From 56041cc44e88267159f2a1ac37a1b8969824ed33 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Tue, 26 Oct 2021 11:23:26 +0200 Subject: [PATCH] week 43 --- doc/pub/week43/html/._week43-bs000.html | 39 ++- doc/pub/week43/html/._week43-bs001.html | 42 ++- doc/pub/week43/html/._week43-bs002.html | 45 ++- doc/pub/week43/html/._week43-bs003.html | 55 ++- doc/pub/week43/html/._week43-bs004.html | 58 ++- doc/pub/week43/html/._week43-bs005.html | 122 +++---- doc/pub/week43/html/._week43-bs006.html | 74 ++-- doc/pub/week43/html/._week43-bs007.html | 207 +++++------ doc/pub/week43/html/._week43-bs008.html | 157 +++------ doc/pub/week43/html/._week43-bs009.html | 187 +++++----- doc/pub/week43/html/._week43-bs010.html | 245 ++++--------- doc/pub/week43/html/._week43-bs011.html | 237 +++++++------ doc/pub/week43/html/._week43-bs012.html | 351 ++++++++++++------- doc/pub/week43/html/week43-bs.html | 39 ++- doc/pub/week43/html/week43-reveal.html | 65 +++- doc/pub/week43/html/week43-solarized.html | 71 +++- doc/pub/week43/html/week43.html | 71 +++- doc/pub/week43/ipynb/ipynb-week43-src.tar.gz | Bin 191 -> 191 bytes doc/pub/week43/ipynb/week43.ipynb | 50 ++- doc/src/week43/week43.do.txt | 48 ++- 20 files changed, 1134 insertions(+), 1029 deletions(-) diff --git a/doc/pub/week43/html/._week43-bs000.html b/doc/pub/week43/html/._week43-bs000.html index f01dbe3ff..ed1c13869 100644 --- a/doc/pub/week43/html/._week43-bs000.html +++ b/doc/pub/week43/html/._week43-bs000.html @@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source - + -Week 43: Convolutional Neural Networks and Recurrent Neural Networks +Week 43: Deep Learning: Recurrent Neural Networks and other methods @@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source - Week 43: Convolutional Neural Networks and Recurrent Neural Networks + Week 43: Deep Learning: Recurrent Neural Networks and other methods
@@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -109,7 +116,7 @@ end of tocinfo -->
-

Week 43: Convolutional Neural Networks and Recurrent Neural Networks

+

Week 43: Deep Learning: Recurrent Neural Networks and other methods

@@ -125,7 +132,7 @@ end of tocinfo -->

[2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University

-

Oct 24, 2021

+

Oct 26, 2021


@@ -149,7 +156,7 @@ end of tocinfo -->

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    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -110,7 +117,7 @@ end of tocinfo -->
    • Thursday: Summary of Convolutional Neural Networks from week 42 and Recurrent Neural Networks
      • -
    • Friday: Recurrent Neural Networks and other Deep Learning methods
      • +
    • Friday: Recurrent Neural Networks and other Deep Learning methods such as Generalized Adversarial Neural Networks
    @@ -132,10 +139,9 @@ end of tocinfo -->

    - -
  • CS231 at Stanford Lecture
    • @@ -156,6 +162,8 @@ end of tocinfo -->
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    • diff --git a/doc/pub/week43/html/._week43-bs002.html b/doc/pub/week43/html/._week43-bs002.html index 10f85bc53..8cc2d2c28 100644 --- a/doc/pub/week43/html/._week43-bs002.html +++ b/doc/pub/week43/html/._week43-bs002.html @@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source - + -Week 43: Convolutional Neural Networks and Recurrent Neural Networks +Week 43: Deep Learning: Recurrent Neural Networks and other methods @@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source - Week 43: Convolutional Neural Networks and Recurrent Neural Networks + Week 43: Deep Learning: Recurrent Neural Networks and other methods
    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,12 +113,13 @@ end of tocinfo --> -

    Summary on CNNs

    +

    Reading Recommendations

    -

    -Material to be added +

    -

    diff --git a/doc/pub/week43/html/._week43-bs003.html b/doc/pub/week43/html/._week43-bs003.html index 8793a06ae..be2e9501c 100644 --- a/doc/pub/week43/html/._week43-bs003.html +++ b/doc/pub/week43/html/._week43-bs003.html @@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source - + -Week 43: Convolutional Neural Networks and Recurrent Neural Networks +Week 43: Deep Learning: Recurrent Neural Networks and other methods @@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source - Week 43: Convolutional Neural Networks and Recurrent Neural Networks + Week 43: Deep Learning: Recurrent Neural Networks and other methods
    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,27 +113,13 @@ end of tocinfo --> -

    Recurrent neural networks: Overarching view

    +

    Summary on Deep Learning Methods

    -Till now our focus has been, including convolutional neural networks -as well, on feedforward neural networks. The output or the activations -flow only in one direction, from the input layer to the output layer. +We have studied fully connected neural networks (also called artifical nueral networks) and convolutional neural networks (CNNs).

    -A recurrent neural network (RNN) looks very much like a feedforward -neural network, except that it also has connections pointing -backward. - -

    -RNNs are used to analyze time series data such as stock prices, and -tell you when to buy or sell. In autonomous driving systems, they can -anticipate car trajectories and help avoid accidents. More generally, -they can work on sequences of arbitrary lengths, rather than on -fixed-sized inputs like all the nets we have discussed so far. For -example, they can take sentences, documents, or audio samples as -input, making them extremely useful for natural language processing -systems such as automatic translation and speech-to-text. +The first type of deep learning networks work very well on homogeneous and structured input data while CCNs are normally tailored to recognizing images.

    @@ -144,6 +137,8 @@ systems such as automatic translation and speech-to-text.

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    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,10 +113,29 @@ end of tocinfo --> -

    Set up of an RNN

    +

    CNNs in brief

    -Text to come. +In summary: + +

    + +For more material on convolutional networks, we strongly recommend +the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231 which is taught at Stanford University (consistently ranked as one of the top computer science programs in the world). Michael Nielsen's book is a must read, in particular chapter 6 which deals with CNNs. + +

    +However, both standard feed forwards networks and CNNs perform well on data with unknown length. + +

    +This is where recurrent nueral networks (RNNs) come to our rescue.

    @@ -127,6 +153,8 @@ Text to come.

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    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,80 +113,31 @@ end of tocinfo --> -

    A simple example

    +

    Recurrent neural networks: Overarching view

    +Till now our focus has been, including convolutional neural networks +as well, on feedforward neural networks. The output or the activations +flow only in one direction, from the input layer to the output layer. - -

    # Start importing packages
-import pandas as pd
-import numpy as np
-import matplotlib.pyplot as plt
-import tensorflow as tf
-from tensorflow.keras import datasets, layers, models
-from tensorflow.keras.layers import Input
-from tensorflow.keras.models import Model, Sequential 
-from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU
-from tensorflow.keras import optimizers     
-from tensorflow.keras import regularizers           
-from tensorflow.keras.utils import to_categorical 
+
    
+A recurrent neural network (RNN) looks very much like a feedforward
+neural network, except that it also has connections pointing
+backward.
 
