So far in our discussion of recurrent neural networks, you have learned:
- The basic intuition behind recurrent neural networks
- The vanishing gradient problem that historically impeded the progress of recurrent neural networks
- How long short-term memory networks (LSTMs) help to solve the vanishing gradient problem
It's now time to build your first recurrent neural network! More specifically, this tutorial will teach you how to build and train an LSTM to predict the stock price of Facebook (FB).
You can skip to a specific section of this Python recurrent neural network tutorial using the table of contents below:
- Downloading the Data Set For This Tutorial
- Importing The Libraries You'll Need For This Tutorial
- Importing Our Training Set Into The Python Script
- Applying Feature Scaling To Our Data Set
- Specifying The Number Of Timesteps For Our Recurrent Neural Network
- Finalizing Our Data Sets By Transforming Them Into NumPy Arrays
- Importing Our TensorFlow Libraries
- Building Our Recurrent Neural Network
- Adding Our First LSTM Layer
- Adding Some Dropout Regularization
- Adding Three More LSTM Layers With Dropout Regularization
- Adding The Output Layer To Our Recurrent Neural Network
- Compiling Our Recurrent Neural Network
- Fitting The Recurrent Neural Network On The Training Set
- The Full Code For This Tutorial
- Final Thoughts
To proceed through this tutorial, you will need two download two data sets:
- A set of training data that contains information on Facebook's stock price from teh start of 2015 to the end of 2019
- A set of test data that contains information on Facebook's stock price during the first month of 2020
Our recurrent neural network will be trained on the 2015-2019 data and will be used to predict the data from January 2020.
You can download the training data and test data using the links below:
Each of these data sets are simply exports from Yahoo! Finance. They look like this (when opened in Microsoft Excel):
Once the files are downloaded, move them to the directory you'd like to work in and open a Jupyter Notebook.
Let's start our Python script by importing some of these libraries:
import numpy as np import pandas as pd import matplotlib.pyplot as plt
The next task that needs to be completed is to import our data set into the Python script.
We will initially import the data set as a pandas DataFrame using the
read_csv method. However, since the
keras module of
TensorFlow only accepts NumPy arrays as parameters, the data structure will need to be transformed post-import.
Let's start by importing the entire
.csv file as a DataFrame:
training_data = pd.read_csv('FB_training_data.csv')
You will notice in looking at the DataFrame that it contains numerous different ways of measuring Facebook's stock price, including opening price, closing price, high and low prices, and volume information:
We will need to select a specific type of stock price before proceeding. Let's use
Close, which indicates the unadjusted closing price of Facebook's stock.
Now we need to select that column of the DataFrame and store it in a NumPy array. Here is the command to do this:
training_data = training_data.iloc[:, 1].values
Note that this command overwrites the existing
training_data variable that we had created previously.
You can now verify that our
training_data variable is indeed a NumPy array by running
type(training_data), which should return:
Let's now take some time to apply some feature scaling to our data set.
As a quick refresher, there are two main ways that you can apply featuer scaling to your data set:
We'll be using normalization to build our recurrent neural network, which involves subtracting the minimum value of the data set and then dividing by the range of the data set.
Here is the normalization function defined mathematically:
scikit-learn makes it very easy to apply normalization to a dataset using its
Let's start by importing this class into our Python script. The
MinMaxScaler class lives within the
preprocessing module of
scikit-learn, so the command to import the class is:
from sklearn.preprocessing import MinMaxScaler
Next we need to create an instance of this class. We will assign the newly-created object to a variable called
scaler. We will be using the default parameters for this class, so we do not need to pass anything in:
scaler = MinMaxScaler()
Since we haven't specified any non-default parameters, this will scale our data set so that every observation is between
We have created our
scaler object but our
training_data data set has not yet been scaled. We need to use the
fit_transform method to modify the original data set. Here's the statement to do this:
training_data = scaler.fit_transform(training_data.reshape(-1, 1))
The next thing we need to do is to specify our number of
timesteps. Timesteps specify how many previous observations should be considered when the recurrent neural network makes a prediction about the current observation.
We will use
40 timesteps in this tutorial. This means that for every day that the neural network predicts, it will consider the previous 40 days of stock prices to determine its output. Note that since there are only ~20 trading days in a given month, using 40 timesteps means we're relying on stock price data from the previous 2 months.
So how do we actually specify the number of timesteps within our Python script?
It's done through creating two special data structures:
- One data structure that we'll call
x_training_datathat contains the last 40 stock price observations in the data set. This is the data that the recurrent neural network will use to make predictions.
