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### Stock Market Prediction Using Multi-Layer Perceptrons With TensorFlow

[https://nicholastsmith.wordpress.com/2016/04/20/stock-market-prediction-using-multi-layer-perceptrons-with-tensorflow/]

In this post a multi-layer perceptron (MLP) class based on the TensorFlow library is discussed. The class is then applied to the problem of performing stock prediction given historical data. Note: This post is not meant to characterize how stock prediction is actually done; it is intended to demonstrate the TensorFlow library and MLPs. Update: See part 2 of this series for more examples of using python and TensorFlow for performing stock prediction. Update 2See a later post Visualizing Neural Network Performance on High-Dimensional Data for code to help visualize neural network learning and performance.

### Data Setup

The data used in this post was collected from finance.yahoo.com. The data consists of historical stock data from Yahoo Inc. over the period of the 12th of April 1996 to the 19th of April 2016. The data can be downloaded as a CSV file from the provided link. To pre-process the data for the neural network, first transform the dates into integer values using LibreOffice’s DATEVALUE function. A screen-shot of the transformed data can be seen as follows: Figure 1: Pre-Processing Data Using LibreOffice

For simplicity sake, the “High” value will be computed based on the “Date Value.” Thus, the goal is to create an MLP that takes as input a date in the form of an integer and returns a predicted high value of the Yahoo Inc. stock price for that day.

With the date values saved the spreadsheet, next the data is loaded into python. To improve the performance of the MLP, the data is first scaled so that both the input and output data have mean 0 and variance 1. This can be accomplished as follows (take note that “Date Value” is in column index 1 and “High” is in column index 4):

 123456789101112131415 import numpy as npfrom TFMLP import MLPRimport matplotlib.pyplot as mplfrom sklearn.preprocessing import scale pth = filePath + 'yahoostock.csv'A = np.loadtxt(pth, delimiter=",", skiprows=1, usecols=(1, 4))A = scale(A)#y is the dependent variabley = A[:, 1].reshape(-1, 1)#A contains the independent variableA = A[:, 0].reshape(-1, 1)#Plot the high value of the stock pricempl.plot(A[:, 0], y[:, 0])mpl.show()

The produced plot is as follows: Figure 2: Scaled Yahoo Stock Data

Next, an MLP is constructed and trained on the scaled data.

### Creating the MLP

The MLP class that will be used follows a simple interface similar to that of the python scikit-learn library. The source code is available here. The interface is as follows:

 12345678910111213141516 #Fit the MLP to the data#param A: numpy matrix where each row is a sample#param y: numpy matrix of target valuesdef fit(self, A, y): #Predict the output given the input (only run after calling fit)#param A: The input values for which to predict outputs#return: The predicted output values (one row per input sample)def predict(self, A): #Predicts the ouputs for input A and then computes the RMSE between#The predicted values and the actualy values#param A: The input values for which to predict outputs#param y: The actual target values#return: The RMSEdef score(self, A, y):

The first step is to create an MLPR object. This can be done as follows:

 123456789 #Number of neurons in the input layeri = 1#Number of neurons in the output layero = 1#Number of neurons in the hidden layersh = 32#The list of layer sizeslayers = [i, h, h, h, h, h, h, h, h, h, o]mlpr = MLPR(layers, maxItr = 1000, tol = 0.40, reg = 0.001, verbose = True)

With this code, an MLPR object will be initialized with the given layer sizes, a training iteration limit of 1000, an error tolerance of 0.40 (for the RMSE), regularization weight of 0.001, and verbose output enabled. The source code for the MLPR class shows how this is accomplished.