+
    
+RNNs are used to analyze time series data such as stock prices, and
+tell you when to buy or sell. In autonomous driving systems, they can
+anticipate car trajectories and help avoid accidents. More generally,
+they can work on sequences of arbitrary lengths, rather than on
+fixed-sized inputs like all the nets we have discussed so far. For
+example, they can take sentences, documents, or audio samples as
+input, making them extremely useful for natural language processing
+systems such as automatic translation and speech-to-text.
 
+
    
+RNNs are also used in "text classification":"Text Classification Algorithms: A Survey"
 
-# convert into dataset matrix
-def convertToMatrix(data, step):
- X, Y =[], []
- for i in range(len(data)-step):
-  d=i+step  
-  X.append(data[i:d,])
-  Y.append(data[d,])
- return np.array(X), np.array(Y)
-
-step = 4
-N = 1000    
-Tp = 800    
-
-t=np.arange(0,N)
-x=np.sin(0.02*t)+2*np.random.rand(N)
-df = pd.DataFrame(x)
-df.head()
-
-plt.plot(df)
-plt.show()
-
-values=df.values
-train,test = values[0:Tp,:], values[Tp:N,:]
-
-# add step elements into train and test
-test = np.append(test,np.repeat(test[-1,],step))
-train = np.append(train,np.repeat(train[-1,],step))
- 
-trainX,trainY =convertToMatrix(train,step)
-testX,testY =convertToMatrix(test,step)
-trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
-testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))
-
-model = Sequential()
-model.add(SimpleRNN(units=32, input_shape=(1,step), activation="relu"))
-model.add(Dense(8, activation="relu")) 
-model.add(Dense(1))
-model.compile(loss='mean_squared_error', optimizer='rmsprop')
-model.summary()
-
-model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2)
-trainPredict = model.predict(trainX)
-testPredict= model.predict(testX)
-predicted=np.concatenate((trainPredict,testPredict),axis=0)
-
-trainScore = model.evaluate(trainX, trainY, verbose=0)
-print(trainScore)
-
-index = df.index.values
-plt.plot(index,df)
-plt.plot(index,predicted)
-plt.axvline(df.index[Tp], c="r")
-plt.show()
-

    @@ -196,6 +154,8 @@ plt.show()

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    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,45 +113,8 @@ end of tocinfo --> -

    An extrapolation example

    +

    Set up of an RNN

    -

    -The following code provides an example of how recurrent neural -networks can be used to extrapolate to unknown values of physics data -sets. Specifically, the data sets used in this program come from -a quantum mechanical many-body calculation of energies as functions of the number of particles. - -

    - - -

    # For matrices and calculations
-import numpy as np
-# For machine learning (backend for keras)
-import tensorflow as tf
-# User-friendly machine learning library
-# Front end for TensorFlow
-import tensorflow.keras
-# Different methods from Keras needed to create an RNN
-# This is not necessary but it shortened function calls 
-# that need to be used in the code.
-from tensorflow.keras import datasets, layers, models
-from tensorflow.keras.layers import Input
-from tensorflow.keras import regularizers
-from tensorflow.keras.models import Model, Sequential
-from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU
-# For timing the code
-from timeit import default_timer as timer
-# For plotting
-import matplotlib.pyplot as plt
-
-
-# The data set
-datatype='VaryDimension'
-X_tot = np.arange(2, 42, 2)
-y_tot = np.array([-0.03077640549, -0.08336233266, -0.1446729567, -0.2116753732, -0.2830637392, -0.3581341341, -0.436462435, -0.5177783846,
-	-0.6019067271, -0.6887363571, -0.7782028952, -0.8702784034, -0.9649652536, -1.062292565, -1.16231451, 
-	-1.265109911, -1.370782966, -1.479465113, -1.591317992, -1.70653767])
-

    @@ -161,6 +131,8 @@ y_tot = np.9

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    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,119 +113,79 @@ end of tocinfo --> -

    Formatting the Data

    - -

    -The way the recurrent neural networks are trained in this program -differs from how machine learning algorithms are usually trained. -Typically a machine learning algorithm is trained by learning the -relationship between the x data and the y data. In this program, the -recurrent neural network will be trained to recognize the relationship -in a sequence of y values. This is type of data formatting is -typically used time series forcasting, but it can also be used in any -extrapolation (time series forecasting is just a specific type of -extrapolation along the time axis). This method of data formatting -does not use the x data and assumes that the y data are evenly spaced. - -

    -For a standard machine learning algorithm, the training data has the -form of (x,y) so the machine learning algorithm learns to assiciate a -y value with a given x value. This is useful when the test data has x -values within the same range as the training data. However, for this -application, the x values of the test data are outside of the x values -of the training data and the traditional method of training a machine -learning algorithm does not work as well. For this reason, the -recurrent neural network is trained on sequences of y values of the -form ((y1, y2), y3), so that the network is concerned with learning -the pattern of the y data and not the relation between the x and y -data. As long as the pattern of y data outside of the training region -stays relatively stable compared to what was inside the training -region, this method of training can produce accurate extrapolations to -y values far removed from the training data set. - -

    - - - - - - +

    A simple example

    -

    # FORMAT_DATA
-def format_data(data, length_of_sequence = 2):  
-    """
-        Inputs:
-            data(a numpy array): the data that will be the inputs to the recurrent neural
-                network
-            length_of_sequence (an int): the number of elements in one iteration of the
-                sequence patter.  For a function approximator use length_of_sequence = 2.
-        Returns:
-            rnn_input (a 3D numpy array): the input data for the recurrent neural network.  Its
-                dimensions are length of data - length of sequence, length of sequence, 
-                dimnsion of data
-            rnn_output (a numpy array): the training data for the neural network
-        Formats data to be used in a recurrent neural network.
-    """
-
-    X, Y = [], []
-    for i in range(len(data)-length_of_sequence):
-        # Get the next length_of_sequence elements
-        a = data[i:i+length_of_sequence]
-        # Get the element that immediately follows that
-        b = data[i+length_of_sequence]
-        # Reshape so that each data point is contained in its own array
-        a = np.reshape (a, (len(a), 1))
-        X.append(a)
-        Y.append(b)
-    rnn_input = np.array(X)
-    rnn_output = np.array(Y)
-
-    return rnn_input, rnn_output
+
    # Start importing packages
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+import tensorflow as tf
+from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Model, Sequential 
+from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU
+from tensorflow.keras import optimizers     
+from tensorflow.keras import regularizers           
+from tensorflow.keras.utils import to_categorical 
 
 
-# ## Defining the Recurrent Neural Network Using Keras
-# 
-# The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer.
 
