network.py

# %load network.py

"""
network.py
~~~~~~~~~~
IT WORKS

A module to implement the stochastic gradient descent learning
algorithm for a feedforward neural network.  Gradients are calculated
using backpropagation.  Note that I have focused on making the code
simple, easily readable, and easily modifiable.  It is not optimized,
and omits many desirable features.
"""

#### Libraries
# Standard library
import random

# Third-party libraries
import numpy as np

# Standard scientific Python imports
import matplotlib.pyplot as plt

# Import datasets, classifiers and performance metrics
from sklearn import datasets, metrics, svm
from sklearn.model_selection import train_test_split

class Network(object):

    def __init__(self, sizes):
        """The list ``sizes`` contains the number of neurons in the
        respective layers of the network.  For example, if the list
        was [2, 3, 1] then it would be a three-layer network, with the
        first layer containing 2 neurons, the second layer 3 neurons,
        and the third layer 1 neuron.  The biases and weights for the
        network are initialized randomly, using a Gaussian
        distribution with mean 0, and variance 1.  Note that the first
        layer is assumed to be an input layer, and by convention we
        won't set any biases for those neurons, since biases are only
        ever used in computing the outputs from later layers."""
        self.num_layers = len(sizes)
        self.sizes = sizes
        self.biases = [np.random.randn(y, 1) for y in sizes[1:]]
        self.weights = [np.random.randn(y, x)
                        for x, y in zip(sizes[:-1], sizes[1:])]

    def feedforward(self, a):
        """Return the output of the network if ``a`` is input."""
        for b, w in zip(self.biases, self.weights):
            a = sigmoid(np.dot(w, a)+b)
        return a

    def SGD(self, training_data, epochs, mini_batch_size, eta,
            test_data=None):
        """Train the neural network using mini-batch stochastic
        gradient descent.  The ``training_data`` is a list of tuples
        ``(x, y)`` representing the training inputs and the desired
        outputs.  The other non-optional parameters are
        self-explanatory.  If ``test_data`` is provided then the
        network will be evaluated against the test data after each
        epoch, and partial progress printed out.  This is useful for
        tracking progress, but slows things down substantially."""

        training_data = list(training_data)
        n = len(training_data)

        if test_data:
            test_data = list(test_data)
            n_test = len(test_data)

        for j in range(epochs):
            random.shuffle(training_data)
            mini_batches = [
                training_data[k:k+mini_batch_size]
                for k in range(0, n, mini_batch_size)]
            for mini_batch in mini_batches:
                self.update_mini_batch(mini_batch, eta)
            #Testing stuff
            mini_batch_length = len(mini_batches)
            if test_data: #We need to add information about each class of each epoch here
                print("Epoch {} : {} / {}".format(j,self.evaluate(test_data),n_test))
                #we also need the number of *incorrectly* classified images for this
                #bro, can't we just say 'self.evaluate(test_data)-n_test' to get the incorrect ones?
                #do we need a for loop?
                for x in range(mini_batch_size):
                    #maybe we need to add up the total (in)correct images in each mini batch for the evaluate function?
                    class_size = int(n/mini_batch_size) #size of each class
                    class_mini_batch_size = int(class_size/10) #number of mini batches that make up a class
                    exact_class_size = len(mini_batches[x:class_mini_batch_size+x])
                    print(mini_batches.shape)
                    print(test_data.shape)
                    #class_x = mini_batches[x:class_mini_batch_size, 0:9] #each class is 500 or so mini batches of 10 images, with x,y in each
                    print("class {} : {} / {}".format(x,self.evaluate(test_data),exact_class_size)) #how do we evaluate the accuracy of a specific class?
                #we need to expose the specifics of each of these mini batches
                #we need the number of images in each class to put in here b/c I really don't think that 10 is correct
                #also I think the length of the last class in an epoch is a little under 5k. How do I get the exact size for each class?
