE. This way, we can judge based on the deviations from the rolling average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Note on Online Training / Inference\n",
    "\n",
    "This algorithm, like all signal processing neural networks, should be able to operate on a rolling basis. The algorithm just needs a segment of the data from a sliding window.\n",
    "\n",
    "When attention mechanism is introduced, online training(input partially observed) becomes more involved. Online and linear-time attention alignment can be achieved with memory mechanism. I might cover attention mechanism for financial data in a future post."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pattern Search\n",
    "\n",
    "![](https://i.imgur.com/wJuLdv8.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stacked Autoencoders\n",
    "\n",
    "This is a good place to introduce how stacked autoencoders work.\n",
    "\n",
    "![](https://www.researchgate.net/profile/Konrad_Kording/publication/274728436/figure/fig2/AS:271715934666753@1441793535194/Figure-2-A-A-stacked-autoencoder-is-trained-on-high-dimensional-data-im-i-1.png)\n",
    "\n",
    "As we have seen above, a simple recurrent autoencoder has 3 layers: encoder LSTM layer, hidden layer, and decoder LSTM layer. Stacked autoencoders is constructed by stacking several single-layer autoencoders. The first single-layer autoencoder maps input to the first hidden vector. After training the first autoencoder, we discard the first decoder layer which is then replaced by the second autoencoder, which has a smaller latent vector dimension. Repeat this process and determine the correct depth and size by trial and error(If you know a better way please let me know.) The depth of stacked autoencoders enable feature invariance and allow for more abstractness in extracted features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "Autoencoders are powerful tools despite their simplistic nature. We use autoencoders to visualize manifold on high dimensional space and detect anomalies in time series.\n",
    "\n",
    "## A Note on Supervised Learning\n",
    "\n",
    "This post only covered the unsupervised usage of autoencoders. Variational recurrent autoencoders can \"denoise\" artifically corrupted data input. I never had any luck with it so I can't recommend the usage on financial data.\n",
    "\n",
    "Financial data is extremely noisy. But when trained with a smaller capacity, autoencoders have the built-in ability of denoising because they only learn the most salient features anyway.\n",
    "\n",
    "## A Note on Variational Inference / Bayesian Method\n",
    "\n",
    "Please refer to this [article](https://jaan.io/what-is-variational-autoencoder-vae-tutorial/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reference\n",
    "\n",
    "https://arxiv.org/pdf/1511.01432.pdf\n",
    "\n",
    "http://www1.icsi.berkeley.edu/~vinyals/Files/rnn_denoise_2012.pdf\n",
    "\n",
    "http://www.deeplearningbook.org/contents/autoencoders.html\n",
    "\n",
    "http://wp.doc.ic.ac.uk/hipeds/wp-content/uploads/sites/78/2017/01/Steven_Hutt_Deep_Networks_Financial.pdf\n",
    "\n",
    "https://www.cs.cmu.edu/~epxing/Class/10708-17/project-reports/project8.pdf\n",
    "\n",
    "https://arxiv.org/pdf/1610.09513.pdf\n",
    "\n",
    "https://arxiv.org/pdf/1012.0349.pdf\n",
    "\n",
    "https://arxiv.org/pdf/1204.1381.pdf"
   ]
  }
 ],
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