-def rnn(length_of_sequences, batch_size = None, stateful = False):
-    """
-        Inputs:
-            length_of_sequences (an int): the number of y values in "x data".  This is determined
-                when the data is formatted
-            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
-            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
-        Returns:
-            model (a Keras model): The recurrent neural network that is built and compiled by this
-                method
-        Builds and compiles a recurrent neural network with one hidden layer and returns the model.
-    """
-    # Number of neurons in the input and output layers
-    in_out_neurons = 1
-    # Number of neurons in the hidden layer
-    hidden_neurons = 200
-    # Define the input layer
-    inp = Input(batch_shape=(batch_size, 
-                length_of_sequences, 
-                in_out_neurons))  
-    # Define the hidden layer as a simple RNN layer with a set number of neurons and add it to 
-    # the network immediately after the input layer
-    rnn = SimpleRNN(hidden_neurons, 
-                    return_sequences=False,
-                    stateful = stateful,
-                    name="RNN")(inp)
-    # Define the output layer as a dense neural network layer (standard neural network layer)
-    #and add it to the network immediately after the hidden layer.
-    dens = Dense(in_out_neurons,name="dense")(rnn)
-    # Create the machine learning model starting with the input layer and ending with the 
-    # output layer
-    model = Model(inputs=[inp],outputs=[dens])
-    # Compile the machine learning model using the mean squared error function as the loss 
-    # function and an Adams optimizer.
-    model.compile(loss="mean_squared_error", optimizer="adam")  
-    return model
+# convert into dataset matrix
+def convertToMatrix(data, step):
+ X, Y =[], []
+ for i in range(len(data)-step):
+  d=i+step  
+  X.append(data[i:d,])
+  Y.append(data[d,])
+ return np.array(X), np.array(Y)
+
+step = 4
+N = 1000    
+Tp = 800    
+
+t=np.arange(0,N)
+x=np.sin(0.02*t)+2*np.random.rand(N)
+df = pd.DataFrame(x)
+df.head()
+
+plt.plot(df)
+plt.show()
+
+values=df.values
+train,test = values[0:Tp,:], values[Tp:N,:]
+
+# add step elements into train and test
+test = np.append(test,np.repeat(test[-1,],step))
+train = np.append(train,np.repeat(train[-1,],step))
+ 
+trainX,trainY =convertToMatrix(train,step)
+testX,testY =convertToMatrix(test,step)
+trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
+testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))
+
+model = Sequential()
+model.add(SimpleRNN(units=32, input_shape=(1,step), activation="relu"))
+model.add(Dense(8, activation="relu")) 
+model.add(Dense(1))
+model.compile(loss='mean_squared_error', optimizer='rmsprop')
+model.summary()
+
+model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2)
+trainPredict = model.predict(trainX)
+testPredict= model.predict(testX)
+predicted=np.concatenate((trainPredict,testPredict),axis=0)
+
+trainScore = model.evaluate(trainX, trainY, verbose=0)
+print(trainScore)
+
+index = df.index.values
+plt.plot(index,df)
+plt.plot(index,predicted)
+plt.axvline(df.index[Tp], c="r")
+plt.show()
 
    
 
    
 
    
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diff --git a/doc/pub/week43/html/._week43-bs008.html b/doc/pub/week43/html/._week43-bs008.html
index 2b61d4365..fa21da2ae 100644
--- a/doc/pub/week43/html/._week43-bs008.html
+++ b/doc/pub/week43/html/._week43-bs008.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source
 
       
       
     
-    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+    Week 43: Deep Learning: Recurrent Neural Networks and other methods
    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,102 +113,44 @@ end of tocinfo --> -

    Predicting New Points With A Trained Recurrent Neural Network

    +

    An extrapolation example

    + +

    +The following code provides an example of how recurrent neural +networks can be used to extrapolate to unknown values of physics data +sets. Specifically, the data sets used in this program come from +a quantum mechanical many-body calculation of energies as functions of the number of particles.

    -

    def test_rnn (x1, y_test, plot_min, plot_max):
-    """
-        Inputs:
-            x1 (a list or numpy array): The complete x component of the data set
-            y_test (a list or numpy array): The complete y component of the data set
-            plot_min (an int or float): the smallest x value used in the training data
-            plot_max (an int or float): the largest x valye used in the training data
-        Returns:
-            None.
-        Uses a trained recurrent neural network model to predict future points in the 
-        series.  Computes the MSE of the predicted data set from the true data set, saves
-        the predicted data set to a csv file, and plots the predicted and true data sets w
-        while also displaying the data range used for training.
-    """
-    # Add the training data as the first dim points in the predicted data array as these
-    # are known values.
-    y_pred = y_test[:dim].tolist()
-    # Generate the first input to the trained recurrent neural network using the last two 
-    # points of the training data.  Based on how the network was trained this means that it
-    # will predict the first point in the data set after the training data.  All of the 
-    # brackets are necessary for Tensorflow.
-    next_input = np.array([[[y_test[dim-2]], [y_test[dim-1]]]])
-    # Save the very last point in the training data set.  This will be used later.
-    last = [y_test[dim-1]]
-
-    # Iterate until the complete data set is created.
-    for i in range (dim, len(y_test)):
-        # Predict the next point in the data set using the previous two points.
-        next = model.predict(next_input)
-        # Append just the number of the predicted data set
-        y_pred.append(next[0][0])
-        # Create the input that will be used to predict the next data point in the data set.
-        next_input = np.array([[last, next[0]]], dtype=np.float64)
-        last = next
-
-    # Print the mean squared error between the known data set and the predicted data set.
-    print('MSE: ', np.square(np.subtract(y_test, y_pred)).mean())
-    # Save the predicted data set as a csv file for later use
-    name = datatype + 'Predicted'+str(dim)+'.csv'
-    np.savetxt(name, y_pred, delimiter=',')
-    # Plot the known data set and the predicted data set.  The red box represents the region that was used
-    # for the training data.
-    fig, ax = plt.subplots()
-    ax.plot(x1, y_test, label="true", linewidth=3)
-    ax.plot(x1, y_pred, 'g-.',label="predicted", linewidth=4)
-    ax.legend()
-    # Created a red region to represent the points used in the training data.
-    ax.axvspan(plot_min, plot_max, alpha=0.25, color='red')
-    plt.show()
-
-# Check to make sure the data set is complete
-assert len(X_tot) == len(y_tot)
-
-# This is the number of points that will be used in as the training data
-dim=12
-
-# Separate the training data from the whole data set
-X_train = X_tot[:dim]
-y_train = y_tot[:dim]
+
    # For matrices and calculations
+import numpy as np
+# For machine learning (backend for keras)
+import tensorflow as tf
+# User-friendly machine learning library
+# Front end for TensorFlow
+import tensorflow.keras
+# Different methods from Keras needed to create an RNN
+# This is not necessary but it shortened function calls 
+# that need to be used in the code.
+from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras import regularizers
+from tensorflow.keras.models import Model, Sequential
+from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU
+# For timing the code
+from timeit import default_timer as timer
+# For plotting
+import matplotlib.pyplot as plt
 
