Part 1 - RNN Time Series.ipynb

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    "# Simple RNN\n",
    "In this notebook, we are training a simple RNN to **time-series predictions**.  \n",
    "Given some set of predictions, we can predict the next time step.  \n",
    "We'll do the subsequent steps:  \n",
    "1. we create our data  \n",
    "2. we define an RNN in PyTorch  \n",
    "3. we will train our network to see how it works\n"
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    "## Import Resources and Create Data\n"
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.figure(figsize=(8,5))\n",
    "\n",
    "# how many time steps/points are in a batch of data\n",
    "seq_length = 20\n",
    "\n",
    "# generate evenly spaced data pts (same space between the points)\n",
    "# we create a range of data from zero to pi\n",
    "# we retain the endpoint\n",
    "time_steps = np.linspace(0, np.pi, seq_length + 1)\n",
    "data = np.sin(time_steps)\n",
    "\n",
    "data.resize((time_steps.size, 1)) # size becomes (seq_length+1, 1), adds an input_size dimension\n",
    "\n",
    "\n",
    "x = data[:-1] # all, but the last data is not retained\n",
    "y = data[1:] # all, but the first data is not retained\n",
    "# display the data\n",
    "plt.plot(time_steps[1:], x, 'r.', label='input, x') # x\n",
    "plt.plot(time_steps[1:], y, 'b.', label='target, y') # y\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## We Define the RNN\n",
    "We define an RNN in PyTorch. We'll use `nn.RNN` to create a RNN layer, and finally we put a fully connected layer to get the output of the size we want.  \n",
    "An RNN takes in input a number of parameters:  \n",
    "- ** input_size ** the size of the input  \n",
    "- ** hidden_dim ** the number of features in the RNN output and in the hidden state\n",
    "- ** n_layers ** the number of layers that make up the RNN, typically 1-3; greater than 1 indicates that you are creating a stacked RNN\n",
    "- ** batch_size ** wheter or not the input/output of the RNN will have the batch size as the first dimension **(batch_size, seq_len, hidden_dim)**\n",
    "  \n",
    "It is suggested to see the [documentation of the RNN](https://pytorch.org/docs/stable/nn.html#recurrent-layers) to read more about the recurrent layers."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "class RNN(nn.Module):\n",
    "    def __init__(self, input_size, output_size, hidden_dim, n_layers):\n",
    "        super(RNN, self).__init__()\n",
    "        \n",
    "        self.hidden_dim=hidden_dim\n",
    "\n",
    "        # define an RNN with specified parameters\n",
    "        # batch_first means that the first dim of the input and output will be the batch_size\n",
    "        self.rnn = nn.RNN(input_size, hidden_dim, n_layers, batch_first=True)\n",
    "        \n",
    "        # last, fully-connected layer\n",
    "        self.fc = nn.Linear(hidden_dim, output_size)\n",
    "\n",
    "    def forward(self, x, hidden):\n",
    "        # x (batch_size, seq_length, input_size)\n",
    "        # hidden (n_layers, batch_size, hidden_dim)\n",
    "        # r_out (batch_size, time_step, hidden_size)\n",
    "        batch_size = x.size(0)\n",
    "        \n",
    "        # get RNN outputs\n",
    "        r_out, hidden = self.rnn(x, hidden)\n",
    "        # shape output to be (batch_size*seq_length, hidden_dim)\n",
    "        r_out = r_out.view(-1, self.hidden_dim)  \n",
    "        \n",
    "        # get final output \n",
    "        output = self.fc(r_out)\n",
    "        \n",
    "        return output, hidden\n"
   ]
  },
  {
   "source": [
    "## Check the input/output dimensions\n",
    "To check if the model is working properly, by testing how is it working with the input data."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Input size:  torch.Size([1, 20, 1])\nOutput size:  torch.Size([20, 1])\nHidden state size:  torch.Size([2, 1, 10])\n"
     ]
    }
   ],
   "source": [
    "# test that dimensions are as expected\n",
    "test_rnn = RNN(input_size=1, output_size=1, hidden_dim=10, n_layers=2)\n",
    "\n",
    "# generate evenly spaced, test data pts\n",
    "time_steps = np.linspace(0, np.pi, seq_length)\n",
    "data = np.sin(time_steps)\n",
    "data.resize((seq_length, 1))\n",
    "\n",
    "test_input = torch.Tensor(data).unsqueeze(0) # give it a batch_size of 1 as first dimension\n",
    "print('Input size: ', test_input.size())\n",
    "\n",
    "# test out rnn sizes\n",