- One data structure that we'll call
y_training_datathat contains the stock price for the next trading day. This is the data point that the recurrent neural network is trying to predict.
To start, let's initialize each of these data structures as an empty Python list:
x_training_data =  y_training_data =
Now we will use a for loop to populate the actual data into each of these Python lists. Here's the code (with further explanation of the code after the code block):
for i in range(40, len(training_data)): x_training_data.append(training_data[i-40:i, 0]) y_training_data.append(training_data[i, 0])
Let's unpack the components of this code block:
range(40, len(training_data))function causes the for loop to iterate from
40to the last index of the training data.
x_training_data.append(training_data[i-40:i, 0])line causes the loop to append the 40 preceding stock prices to
x_training_datawith each iteration of the loop.
- Similarly, the
y_training_data.append(training_data[i, 0])causes the loop to append the next day's stock price to
y_training_datawith each iteration of the loop.
TensorFlow is designed to work primarily with NumPy arrays. Because of this, the last thing we need to do is transform the two Python lists we just created into NumPy arrays.
Fortunately, this is simple. You simply need to wrap the Python lists in the
np.array function. Here's the code:
x_training_data = np.array(x_training_data) y_training_data = np.array(y_training_data)
One important way that you can make sure your script is running as intended is to verify the shape of both NumPy arrays.
x_training_data array should be a two-directional NumPy array with one dimension being
40 (the number of timesteps) and the second dimension being
len(training_data) - 40, which evaluates to
1218 in our case.
y_training_data object should be a one-dimensional NumPy array of length
1218 (which, again, is
len(training_data) - 40).
You can verify the shape of the arrays by printing their
shape attribute, like this:
(1218, 40) (1218,)
Both arrays have the dimensions you'd expect. However, we need to reshape our
x_training_data object one more time before proceeding to build our recurrent neural network.
The reason for this is that the recurrent neural network layer available in TensorFlow only accepts data in a very specific format. You can read the TensorFlow documentation on this topic here.
To reshape the
x_training_data object, I will use the np.reshape method. Here's the code to do this:
x_training_data = np.reshape(x_training_data, (x_training_data.shape, x_training_data.shape, 1))
Now let's print the shape of
x_training_data once again:
(1218, 40, 1)
Our arrays have the desired shape, so we can proceed to building our recurrent neural network.
Before we can begin building our recurrent neural network, we'll need to import a number of classes from TensorFlow. Here are the statements you should run before proceeding:
from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense from tensorflow.keras.layers import LSTM from tensorflow.keras.layers import Dropout
It's now time to build our recurrent neural network.
The first thing that needs to be done is initializing an object from TensorFlow's
Sequential class. As its name implies, the
Sequential class is designed to build neural networks by adding sequences of layers over time.
Here's the code to initialize our recurrent neural network:
rnn = Sequential()
The first layer that we will add is an LSTM layer. To do this, pass an invocation of the
LSTM class (that we just imported) into the
LSTM class accepts several parameters. More precisely, we will specify three arguments:
- The number of LSTM neurons that you'd like to include in this layer. Increasing the number of neurons is one method for increasing the dimensionality of your recurrent neural network. In our case, we will specify
units = 45.
return_sequences = True- this must always be specified if you plan on including another LSTM layer after the one you're adding. You should specify
return_sequences = Falsefor the last LSTM layer in your recurrent neural network.
input_shape: the number of timesteps and the number of predictors in our training data. In our case, we are using
40timesteps and only
1predictor (stock price), so we will add
Here is the full
rnn.add(LSTM(units = 45, return_sequences = True, input_shape = (x_training_data.shape, 1)))
Note that I used
x_training_data.shape instead of the hardcoded value in case we decide to train the recurrent neural network on a larger model at a later date.
Dropout regularization is a technique used to avoid overfitting when training neural networks.
It involves randomly excluding - or "dropping out" - certain layer outputs during the training stage.
TensorFlow makes it easy to implement dropout regularization using the
Dropout class that we imported earlier in our Python script. The
Dropout class accepts a single parameter: the dropout rate.
The dropout rate indicates how many neurons should be dropped in a specific layer of the neural network. It is common to use a dropout rate of 20%. We will follow this convention in our recurrent neural network.
Here's how you can instruct TensorFlow to drop 20% of the LSTM layer's neuron during each iteration of the training stage:
We will now add three more LSTM layers (with dropout regularization) to our recurrent neural network. You will see that after specifying the first LSTM layer, adding more is trivial.