 
-# Generate the training data for the RNN, using a sequence of 2
-rnn_input, rnn_training = format_data(y_train, 2)
-
-
-# Create a recurrent neural network in Keras and produce a summary of the 
-# machine learning model
-model = rnn(length_of_sequences = rnn_input.shape[1])
-model.summary()
-
-# Start the timer.  Want to time training+testing
-start = timer()
-# Fit the model using the training data genenerated above using 150 training iterations and a 5%
-# validation split.  Setting verbose to True prints information about each training iteration.
-hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
-                 verbose=True,validation_split=0.05)
-
-for label in ["loss","val_loss"]:
-    plt.plot(hist.history[label],label=label)
-
-plt.ylabel("loss")
-plt.xlabel("epoch")
-plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
-plt.legend()
-plt.show()
-
-# Use the trained neural network to predict more points of the data set
-test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
-# Stop the timer and calculate the total time needed.
-end = timer()
-print('Time: ', end-start)
+# The data set
+datatype='VaryDimension'
+X_tot = np.arange(2, 42, 2)
+y_tot = np.array([-0.03077640549, -0.08336233266, -0.1446729567, -0.2116753732, -0.2830637392, -0.3581341341, -0.436462435, -0.5177783846,
+	-0.6019067271, -0.6887363571, -0.7782028952, -0.8702784034, -0.9649652536, -1.062292565, -1.16231451, 
+	-1.265109911, -1.370782966, -1.479465113, -1.591317992, -1.70653767])
 
    
 
    
 
    
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diff --git a/doc/pub/week43/html/._week43-bs009.html b/doc/pub/week43/html/._week43-bs009.html
index 52b5bd2c7..e33c84714 100644
--- a/doc/pub/week43/html/._week43-bs009.html
+++ b/doc/pub/week43/html/._week43-bs009.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source
 
       
       
     
-    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+    Week 43: Deep Learning: Recurrent Neural Networks and other methods
    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,24 +113,84 @@ end of tocinfo --> -

    Other Things to Try

    +

    Formatting the Data

    -Changing the size of the recurrent neural network and its parameters -can drastically change the results you get from the model. The below -code takes the simple recurrent neural network from above and adds a -second hidden layer, changes the number of neurons in the hidden -layer, and explicitly declares the activation function of the hidden -layers to be a sigmoid function. The loss function and optimizer can -also be changed but are kept the same as the above network. These -parameters can be tuned to provide the optimal result from the -network. For some ideas on how to improve the performance of a -recurrent neural network. +The way the recurrent neural networks are trained in this program +differs from how machine learning algorithms are usually trained. +Typically a machine learning algorithm is trained by learning the +relationship between the x data and the y data. In this program, the +recurrent neural network will be trained to recognize the relationship +in a sequence of y values. This is type of data formatting is +typically used time series forcasting, but it can also be used in any +extrapolation (time series forecasting is just a specific type of +extrapolation along the time axis). This method of data formatting +does not use the x data and assumes that the y data are evenly spaced. + +

    +For a standard machine learning algorithm, the training data has the +form of (x,y) so the machine learning algorithm learns to assiciate a +y value with a given x value. This is useful when the test data has x +values within the same range as the training data. However, for this +application, the x values of the test data are outside of the x values +of the training data and the traditional method of training a machine +learning algorithm does not work as well. For this reason, the +recurrent neural network is trained on sequences of y values of the +form ((y1, y2), y3), so that the network is concerned with learning +the pattern of the y data and not the relation between the x and y +data. As long as the pattern of y data outside of the training region +stays relatively stable compared to what was inside the training +region, this method of training can produce accurate extrapolations to +y values far removed from the training data set. + +

    + + + + + +

    -

    def rnn_2layers(length_of_sequences, batch_size = None, stateful = False):
+
    # FORMAT_DATA
+def format_data(data, length_of_sequence = 2):  
+    """
+        Inputs:
+            data(a numpy array): the data that will be the inputs to the recurrent neural
+                network
+            length_of_sequence (an int): the number of elements in one iteration of the
+                sequence patter.  For a function approximator use length_of_sequence = 2.
+        Returns:
+            rnn_input (a 3D numpy array): the input data for the recurrent neural network.  Its
+                dimensions are length of data - length of sequence, length of sequence, 
+                dimnsion of data
+            rnn_output (a numpy array): the training data for the neural network
+        Formats data to be used in a recurrent neural network.
+    """
+
+    X, Y = [], []
+    for i in range(len(data)-length_of_sequence):
+        # Get the next length_of_sequence elements
+        a = data[i:i+length_of_sequence]
+        # Get the element that immediately follows that
+        b = data[i+length_of_sequence]
+        # Reshape so that each data point is contained in its own array
+        a = np.reshape (a, (len(a), 1))
+        X.append(a)
+        Y.append(b)
+    rnn_input = np.array(X)
+    rnn_output = np.array(Y)
+
+    return rnn_input, rnn_output
+
+
+# ## Defining the Recurrent Neural Network Using Keras
+# 
+# The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer.
+
+def rnn(length_of_sequences, batch_size = None, stateful = False):
     """
         Inputs:
             length_of_sequences (an int): the number of y values in "x data".  This is determined
@@ -133,29 +200,25 @@ network.  For some ideas on how to improve the performance of a
         Returns:
             model (a Keras model): The recurrent neural network that is built and compiled by this
                 method
-        Builds and compiles a recurrent neural network with two hidden layers and returns the model.
+        Builds and compiles a recurrent neural network with one hidden layer and returns the model.
     """
     # Number of neurons in the input and output layers
     in_out_neurons = 1
-    # Number of neurons in the hidden layer, increased from the first network
-    hidden_neurons = 500
+    # Number of neurons in the hidden layer
+    hidden_neurons = 200
     # Define the input layer
     inp = Input(batch_shape=(batch_size, 
                 length_of_sequences, 
                 in_out_neurons))  
-    # Create two hidden layers instead of one hidden layer.  Explicitly set the activation
-    # function to be the sigmoid function (the default value is hyperbolic tangent)
-    rnn1 = SimpleRNN(hidden_neurons, 
-                    return_sequences=True,  # This needs to be True if another hidden layer is to follow
-                    stateful = stateful, activation = 'sigmoid',
-                    name="RNN1")(inp)
-    rnn2 = SimpleRNN(hidden_neurons, 
-                    return_sequences=False, activation = 'sigmoid',
+    # Define the hidden layer as a simple RNN layer with a set number of neurons and add it to 
+    # the network immediately after the input layer
+    rnn = SimpleRNN(hidden_neurons, 
+                    return_sequences=False,
                     stateful = stateful,
-                    name="RNN2")(rnn1)
+                    name="RNN")(inp)
     # Define the output layer as a dense neural network layer (standard neural network layer)
     #and add it to the network immediately after the hidden layer.
-    dens = Dense(in_out_neurons,name="dense")(rnn2)
+    dens = Dense(in_out_neurons,name="dense")(rnn)
     # Create the machine learning model starting with the input layer and ending with the 
     # output layer
     model = Model(inputs=[inp],outputs=[dens])
@@ -163,52 +226,6 @@ network.  For some ideas on how to improve the performance of a
     # function and an Adams optimizer.
     model.compile(loss="mean_squared_error", optimizer="adam")  
     return model
-
-# Check to make sure the data set is complete
-assert len(X_tot) == len(y_tot)
-
-# This is the number of points that will be used in as the training data
-dim=12
-
-# Separate the training data from the whole data set
-X_train = X_tot[:dim]
-y_train = y_tot[:dim]
-
-
-# Generate the training data for the RNN, using a sequence of 2
-rnn_input, rnn_training = format_data(y_train, 2)
-
-
-# Create a recurrent neural network in Keras and produce a summary of the 
-# machine learning model
-model = rnn_2layers(length_of_sequences = 2)
-model.summary()
-
-# Start the timer.  Want to time training+testing
-start = timer()
-# Fit the model using the training data genenerated above using 150 training iterations and a 5%
-# validation split.  Setting verbose to True prints information about each training iteration.
-hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
-                 verbose=True,validation_split=0.05)
-
-
-# This section plots the training loss and the validation loss as a function of training iteration.
-# This is not required for analyzing the couple cluster data but can help determine if the network is
-# being overtrained.
-for label in ["loss","val_loss"]:
-    plt.plot(hist.history[label],label=label)
-
-plt.ylabel("loss")
-plt.xlabel("epoch")
-plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
-plt.legend()
-plt.show()
-
-# Use the trained neural network to predict more points of the data set
-test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
-# Stop the timer and calculate the total time needed.
-end = timer()
-print('Time: ', end-start)
 
