\n",
"\n",
"\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" yr holiday temp hum windspeed casual registered cnt season_1 \\\n",
"0 0 0 0.24 0.81 0.0 3 13 16 1 \n",
"1 0 0 0.22 0.80 0.0 8 32 40 1 \n",
"2 0 0 0.22 0.80 0.0 5 27 32 1 \n",
"3 0 0 0.24 0.75 0.0 3 10 13 1 \n",
"4 0 0 0.24 0.75 0.0 0 1 1 1 \n",
"\n",
" season_2 ... hr_21 hr_22 hr_23 weekday_0 weekday_1 weekday_2 \\\n",
"0 0 ... 0 0 0 0 0 0 \n",
"1 0 ... 0 0 0 0 0 0 \n",
"2 0 ... 0 0 0 0 0 0 \n",
"3 0 ... 0 0 0 0 0 0 \n",
"4 0 ... 0 0 0 0 0 0 \n",
"\n",
" weekday_3 weekday_4 weekday_5 weekday_6 \n",
"0 0 0 0 1 \n",
"1 0 0 0 1 \n",
"2 0 0 0 1 \n",
"3 0 0 0 1 \n",
"4 0 0 0 1 \n",
"\n",
"[5 rows x 59 columns]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dummy_fields = ['season', 'weathersit', 'mnth', 'hr', 'weekday']\n",
"for each in dummy_fields:\n",
" dummies = pd.get_dummies(rides[each], prefix=each, drop_first=False)\n",
" rides = pd.concat([rides, dummies], axis=1)\n",
"\n",
"fields_to_drop = ['instant', 'dteday', 'season', 'weathersit', \n",
" 'weekday', 'atemp', 'mnth', 'workingday', 'hr']\n",
"data = rides.drop(fields_to_drop, axis=1)\n",
"data.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Scaling Target Variables\n",
"To make training the network easier, we'll standardize each of the continuous variables. That is, we'll shift and scale the variables such that they have zero mean and a standard deviation of 1.\n",
"\n",
"The scaling factors are saved so we can go backwards when we use the network for predictions."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"quant_features = ['casual', 'registered', 'cnt', 'temp', 'hum', 'windspeed']\n",
"\n",
"# Store scalings in a dictionary so we can convert back later\n",
"scaled_features = {}\n",
"for each in quant_features:\n",
" mean, std = data[each].mean(), data[each].std()\n",
" scaled_features[each] = [mean, std]\n",
" data.loc[:, each] = (data[each] - mean)/std"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Splitting the Data into Training, Testing, and Validation Sets\n",
"\n",
"We'll save the data for the last approximately 21 days to use as a test set after we've trained the network. We'll use this set to make predictions and compare them with the actual number of riders."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Save data for approximately the last 21 days \n",
"test_data = data[-21*24:]\n",
"\n",
"# Now remove the test data from the data set \n",
"data = data[:-21*24]\n",
"\n",
"# Separate the data into features and targets\n",
"target_fields = ['cnt', 'casual', 'registered']\n",
"features, targets = data.drop(target_fields, axis=1), data[target_fields]\n",
"test_features, test_targets = test_data.drop(target_fields, axis=1), test_data[target_fields]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll split the data into two sets, one for training and one for validating as the network is being trained. Since this is time series data, we'll train on historical data, then try to predict on future data (the validation set)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Hold out the last 60 days or so of the remaining data as a validation set\n",
"train_features, train_targets = features[:-60*24], targets[:-60*24]\n",
"val_features, val_targets = features[-60*24:], targets[-60*24:]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Time to Build The Network\n",
"\n",
"Below you'll build your network. We've built out the structure. You'll implement both the forward pass and backwards pass through the network. You'll also set the hyperparameters: the learning rate, the number of hidden units, and the number of training passes.\n",
"\n",
"| \n", " | yr | \n", "holiday | \n", "temp | \n", "hum | \n", "windspeed | \n", "casual | \n", "registered | \n", "cnt | \n", "season_1 | \n", "season_2 | \n", "... | \n", "hr_21 | \n", "hr_22 | \n", "hr_23 | \n", "weekday_0 | \n", "weekday_1 | \n", "weekday_2 | \n", "weekday_3 | \n", "weekday_4 | \n", "weekday_5 | \n", "weekday_6 | \n", "
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "0 | \n", "0 | \n", "0.24 | \n", "0.81 | \n", "0.0 | \n", "3 | \n", "13 | \n", "16 | \n", "1 | \n", "0 | \n", "... | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "1 | \n", "
| 1 | \n", "0 | \n", "0 | \n", "0.22 | \n", "0.80 | \n", "0.0 | \n", "8 | \n", "32 | \n", "40 | \n", "1 | \n", "0 | \n", "... | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "1 | \n", "
| 2 | \n", "0 | \n", "0 | \n", "0.22 | \n", "0.80 | \n", "0.0 | \n", "5 | \n", "27 | \n", "32 | \n", "1 | \n", "0 | \n", "... | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "1 | \n", "
| 3 | \n", "0 | \n", "0 | \n", "0.24 | \n", "0.75 | \n", "0.0 | \n", "3 | \n", "10 | \n", "13 | \n", "1 | \n", "0 | \n", "... | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "1 | \n", "
| 4 | \n", "0 | \n", "0 | \n", "0.24 | \n", "0.75 | \n", "0.0 | \n", "0 | \n", "1 | \n", "1 | \n", "1 | \n", "0 | \n", "... | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "0 | \n", "1 | \n", "
5 rows × 59 columns
\n", "![](\"images/neural_network.png\")
\n",
"\n",
"The network has two layers, a hidden layer and an output layer. The hidden layer will use the sigmoid function for activations. The output layer has only one node and is used for the regression, the output of the node is the same as the input of the node. That is, the activation function is $f(x)=x$. A function that takes the input signal and generates an output signal, but takes into account the threshold, is called an activation function. We work through each layer of our network calculating the outputs for each neuron. All of the outputs from one layer become inputs to the neurons on the next layer. This process is called *forward propagation*.\n",
"\n",
"We use the weights to propagate signals forward from the input to the output layers in a neural network. We use the weights to also propagate error backwards from the output back into the network to update our weights. This is called *backpropagation*.\n",
"\n",
"> **Hint:** You'll need the derivative of the output activation function ($f(x) = x$) for the backpropagation implementation. If you aren't familiar with calculus, this function is equivalent to the equation $y = x$. What is the slope of that equation? That is the derivative of $f(x)$.\n",
"\n",
"Below, you have these tasks:\n",
"1. Implement the sigmoid function to use as the activation function. Set `self.activation_function` in `__init__` to your sigmoid function.\n",
"2. Implement the forward pass in the `train` method.\n",
"3. Implement the backpropagation algorithm in the `train` method, including calculating the output error.\n",
"4. Implement the forward pass in the `run` method.\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from my_answers import NeuralNetwork"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def MSE(y, Y):\n",
" return np.mean((y-Y)**2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Unit Tests\n",
"\n",
"Run these unit tests to check the correctness of your network implementation. This will help you be sure your network was implemented correctly befor you starting trying to train it. These tests must all be successful to pass the project."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
".....\n",
"----------------------------------------------------------------------\n",
"Ran 5 tests in 0.013s\n",
"\n",
"OK\n"
]
},
{
"data": {
"text/plain": [
"