To add more layers, all that needs to be done is copying the first two
add methods with one small change. Namely, we should remove the
input_shape argument from the
We will keep the number of neurons (or
units) and the dropout rate the same in each of the
LSTM class invocations. Since the third
LSTM layer we're adding in this section will be our last LSTM layer, we can remove the
return_sequences = True parameter as mentioned earlier. Removing the parameter sets
return_sequences to its default value of
Here's the full code to add our next three LSTM layers:
rnn.add(LSTM(units = 45, return_sequences = True)) rnn.add(Dropout(0.2)) rnn.add(LSTM(units = 45, return_sequences = True)) rnn.add(Dropout(0.2)) rnn.add(LSTM(units = 45)) rnn.add(Dropout(0.2))
This code is very repetitive and violates the DRY (Don't repeat yourself) principle of software development. Let's nest it in a loop instead:
for i in [True, True, False]: rnn.add(LSTM(units = 45, return_sequences = i)) rnn.add(Dropout(0.2))
Let's finish architecting our recurrent neural network by adding our output layer.
The output layer will be an instance of the
Dense class, which is the same class we used to create the full connection layer of our convolutional neural network earlier in this course.
The only parameter we need to specify is
units, which is the desired number of dimensions that the output layer should generate. Since we want to output the next day's stock price (a single value), we'll specify
units = 1.
Here's the code to create our output layer:
rnn.add(Dense(units = 1))
As you'll recall from the tutorials on artificial neural networks and convolutional neural networks, the compilation step of building a neural network is where we specify the neural net's optimizer and loss function.
TensorFlow allows us to compile a neural network using the aptly-named
compile method. It accepts two arguments:
loss. Let's start by creating an empty
rnn.compile(optimizer = '', loss = '')
We now need to specify the
Let's start by discussing the
optimizer parameter. Recurrent neural networks typically use the RMSProp optimizer in their compilation stage. With that said, we will use the Adam optimizer (as before). The Adam optimizer is a workhorse optimizer that is useful in a wide variety of neural network architectures.
loss parameter is fairly simple. Since we're predicting a continuous variable, we can use mean squared error - just like you would when measuring the performance of a linear regression machine learning model. This means we can specify
loss = mean_squared_error.
Here's the final
rnn.compile(optimizer = 'adam', loss = 'mean_squared_error')
It's now time to train our recurrent network on our training data.
To do this, we use the
fit method. The
fit method accepts four arguments in this case:
- The training data: in our case, this will be
- Epochs: the number of iterations you'd like the recurrent neural network to be trained on. We will specify
epochs = 100in this case.
- The batch size: the size of batches that the network will be trained in through each epoch.
Here is the code to train this recurrent neural network according to our specifications:
rnn.fit(x_training_data, y_training_data, epochs = 100, batch_size = 32)
Your Jupyter Notebook will now generate a number of printed outputs for every epoch in the training algorithm. They look like this:
As you can see, every output shows how long the epoch took to compute as well as the computed loss function at that epoch.
You should see the loss function's value slowly decline as the recurrent neural network is fitted to the training data over time. In my case, the loss function's value declined from
0.0504 in the first iteration to
0.0017 in the last iteration.
We have built our recurrent neural network and trained it on data of Facebook's stock price over the last 5 years. It's now time to make some predictions!
To start, let's import the actual stock price data for the first month of 2020. This will give us something to compare our predicted values to.
Here's the code to do this. Note that it is very similar to the code that we used to import our training data at the start of our Python script:
test_data = pd.read_csv('FB_test_data.csv') test_data = test_data.iloc[:, 1].values
If you run the statement
print(test_data.shape), it will return
(21,). This shows that our test data is a one-dimensional NumPy array with 21 entries - which means there were 21 stock market trading days in January 2020.
You can also generate a quick plot of the data using
plt.plot(test_data). This should generate the following Python visualization:
With any luck, our predicted values should follow the same distribution.
Before we can actually make predictions for Facebook's stock price in January 2020, we first need to make some changes to our data set.
The reason for this is that to predict each of the
21 observations in January, we will need the
40 previous trading days. Some of these trading days will come from the test set while the remainder will come from the training set. Because of this, some concatenation is necessary.
Unfortunately, you can just concatenate the NumPy arrays immediately. This is because we've already applied feature scaling to the training data but haven't applied any feature scaling to the test data.