    
 
    
 
    
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diff --git a/doc/pub/week43/html/._week43-bs010.html b/doc/pub/week43/html/._week43-bs010.html
index e90043c62..e8f6afc19 100644
--- a/doc/pub/week43/html/._week43-bs010.html
+++ b/doc/pub/week43/html/._week43-bs010.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source
 
       
       
     
-    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+    Week 43: Deep Learning: Recurrent Neural Networks and other methods
    @@ -82,15 +87,17 @@ end of tocinfo --> Contents @@ -106,105 +113,60 @@ end of tocinfo --> -

    Other Types of Recurrent Neural Networks

    - -

    -Besides a simple recurrent neural network layer, there are two other -commonly used types of recurrent neural network layers: Long Short -Term Memory (LSTM) and Gated Recurrent Unit (GRU). For a short -introduction to these layers see https://medium.com/mindboard/lstm-vs-gru-experimental-comparison-955820c21e8b -and https://medium.com/mindboard/lstm-vs-gru-experimental-comparison-955820c21e8b. - -

    -The first network created below is similar to the previous network, -but it replaces the SimpleRNN layers with LSTM layers. The second -network below has two hidden layers made up of GRUs, which are -preceeded by two dense (feeddorward) neural network layers. These -dense layers "preprocess" the data before it reaches the recurrent -layers. This architecture has been shown to improve the performance -of recurrent neural networks (see the link above and also -https://arxiv.org/pdf/1807.02857.pdf. +

    Predicting New Points With A Trained Recurrent Neural Network

    -

    def lstm_2layers(length_of_sequences, batch_size = None, stateful = False):
+
    def test_rnn (x1, y_test, plot_min, plot_max):
     """
         Inputs:
-            length_of_sequences (an int): the number of y values in "x data".  This is determined
-                when the data is formatted
-            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
-            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+            x1 (a list or numpy array): The complete x component of the data set
+            y_test (a list or numpy array): The complete y component of the data set
+            plot_min (an int or float): the smallest x value used in the training data
+            plot_max (an int or float): the largest x valye used in the training data
         Returns:
-            model (a Keras model): The recurrent neural network that is built and compiled by this
-                method
-        Builds and compiles a recurrent neural network with two LSTM hidden layers and returns the model.
+            None.
+        Uses a trained recurrent neural network model to predict future points in the 
+        series.  Computes the MSE of the predicted data set from the true data set, saves
+        the predicted data set to a csv file, and plots the predicted and true data sets w
+        while also displaying the data range used for training.
     """
-    # Number of neurons on the input/output layer and the number of neurons in the hidden layer
-    in_out_neurons = 1
-    hidden_neurons = 250
-    # Input Layer
-    inp = Input(batch_shape=(batch_size, 
-                length_of_sequences, 
-                in_out_neurons)) 
-    # Hidden layers (in this case they are LSTM layers instead if SimpleRNN layers)
-    rnn= LSTM(hidden_neurons, 
-                    return_sequences=True,
-                    stateful = stateful,
-                    name="RNN", use_bias=True, activation='tanh')(inp)
-    rnn1 = LSTM(hidden_neurons, 
-                    return_sequences=False,
-                    stateful = stateful,
-                    name="RNN1", use_bias=True, activation='tanh')(rnn)
-    # Output layer
-    dens = Dense(in_out_neurons,name="dense")(rnn1)
-    # Define the midel
-    model = Model(inputs=[inp],outputs=[dens])
-    # Compile the model
-    model.compile(loss='mean_squared_error', optimizer='adam')  
-    # Return the model
-    return model
+    # Add the training data as the first dim points in the predicted data array as these
+    # are known values.
+    y_pred = y_test[:dim].tolist()
+    # Generate the first input to the trained recurrent neural network using the last two 
+    # points of the training data.  Based on how the network was trained this means that it
+    # will predict the first point in the data set after the training data.  All of the 
+    # brackets are necessary for Tensorflow.
+    next_input = np.array([[[y_test[dim-2]], [y_test[dim-1]]]])
+    # Save the very last point in the training data set.  This will be used later.
+    last = [y_test[dim-1]]
 
-def dnn2_gru2(length_of_sequences, batch_size = None, stateful = False):
-    """
-        Inputs:
-            length_of_sequences (an int): the number of y values in "x data".  This is determined
-                when the data is formatted
-            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
-            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
-        Returns:
-            model (a Keras model): The recurrent neural network that is built and compiled by this
-                method
-        Builds and compiles a recurrent neural network with four hidden layers (two dense followed by
-        two GRU layers) and returns the model.
-    """    
-    # Number of neurons on the input/output layers and hidden layers
-    in_out_neurons = 1
-    hidden_neurons = 250
-    # Input layer
-    inp = Input(batch_shape=(batch_size, 
-                length_of_sequences, 
-                in_out_neurons)) 
-    # Hidden Dense (feedforward) layers
-    dnn = Dense(hidden_neurons/2, activation='relu', name='dnn')(inp)
-    dnn1 = Dense(hidden_neurons/2, activation='relu', name='dnn1')(dnn)
-    # Hidden GRU layers
-    rnn1 = GRU(hidden_neurons, 
-                    return_sequences=True,
-                    stateful = stateful,
-                    name="RNN1", use_bias=True)(dnn1)
-    rnn = GRU(hidden_neurons, 
-                    return_sequences=False,
-                    stateful = stateful,
-                    name="RNN", use_bias=True)(rnn1)
-    # Output layer
-    dens = Dense(in_out_neurons,name="dense")(rnn)
-    # Define the model
-    model = Model(inputs=[inp],outputs=[dens])
-    # Compile the mdoel
-    model.compile(loss='mean_squared_error', optimizer='adam')  
-    # Return the model
-    return model
+    # Iterate until the complete data set is created.
+    for i in range (dim, len(y_test)):
+        # Predict the next point in the data set using the previous two points.
+        next = model.predict(next_input)
+        # Append just the number of the predicted data set
+        y_pred.append(next[0][0])
+        # Create the input that will be used to predict the next data point in the data set.
+        next_input = np.array([[last, next[0]]], dtype=np.float64)
+        last = next
+
+    # Print the mean squared error between the known data set and the predicted data set.
+    print('MSE: ', np.square(np.subtract(y_test, y_pred)).mean())
+    # Save the predicted data set as a csv file for later use
+    name = datatype + 'Predicted'+str(dim)+'.csv'
+    np.savetxt(name, y_pred, delimiter=',')
+    # Plot the known data set and the predicted data set.  The red box represents the region that was used
+    # for the training data.
+    fig, ax = plt.subplots()
+    ax.plot(x1, y_test, label="true", linewidth=3)
+    ax.plot(x1, y_pred, 'g-.',label="predicted", linewidth=4)
+    ax.legend()
+    # Created a red region to represent the points used in the training data.
+    ax.axvspan(plot_min, plot_max, alpha=0.25, color='red')
+    plt.show()
 