 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172 #Create the MLP variables for TF graph#_X: The input matrix#_W: The weight matrices#_B: The bias vectors#_AF: The activation functiondef _CreateMLP(_X, _W, _B, _AF):    n = len(_W)    for i in range(n - 1):        _X = _AF(tf.matmul(_X, _W[i]) + _B[i])    return tf.matmul(_X, _W[n - 1]) + _B[n - 1] #Add L2 regularizers for the weight and bias matrices#_W: The weight matrices#_B: The bias matrices#return: tensorflow variable representing l2 regularization costdef _CreateL2Reg(_W, _B):    n = len(_W)    regularizers = tf.nn.l2_loss(_W) + tf.nn.l2_loss(_B)    for i in range(1, n):        regularizers += tf.nn.l2_loss(_W[i]) + tf.nn.l2_loss(_B[i])    return regularizers #Create weight and bias vectors for an MLP#layers: The number of neurons in each layer (including input and output)#return: A tuple of lists of the weight and bias matrices respectivelydef _CreateVars(layers):    weight = []    bias = []    n = len(layers)    for i in range(n - 1):        #Fan-in for layer; used as standard dev        lyrstd = np.sqrt(1.0 / layers[i])        curW = tf.Variable(tf.random_normal([layers[i], layers[i + 1]], stddev = lyrstd))        weight.append(curW)        curB = tf.Variable(tf.random_normal([layers[i + 1]], stddev = lyrstd))        bias.append(curB)    return (weight, bias) ... #The constructor#param layers: A list of layer sizes#param actvFn: The activation function to use: 'tanh', 'sig', or 'relu'#param learnRate: The learning rate parameter#param decay: The decay parameter#param maxItr: Maximum number of training iterations#param tol: Maximum error tolerated#param batchSize: Size of training batches to use (use all if None)#param verbose: Print training information#param reg: Regularization weightdef __init__(self, layers, actvFn = 'tanh', learnRate = 0.001, decay = 0.9, maxItr = 2000,             tol = 1e-2, batchSize = None, verbose = False, reg = 0.001):    #Parameters    self.tol = tol    self.mItr = maxItr    self.vrbse = verbose    self.batSz = batchSize    #Input size    self.x = tf.placeholder("float", [None, layers])    #Output size    self.y = tf.placeholder("float", [None, layers[-1]])    #Setup the weight and bias variables    weight, bias = _CreateVars(layers)    #Create the tensorflow MLP model    self.pred = _CreateMLP(self.x, weight, bias, _GetActvFn(actvFn))    #Use L2 as the cost function    self.loss = tf.reduce_sum(tf.nn.l2_loss(self.pred - self.y))    #Use regularization to prevent over-fitting    if(reg is not None):        self.loss += _CreateL2Reg(weight, bias) * reg    #Use ADAM method to minimize the loss function    self.optmzr = tf.train.AdamOptimizer(learning_rate=learnRate).minimize(self.loss)

As seen above, tensorflow placeholder variables are created for the input (x) and the output (y). Next, tensorflow variables for the weight matrices and bias vectors are created using the _CreateVars() function. The weights are initialized as random normal numbers distributed as $\mathcal{N}(0, 1/\sqrt{f})$, where $f$ is the fan-in to the layer.

Next, the MLP model is constructed using its definition as discussed in an earlier post. After that, the loss and regularization functions are defined as the L2 loss. Regularization penalizes larger values in the weight matrices and bias vectors to help prevent over-fitting. Lastly, tensorflow’s AdamOptimizer is employed as the training optimizer with the goal of minimizing the loss function. Note that at this stage the learning has not yet been done, only the tensorflow graph has been initialized with the necessary components of the MLP.

Next, the MLP is trained with the Yahoo stock data. A hold-out period is used to assess how well the MLP is performing. This can be accomplished as follows:

 12345 #Length of the hold-out periodnDays = 5n = len(A)#Learn the datamlpr.fit(A[0:(n-nDays)], y[0:(n-nDays)])

When the fit function is called, the actual training process begins. First, a tensorflow session must be created and all variables defined in the constructor must be initialized. Then, training iterations are performed up to the iteration limit provided, the weights are updated, and the error is recorded. The feed_dict parameter specifies the values of our inputs (x) and outputs (y). If the error falls below the tolerance level, training is completed, otherwise the maximum number of iterations is exhausted.

 123456789101112131415161718192021222324 #Fit the MLP to the data#param A: numpy matrix where each row is a sample#param y: numpy matrix of target valuesdef fit(self, A, y):    m = len(A)    #Start the tensorflow session and initializer    #all variables    self.sess = tf.Session()    init = tf.initialize_all_variables()    self.sess.run(init)    #Begin training    for i in range(self.mItr):        #Batch mode or all at once        if(self.batSz is None):            self.sess.run(self.optmzr, feed_dict={self.x:A, self.y:y})        else:            for j in range(0, m, self.batSz):                batA, batY = _NextBatch(A, y, j, self.batSz)                self.sess.run(self.optmzr, feed_dict={self.x:batA, self.y:batY})        err = np.sqrt(self.sess.run(self.loss, feed_dict={self.x:A, self.y:y}) * 2.0 / m)        if(self.vrbse):            print("Iter " + str(i + 1) + ": " + str(err))        if(err < self.tol):            break

With the MLP network trained, prediction can be performed and the results plotted using matplotlib.

 123456 #Begin predictionyHat = mlpr.predict(A)#Plot the resultsmpl.plot(A, y, c='#b0403f')mpl.plot(A, yHat, c='#5aa9ab')mpl.show() Figure 3: Actual vs Predicted Stock Data

As can be seen, the MLP smooths the original stock data. The amount of smoothing is dependent upon the MLP parameters including the number layers, the size of the layers, the error tolerance, and the amount of regularization. In practice it requires a lot of parameter tuning in order to get decent results from a neural network.