To fix this, we need to re-import the original
x_training_data object under a new variable name called
unscaled_x_training_data. For consistency, we will also re-import the test data as a DataFrame called
unscaled_training_data = pd.read_csv('FB_training_data.csv') unscaled_test_data = pd.read_csv('FB_test_data.csv')
Now we can concatenate together the
Open column from each DataFrame with the following statement:
all_data = pd.concat((unscaled_x_training_data['Open'], unscaled_test_data['Open']), axis = 0)
all_data object is a pandas Series of length 1279.
Now we need to create an array of all the stock prices from January 2020 and the 40 trading days prior to January. We will call this object
x_test_data since it contains the
x values that we'll use to make stock price predictions for January 2020.
The first thing you need to do is find the index of the first trading day in January within our
all_data object. The statement
len(all_data) - len(test_data) identifies this index for us.
This represents the upper bound of the first item in the array. To get the lower bound, just subtract
40 from this number. Said differently, the lower bound is
len(all_data) - len(test_data) - 40.
The upper bound of the entire
x_test_data array will be the last item in the data set. Accordingly, we can create this NumPy array with the following statement:
x_test_data = all_data[len(all_data) - len(test_data) - 40:].values
You can check whether or not this object has been created as desired by printing
len(x_test_data), which has a value of
61. This makes sense - it should contain the
21 values for January 2020 as well as the
40 values prior.
The last step of this section is to quickly reshape our NumPy array to make it suitable for the
x_test_data = np.reshape(x_test_data, (-1, 1))
Note that if you neglected to do this step, TensorFlow would print a handy message that would explain exactly how you'd need to transform your data.
Our recurrent neural network was trained on scaled data. Because of this, we need to scale our
x_test_data variable before we can use the model to make predictions.
x_test_data = scaler.transform(x_test_data)
Note that we used the
transform method here instead of the
fit_transform method (like before). This is because we want to transform the test data according to the fit generated from the entire training data set.
This means that the transformation that is applied to the test data will be the same as the one applied to the training data - which is necessary for our recurrent neural network to make accurate predictions.
The last thing we need to do is group our test data into
21 arrays of size
40. Said differently, we'll now create an array where each entry corresponds to a date in January and contains the stock prices of the
40 previous trading days.
The code to do this is similar to something we used earlier:
final_x_test_data =  for i in range(40, len(x_test_data)): final_x_test_data.append(x_test_data[i-40:i, 0]) final_x_test_data = np.array(final_x_test_data)
Lastly, we need to reshape the
final_x_test_data variable to meet TensorFlow standards.
We saw this previously, so the code should need no explanation:
final_x_test_data = np.reshape(final_x_test_data, (final_x_test_data.shape, final_x_test_data.shape, 1))
After an absurd amount of data reprocessing, we are now ready to make predictions using our test data!
This step is simple. Simply pass in our
final_x_test_data object into the
predict method called on the
rnn object. As an example, here is how you could generate these predictions and store them in an aptly-named variable called
predictions = rnn.predict(final_x_test_data)
Let's plot these predictions by running
plt.plot(predictions) (note that you'll need to run
plt.clf() to clear your canvas first):
As you can see, the predicted values in this plot are all between
1. This is because our data set is still scaled! We need to un-scale it for the predictions to have any practical meaning.
MinMaxScaler class that we used to originally scale our data set comes with a useful
inverse_transform method to un-scale the data. Here's how you could un-scale the data and generate a new plot:
unscaled_predictions = scaler.inverse_transform(predictions) plt.clf() #This clears the first prediction plot from our canvas plt.plot(unscaled_predictions)
This looks much better! Anyone who's followed Facebook's stock price for any length of time can see that this seems fairly close to where Facebook has actually traded.