 # Check to make sure the data set is complete
 assert len(X_tot) == len(y_tot)
@@ -223,8 +185,7 @@ rnn_input, rnn_training = format_data(y_trai
 
 # Create a recurrent neural network in Keras and produce a summary of the 
 # machine learning model
-# Change the method name to reflect which network you want to use
-model = dnn2_gru2(length_of_sequences = 2)
+model = rnn(length_of_sequences = rnn_input.shape[1])
 model.summary()
 
 # Start the timer.  Want to time training+testing
@@ -234,10 +195,6 @@ start = timer()
 hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
                  verbose=True,validation_split=0.05)
 
-
-# This section plots the training loss and the validation loss as a function of training iteration.
-# This is not required for analyzing the couple cluster data but can help determine if the network is
-# being overtrained.
 for label in ["loss","val_loss"]:
     plt.plot(hist.history[label],label=label)
 
@@ -252,75 +209,8 @@ test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim# Stop the timer and calculate the total time needed.
 end = timer()
 print('Time: ', end-start)
-
-
-# ### Training Recurrent Neural Networks in the Standard Way (i.e. learning the relationship between the X and Y data)
-# 
-# Finally, comparing the performace of a recurrent neural network using the standard data formatting to the performance of the network with time sequence data formatting shows the benefit of this type of data formatting with extrapolation.
-
-# Check to make sure the data set is complete
-assert len(X_tot) == len(y_tot)
-
-# This is the number of points that will be used in as the training data
-dim=12
-
-# Separate the training data from the whole data set
-X_train = X_tot[:dim]
-y_train = y_tot[:dim]
-
-# Reshape the data for Keras specifications
-X_train = X_train.reshape((dim, 1))
-y_train = y_train.reshape((dim, 1))
-
-
-# Create a recurrent neural network in Keras and produce a summary of the 
-# machine learning model
-# Set the sequence length to 1 for regular data formatting 
-model = rnn(length_of_sequences = 1)
-model.summary()
-
-# Start the timer.  Want to time training+testing
-start = timer()
-# Fit the model using the training data genenerated above using 150 training iterations and a 5%
-# validation split.  Setting verbose to True prints information about each training iteration.
-hist = model.fit(X_train, y_train, batch_size=None, epochs=150, 
-                 verbose=True,validation_split=0.05)
-
-
-# This section plots the training loss and the validation loss as a function of training iteration.
-# This is not required for analyzing the couple cluster data but can help determine if the network is
-# being overtrained.
-for label in ["loss","val_loss"]:
-    plt.plot(hist.history[label],label=label)
-
-plt.ylabel("loss")
-plt.xlabel("epoch")
-plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
-plt.legend()
-plt.show()
-
-# Use the trained neural network to predict the remaining data points
-X_pred = X_tot[dim:]
-X_pred = X_pred.reshape((len(X_pred), 1))
-y_model = model.predict(X_pred)
-y_pred = np.concatenate((y_tot[:dim], y_model.flatten()))
-
-# Plot the known data set and the predicted data set.  The red box represents the region that was used
-# for the training data.
-fig, ax = plt.subplots()
-ax.plot(X_tot, y_tot, label="true", linewidth=3)
-ax.plot(X_tot, y_pred, 'g-.',label="predicted", linewidth=4)
-ax.legend()
-# Created a red region to represent the points used in the training data.
-ax.axvspan(X_tot[0], X_tot[dim], alpha=0.25, color='red')
-plt.show()
-
-# Stop the timer and calculate the total time needed.
-end = timer()
-print('Time: ', end-start)
 
    
 
    
-
 
    
 
 
      
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diff --git a/doc/pub/week43/html/._week43-bs011.html b/doc/pub/week43/html/._week43-bs011.html
index 2a24bbef8..11e5b1389 100644
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+++ b/doc/pub/week43/html/._week43-bs011.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -42,60 +42,12 @@ Automatically generated HTML file from DocOnce source
 
 
 
 
-
-
-
-
-
-
-
     
 
 
    
@@ -142,7 +78,7 @@ MathJax.Hub.Config({
       
       
     
-    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+    Week 43: Deep Learning: Recurrent Neural Networks and other methods
   
    
 
   
    
@@ -151,39 +87,17 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -199,15 +113,110 @@ MathJax.Hub.Config({
 
 
 
-
    Setting it up 
    
+
    Other Things to Try 
    
 
 
    
-It means that to represent the entire
-dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions:  
-$$  
-(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
-$$
+Changing the size of the recurrent neural network and its parameters
+can drastically change the results you get from the model.  The below
+code takes the simple recurrent neural network from above and adds a
+second hidden layer, changes the number of neurons in the hidden
+layer, and explicitly declares the activation function of the hidden
+layers to be a sigmoid function.  The loss function and optimizer can
+also be changed but are kept the same as the above network.  These
+parameters can be tuned to provide the optimal result from the
+network.  For some ideas on how to improve the performance of a
+recurrent neural network.
 
+
    
+
+
+
    def rnn_2layers(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with two hidden layers and returns the model.
+    """
+    # Number of neurons in the input and output layers
+    in_out_neurons = 1
+    # Number of neurons in the hidden layer, increased from the first network
+    hidden_neurons = 500
+    # Define the input layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons))  
+    # Create two hidden layers instead of one hidden layer.  Explicitly set the activation
+    # function to be the sigmoid function (the default value is hyperbolic tangent)
+    rnn1 = SimpleRNN(hidden_neurons, 
+                    return_sequences=True,  # This needs to be True if another hidden layer is to follow
+                    stateful = stateful, activation = 'sigmoid',
+                    name="RNN1")(inp)
+    rnn2 = SimpleRNN(hidden_neurons, 
+                    return_sequences=False, activation = 'sigmoid',
+                    stateful = stateful,
+                    name="RNN2")(rnn1)
+    # Define the output layer as a dense neural network layer (standard neural network layer)
+    #and add it to the network immediately after the hidden layer.
+    dens = Dense(in_out_neurons,name="dense")(rnn2)
+    # Create the machine learning model starting with the input layer and ending with the 
+    # output layer
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the machine learning model using the mean squared error function as the loss 
+    # function and an Adams optimizer.
+    model.compile(loss="mean_squared_error", optimizer="adam")  
+    return model
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+
+# Generate the training data for the RNN, using a sequence of 2
+rnn_input, rnn_training = format_data(y_train, 2)
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+model = rnn_2layers(length_of_sequences = 2)
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+
+# This section plots the training loss and the validation loss as a function of training iteration.
+# This is not required for analyzing the couple cluster data but can help determine if the network is
+# being overtrained.
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict more points of the data set
+test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
    