    "test_out, test_h = test_rnn(test_input, None)\n",
    "print('Output size: ', test_out.size())\n",
    "print('Hidden state size: ', test_h.size())"
   ]
  },
  {
   "source": [
    "## Training the RNN\n",
    "Next, we will initializate the RNN with some hyperparameters. Then, we train it over a series of steps and see how it performs."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "RNN(\n  (rnn): RNN(1, 32, batch_first=True)\n  (fc): Linear(in_features=32, out_features=1, bias=True)\n)\n"
     ]
    }
   ],
   "source": [
    "# decide on hyperparameters\n",
    "input_size=1 \n",
    "output_size=1\n",
    "hidden_dim=32\n",
    "n_layers=1\n",
    "\n",
    "# instantiate an RNN\n",
    "rnn = RNN(input_size, output_size, hidden_dim, n_layers)\n",
    "print(rnn)"
   ]
  },
  {
   "source": [
    "## Loss and Optimization\n",
    "It is a regression problem: can we train a RNN to accurately predict the next data point, given the current data point?\n",
    "- The data points are coordinate values, so to compare it with a predicted data point, we'll use a regression point: the mean squared error\n",
    "- It is typical to use Adam optimizer to train the RNN models"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MSE loss and Adam optimizer with a learning rate of 0.01\n",
    "criterion = nn.MSELoss()\n",
    "optimizer = torch.optim.Adam(rnn.parameters(), lr=0.01) "
   ]
  },
  {
   "source": [
    "## Defining the Training Function\n",
    "This functions takes an rnn, a number of steps to train for, and returns a trained rnn. This function is responsible to show the loss and the predictions, every so often.  \n",
    "  \n",
    "\n",
    "### Hidden State\n",
    "We have to have a very high attention over the hidden state:  \n",
    "- Before looping over a batch of training data, the hidden state is initialized  \n",
    "- After a new hidden state is generated by the rnn, we get the latest hidden state, and use that as input to the rnn for the following steps"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# train the RNN\n",
    "def train(rnn, n_steps, print_every):\n",
    "    \n",
    "    # initialize the hidden state\n",
    "    hidden = None      \n",
    "    \n",
    "    for batch_i, step in enumerate(range(n_steps)):\n",
    "        # defining the training data \n",
    "        time_steps = np.linspace(step * np.pi, (step+1)*np.pi, seq_length + 1)\n",
    "        data = np.sin(time_steps)\n",
    "        data.resize((seq_length + 1, 1)) # input_size=1\n",
    "\n",
    "        x = data[:-1]\n",
    "        y = data[1:]\n",
    "        \n",
    "        # convert data into Tensors\n",
    "        x_tensor = torch.Tensor(x).unsqueeze(0) # unsqueeze gives a 1, batch_size dimension\n",
    "        y_tensor = torch.Tensor(y)\n",
    "\n",
    "        # outputs from the rnn\n",
    "        prediction, hidden = rnn(x_tensor, hidden)\n",
    "\n",
    "        ## Representing Memory ##\n",
    "        # make a new variable for hidden and detach the hidden state from its history\n",
    "        # this way, we don't backpropagate through the entire history\n",
    "        hidden = hidden.data\n",
    "\n",
    "        # calculate the loss\n",
    "        loss = criterion(prediction, y_tensor)\n",
    "        # zero gradients\n",
    "        optimizer.zero_grad()\n",
    "        # perform backprop and update weights\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "        # display loss and predictions\n",
    "        if batch_i%print_every == 0:        \n",
    "            print('Loss: ', loss.item())\n",
    "            plt.plot(time_steps[1:], x, 'r.') # input\n",
    "            plt.plot(time_steps[1:], prediction.data.numpy().flatten(), 'b.') # predictions\n",
    "            plt.show()\n",
    "    \n",
    "    return rnn\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Loss:  0.426058828830719\n"
     ]
    },
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# train the rnn and monitor results\n",
    "n_steps = 75\n",
    "print_every = 15\n",
    "\n",
    "trained_rnn = train(rnn, n_steps, print_every)"
   ]
  },
  {
   "source": [
    "## Time-Series Prediction\n",
    "Time-series prediction can be applied to many tasks. Think about weather forecasting or predicting the ebb and flow of stock market prices. You can even try to generate predictions much further in the future than just one time step!"
   ],
   "cell_type": "markdown",
   "metadata": {}
  }
 ]
}