Let's generate plot that compares our predicted stock prices with Facebook's actual stock price:
plt.plot(unscaled_predictions, color = '#135485', label = "Predictions") plt.plot(test_data, color = 'black', label = "Real Data") plt.title('Facebook Stock Price Predictions')
You can view the full code for this tutorial in this GitHub repository. It is also pasted below for your reference:
#Import the necessary data science libraries import numpy as np import pandas as pd import matplotlib.pyplot as plt #Import the data set as a pandas DataFrame training_data = pd.read_csv('FB_training_data.csv') #Transform the data set into a NumPy array training_data = training_data.iloc[:, 1].values #Apply feature scaling to the data set from sklearn.preprocessing import MinMaxScaler scaler = MinMaxScaler() training_data = scaler.fit_transform(training_data.reshape(-1, 1)) #Initialize our x_training_data and y_training_data variables #as empty Python lists x_training_data =  y_training_data = #Populate the Python lists using 40 timesteps for i in range(40, len(training_data)): x_training_data.append(training_data[i-40:i, 0]) y_training_data.append(training_data[i, 0]) #Transforming our lists into NumPy arrays x_training_data = np.array(x_training_data) y_training_data = np.array(y_training_data) #Verifying the shape of the NumPy arrays print(x_training_data.shape) print(y_training_data.shape) #Reshaping the NumPy array to meet TensorFlow standards x_training_data = np.reshape(x_training_data, (x_training_data.shape, x_training_data.shape, 1)) #Printing the new shape of x_training_data print(x_training_data.shape) #Importing our TensorFlow libraries from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense from tensorflow.keras.layers import LSTM from tensorflow.keras.layers import Dropout #Initializing our recurrent neural network rnn = Sequential() #Adding our first LSTM layer rnn.add(LSTM(units = 45, return_sequences = True, input_shape = (x_training_data.shape, 1))) #Perform some dropout regularization rnn.add(Dropout(0.2)) #Adding three more LSTM layers with dropout regularization for i in [True, True, False]: rnn.add(LSTM(units = 45, return_sequences = i)) rnn.add(Dropout(0.2)) #(Original code for the three additional LSTM layers) # rnn.add(LSTM(units = 45, return_sequences = True)) # rnn.add(Dropout(0.2)) # rnn.add(LSTM(units = 45, return_sequences = True)) # rnn.add(Dropout(0.2)) # rnn.add(LSTM(units = 45)) # rnn.add(Dropout(0.2)) #Adding our output layer rnn.add(Dense(units = 1)) #Compiling the recurrent neural network rnn.compile(optimizer = 'adam', loss = 'mean_squared_error') #Training the recurrent neural network rnn.fit(x_training_data, y_training_data, epochs = 100, batch_size = 32) #Import the test data set and transform it into a NumPy array test_data = pd.read_csv('FB_test_data.csv') test_data = test_data.iloc[:, 1].values #Make sure the test data's shape makes sense print(test_data.shape) #Plot the test data plt.plot(test_data) #Create unscaled training data and test data objects unscaled_training_data = pd.read_csv('FB_training_data.csv') unscaled_test_data = pd.read_csv('FB_test_data.csv') #Concatenate the unscaled data all_data = pd.concat((unscaled_x_training_data['Open'], unscaled_test_data['Open']), axis = 0) #Create our x_test_data object, which has each January day + the 40 prior days x_test_data = all_data[len(all_data) - len(test_data) - 40:].values x_test_data = np.reshape(x_test_data, (-1, 1)) #Scale the test data x_test_data = scaler.transform(x_test_data) #Grouping our test data final_x_test_data =  for i in range(40, len(x_test_data)): final_x_test_data.append(x_test_data[i-40:i, 0]) final_x_test_data = np.array(final_x_test_data) #Reshaping the NumPy array to meet TensorFlow standards final_x_test_data = np.reshape(final_x_test_data, (final_x_test_data.shape, final_x_test_data.shape, 1)) #Generating our predicted values predictions = rnn.predict(final_x_test_data) #Plotting our predicted values plt.clf() #This clears the old plot from our canvas plt.plot(predictions) #Unscaling the predicted values and re-plotting the data unscaled_predictions = scaler.inverse_transform(predictions) plt.clf() #This clears the first prediction plot from our canvas plt.plot(unscaled_predictions) #Plotting the predicted values against Facebook's actual stock price plt.plot(unscaled_predictions, color = '#135485', label = "Predictions") plt.plot(test_data, color = 'black', label = "Real Data") plt.title('Facebook Stock Price Predictions')
In this tutorial, you learned how to build and train a recurrent neural network.
Here is a brief summary of what you learned:
- How to apply feature scaling to a data set that a recurrent neural network will be trained on
- The role of
timestepsin training a recurrent neural network
- That TensorFlow primarily uses NumPy arrays as the data structure to train models with
- How to add
Dropoutlayers to a recurrent neural network
- Why dropout regularization is commonly used to avoid overfitting when training neural networks
- That the
Denselayer from TensorFlow is commonly used as the output layer of a recurrent neural network
- That the
compilationstep of building a neural network involves specifying its optimizer and its loss function
- How to make predictions using a recurrent neural network
- That predictions make using a neural network trained on scaled data must be unscaled to be interpretable by humans