 
    
 
    
 
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diff --git a/doc/pub/week43/html/._week43-bs012.html b/doc/pub/week43/html/._week43-bs012.html
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+++ b/doc/pub/week43/html/._week43-bs012.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -42,60 +42,12 @@ Automatically generated HTML file from DocOnce source
 
 
 
 
-
-
-
-
-
-
-
     
 
 
    
@@ -142,7 +78,7 @@ MathJax.Hub.Config({
       
       
     
-    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+    Week 43: Deep Learning: Recurrent Neural Networks and other methods
   
    
 
   
    
@@ -151,39 +87,17 @@ MathJax.Hub.Config({
         Contents 
         
       
@@ -199,22 +113,221 @@ MathJax.Hub.Config({
 
 
 
-
    The MNIST dataset again 
    
+
    Other Types of Recurrent Neural Networks 
    
 
 
    
-The MNIST dataset consists of grayscale images with a pixel size of
-\( 28\times 28 \), meaning we require \( 28 \times 28 = 724 \) weights to each
-neuron in the first hidden layer.
+Besides a simple recurrent neural network layer, there are two other
+commonly used types of recurrent neural network layers: Long Short
+Term Memory (LSTM) and Gated Recurrent Unit (GRU).  For a short
+introduction to these layers see https://medium.com/mindboard/lstm-vs-gru-experimental-comparison-955820c21e8b
+and https://medium.com/mindboard/lstm-vs-gru-experimental-comparison-955820c21e8b.
 
 
    
-If we were to analyze images of size \( 128\times 128 \) we would require
-\( 128 \times 128 = 16384 \) weights to each neuron. Even worse if we were
-dealing with color images, as most images are, we have an image matrix
-of size \( 128\times 128 \) for each color dimension (Red, Green, Blue),
-meaning 3 times the number of weights \( = 49152 \) are required for every
-single neuron in the first hidden layer.
+The first network created below is similar to the previous network,
+but it replaces the SimpleRNN layers with LSTM layers.  The second
+network below has two hidden layers made up of GRUs, which are
+preceeded by two dense (feeddorward) neural network layers.  These
+dense layers "preprocess" the data before it reaches the recurrent
+layers.  This architecture has been shown to improve the performance
+of recurrent neural networks (see the link above and also
+https://arxiv.org/pdf/1807.02857.pdf.
 
 
    
+
+
+
    def lstm_2layers(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with two LSTM hidden layers and returns the model.
+    """
+    # Number of neurons on the input/output layer and the number of neurons in the hidden layer
+    in_out_neurons = 1
+    hidden_neurons = 250
+    # Input Layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons)) 
+    # Hidden layers (in this case they are LSTM layers instead if SimpleRNN layers)
+    rnn= LSTM(hidden_neurons, 
+                    return_sequences=True,
+                    stateful = stateful,
+                    name="RNN", use_bias=True, activation='tanh')(inp)
+    rnn1 = LSTM(hidden_neurons, 
+                    return_sequences=False,
+                    stateful = stateful,
+                    name="RNN1", use_bias=True, activation='tanh')(rnn)
+    # Output layer
+    dens = Dense(in_out_neurons,name="dense")(rnn1)
+    # Define the midel
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the model
+    model.compile(loss='mean_squared_error', optimizer='adam')  
+    # Return the model
+    return model
+
+def dnn2_gru2(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with four hidden layers (two dense followed by
+        two GRU layers) and returns the model.
+    """    
+    # Number of neurons on the input/output layers and hidden layers
+    in_out_neurons = 1
+    hidden_neurons = 250
+    # Input layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons)) 
+    # Hidden Dense (feedforward) layers
+    dnn = Dense(hidden_neurons/2, activation='relu', name='dnn')(inp)
+    dnn1 = Dense(hidden_neurons/2, activation='relu', name='dnn1')(dnn)
+    # Hidden GRU layers
+    rnn1 = GRU(hidden_neurons, 
+                    return_sequences=True,
+                    stateful = stateful,
+                    name="RNN1", use_bias=True)(dnn1)
+    rnn = GRU(hidden_neurons, 
+                    return_sequences=False,
+                    stateful = stateful,
+                    name="RNN", use_bias=True)(rnn1)
+    # Output layer
+    dens = Dense(in_out_neurons,name="dense")(rnn)
+    # Define the model
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the mdoel
+    model.compile(loss='mean_squared_error', optimizer='adam')  
+    # Return the model
+    return model
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+
+# Generate the training data for the RNN, using a sequence of 2
+rnn_input, rnn_training = format_data(y_train, 2)
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+# Change the method name to reflect which network you want to use
+model = dnn2_gru2(length_of_sequences = 2)
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+
+# This section plots the training loss and the validation loss as a function of training iteration.
+# This is not required for analyzing the couple cluster data but can help determine if the network is
+# being overtrained.
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict more points of the data set
+test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
+
+# ### Training Recurrent Neural Networks in the Standard Way (i.e. learning the relationship between the X and Y data)
+# 
+# Finally, comparing the performace of a recurrent neural network using the standard data formatting to the performance of the network with time sequence data formatting shows the benefit of this type of data formatting with extrapolation.
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+# Reshape the data for Keras specifications
+X_train = X_train.reshape((dim, 1))
+y_train = y_train.reshape((dim, 1))
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+# Set the sequence length to 1 for regular data formatting 
+model = rnn(length_of_sequences = 1)
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(X_train, y_train, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+
+# This section plots the training loss and the validation loss as a function of training iteration.
+# This is not required for analyzing the couple cluster data but can help determine if the network is
+# being overtrained.
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict the remaining data points
+X_pred = X_tot[dim:]
+X_pred = X_pred.reshape((len(X_pred), 1))
+y_model = model.predict(X_pred)
+y_pred = np.concatenate((y_tot[:dim], y_model.flatten()))
+
+# Plot the known data set and the predicted data set.  The red box represents the region that was used
+# for the training data.
+fig, ax = plt.subplots()
+ax.plot(X_tot, y_tot, label="true", linewidth=3)
+ax.plot(X_tot, y_pred, 'g-.',label="predicted", linewidth=4)
+ax.legend()
+# Created a red region to represent the points used in the training data.
+ax.axvspan(X_tot[0], X_tot[dim], alpha=0.25, color='red')
+plt.show()
+
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
    
+
    
+
 
    
 
 
    
 
 
diff --git a/doc/pub/week43/html/week43-bs.html b/doc/pub/week43/html/week43-bs.html
index f01dbe3ff..ed1c13869 100644
--- a/doc/pub/week43/html/week43-bs.html
+++ b/doc/pub/week43/html/week43-bs.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -42,7 +42,12 @@ Automatically generated HTML file from DocOnce source
 
       
       
     
-    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+    Week 43: Deep Learning: Recurrent Neural Networks and other methods
   
    
 
   
    
@@ -82,15 +87,17 @@ end of tocinfo -->
         Contents 
         
       
@@ -109,7 +116,7 @@ end of tocinfo -->
 
 
 
    
-
    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
      
+
    Week 43: Deep Learning: Recurrent Neural Networks and other methods
      
 
 
    
 
@@ -125,7 +132,7 @@ end of tocinfo -->
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Oct 24, 2021
     
+
    Oct 26, 2021
     
 
    
 
    
 
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diff --git a/doc/pub/week43/html/week43-reveal.html b/doc/pub/week43/html/week43-reveal.html
index 7bb548a6e..cbbe63459 100644
--- a/doc/pub/week43/html/week43-reveal.html
+++ b/doc/pub/week43/html/week43-reveal.html
@@ -3,9 +3,9 @@
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -116,7 +116,7 @@ td.padding {
 
 
 
-
    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
      
+
    Week 43: Deep Learning: Recurrent Neural Networks and other methods
      
 
 
    
 
@@ -132,7 +132,7 @@ td.padding {
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
     
    
-
    Oct 24, 2021
     
+
    Oct 26, 2021
     
 
    
 
    
 
@@ -147,7 +147,7 @@ td.padding {
 
 
      
 
    •  Thursday: Summary of Convolutional Neural Networks from week 42 and Recurrent Neural Networks
      • 
-
    •  Friday: Recurrent Neural Networks and other Deep Learning methods
      • 
+
    •  Friday: Recurrent Neural Networks and other Deep Learning methods such as Generalized Adversarial Neural Networks
      • 
 
    
 
    
 
@@ -164,18 +164,59 @@ td.padding {
 
    
 More resources
 
-
  •  CS231 at Stanford Lecture
 
    • 
 
 
 
 
    
-
    Summary on CNNs 
    
+
    Reading Recommendations 
    
+
+
      
+
    •  Goodfellow et al, chapter 10 on Recurrent NNs, chapters 11 and 12 on various practicalities around deep learning are also recommended.
      • 
+
    •  Aurelien Geron, chapter 14 on RNNs.
      • 
+
    
+
    
+
+
+
    
+
    Summary on Deep Learning Methods 
    
 
 
    
-Material to be added
+We have studied fully connected neural networks (also called artifical nueral networks) and convolutional neural networks (CNNs).
+
+
    
+The first type of deep learning networks work very well on homogeneous and structured input data while CCNs are normally tailored to recognizing images.
+
    
+
+
+
    
+
    CNNs in brief 
    
+
+
    
+In summary:
+
+
      
+
    •  A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)
      • 
+
    •  There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • 
+
    •  Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • 
+
    •  Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • 
+
    •  Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • 
+
    
+
    
+
+For more material on convolutional networks, we strongly recommend
+the course
+IN5400 – Machine Learning for Image Analysis
+and the slides of CS231 which is taught at Stanford University (consistently ranked as one of the top computer science programs in the world). Michael Nielsen's book is a must read, in particular chapter 6 which deals with CNNs.
+
+
    
+However, both standard feed forwards networks and CNNs perform well on data with unknown length.
+
+
    
+This is where recurrent nueral networks (RNNs) come to our rescue.
 
    
 
 
@@ -201,14 +242,14 @@ fixed-sized inputs like all the nets we have discussed so far. For
 example, they can take sentences, documents, or audio samples as
 input, making them extremely useful for natural language processing
 systems such as automatic translation and speech-to-text.
+
+
    
+RNNs are also used in "text classification":"Text Classification Algorithms: A Survey"
 
 
 
 
    
 
    Set up of an RNN 
    
-
-
    
-Text to come.
 
    
 
 
diff --git a/doc/pub/week43/html/week43-solarized.html b/doc/pub/week43/html/week43-solarized.html
index e4eb8c251..637c55d82 100644
--- a/doc/pub/week43/html/week43-solarized.html
+++ b/doc/pub/week43/html/week43-solarized.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods
 
 
 
@@ -62,7 +62,12 @@ div { text-align: justify; text-justify: inter-word; }
 
 
 
 
-
    Week 43: Convolutional Neural Networks and Recurrent Neural Networks
      
+
    Week 43: Deep Learning: Recurrent Neural Networks and other methods
      
 
 
    
 
@@ -105,7 +110,7 @@ end of tocinfo -->
 
    [2] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University
    
 
    
 
    
-
    Oct 24, 2021
     
+
    Oct 26, 2021
     
 
    
 
    
 









    
@@ -114,7 +119,7 @@ end of tocinfo -->
 
 
      
 
    •  Thursday: Summary of Convolutional Neural Networks from week 42 and Recurrent Neural Networks
      • 
-
    •  Friday: Recurrent Neural Networks and other Deep Learning methods
      • 
+
    •  Friday: Recurrent Neural Networks and other Deep Learning methods such as Generalized Adversarial Neural Networks
      • 
 
    
 
 
    
@@ -135,20 +140,58 @@ end of tocinfo -->
 
    
 
 
    
-
-
  •  CS231 at Stanford Lecture
 
    • 
 
 
 
    
 









    
 
-
    Summary on CNNs 
    
+
    Reading Recommendations 
    
+
+
      
+
    •  Goodfellow et al, chapter 10 on Recurrent NNs, chapters 11 and 12 on various practicalities around deep learning are also recommended.
      • 
+
    •  Aurelien Geron, chapter 14 on RNNs.
      • 
+
    
+
+









    
+
+
    Summary on Deep Learning Methods 
    
 
 
    
-Material to be added
+We have studied fully connected neural networks (also called artifical nueral networks) and convolutional neural networks (CNNs).
+
+
    
+The first type of deep learning networks work very well on homogeneous and structured input data while CCNs are normally tailored to recognizing images.
+
+
    
+









    
+
+
    CNNs in brief 
    
+
+
    
+In summary:
+
+
      
+
    •  A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)
      • 
+
    •  There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)
      • 
+
    •  Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function
      • 
+
    •  Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)
      • 
+
    •  Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)
      • 
+
    
+
+For more material on convolutional networks, we strongly recommend
+the course
+IN5400 – Machine Learning for Image Analysis
+and the slides of CS231 which is taught at Stanford University (consistently ranked as one of the top computer science programs in the world). Michael Nielsen's book is a must read, in particular chapter 6 which deals with CNNs.
+
+
    
+However, both standard feed forwards networks and CNNs perform well on data with unknown length.
+
+
    
+This is where recurrent nueral networks (RNNs) come to our rescue.
 
 
    
 









    
@@ -175,14 +218,14 @@ example, they can take sentences, documents, or audio samples as
 input, making them extremely useful for natural language processing
 systems such as automatic translation and speech-to-text.
 
+
    
+RNNs are also used in "text classification":"Text Classification Algorithms: A Survey"
+
 
    
 









    
 
 
    Set up of an RNN 
    
 
-
    
-Text to come.
-
 
    
 









    
 
diff --git a/doc/pub/week43/html/week43.html b/doc/pub/week43/html/week43.html
index 35a7199e5..114e1d9fa 100644
--- a/doc/pub/week43/html/week43.html
+++ b/doc/pub/week43/html/week43.html
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
 
 
 
-
+
 
-Week 43: Convolutional Neural Networks and Recurrent Neural Networks
+Week 43: Deep Learning: Recurrent Neural Networks and other methods