                #len()
            else:
                print("Epoch {} complete".format(j))
            if j==19:
                """_, axes = plt.subplots(nrows=1, ncols=10, figsize=(10, 3)) #we're printing the ten incorrect in epoch 19
                for ax, image, prediction, expected in zip(axes, X_test, predicted, y_test): #maybe we need to change something here... the actual stuff!
                #if (i in prediction != i in y_test): #how do I compare these two??
                    ax.set_axis_off() #which two sets are we comparing here? 
                    image = image.reshape(8, 8) #we're comparing what we're guessing at with an actual display image and zipping them together
                    ax.imshow(image, cmap=plt.cm.gray_r, interpolation="nearest")
                    ax.set_title(f"Prediction: {prediction}\nActual: {expected}")""" #add this to show what the actual value was (incorrect)

        #This is where we need to print epoch 19's first incorrect image from each class
        #How do we know what the first incorrect one is?
        #Where would we save that info? Should we do it right here, or in the printing section? 


    def update_mini_batch(self, mini_batch, eta):
        """Update the network's weights and biases by applying
        gradient descent using backpropagation to a single mini batch.
        The ``mini_batch`` is a list of tuples ``(x, y)``, and ``eta``
        is the learning rate."""
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        for x, y in mini_batch:
            delta_nabla_b, delta_nabla_w = self.backprop(x, y)
            nabla_b = [nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]
            nabla_w = [nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]
        self.weights = [w-(eta/len(mini_batch))*nw
                        for w, nw in zip(self.weights, nabla_w)]
        self.biases = [b-(eta/len(mini_batch))*nb
                       for b, nb in zip(self.biases, nabla_b)]

    def backprop(self, x, y):
        """Return a tuple ``(nabla_b, nabla_w)`` representing the
        gradient for the cost function C_x.  ``nabla_b`` and
        ``nabla_w`` are layer-by-layer lists of numpy arrays, similar
        to ``self.biases`` and ``self.weights``."""
        nabla_b = [np.zeros(b.shape) for b in self.biases]
        nabla_w = [np.zeros(w.shape) for w in self.weights]
        # feedforward
        activation = x
        activations = [x] # list to store all the activations, layer by layer
        zs = [] # list to store all the z vectors, layer by layer
        for b, w in zip(self.biases, self.weights):
            z = np.dot(w, activation)+b
            zs.append(z)
            activation = sigmoid(z)
            activations.append(activation)
        # backward pass
        delta = self.cost_derivative(activations[-1], y) * \
            sigmoid_prime(zs[-1])
        nabla_b[-1] = delta
        nabla_w[-1] = np.dot(delta, activations[-2].transpose())
        # Note that the variable l in the loop below is used a little
        # differently to the notation in Chapter 2 of the book.  Here,
        # l = 1 means the last layer of neurons, l = 2 is the
        # second-last layer, and so on.  It's a renumbering of the
        # scheme in the book, used here to take advantage of the fact
        # that Python can use negative indices in lists.
        for l in range(2, self.num_layers):
            z = zs[-l]
            sp = sigmoid_prime(z)
            delta = np.dot(self.weights[-l+1].transpose(), delta) * sp
            nabla_b[-l] = delta
            nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())
        return (nabla_b, nabla_w)

    def evaluate(self, test_data):
        """Return the number of test inputs for which the neural
        network outputs the correct result. Note that the neural
        network's output is assumed to be the index of whichever
        neuron in the final layer has the highest activation."""
        test_results = [(np.argmax(self.feedforward(x)), y)
                        for (x, y) in test_data]
        return sum(int(x == y) for (x, y) in test_results)


    def evaluate_batches(self, test_data): #we need this to check each set of mini batches
        """Return the number of test inputs for which the neural
        network outputs the correct result. Note that the neural
        network's output is assumed to be the index of whichever
        neuron in the final layer has the highest activation."""
        test_results = [(np.argmax(self.feedforward(x)), y)
                        for (x, y) in test_data]
        return sum(int(x != y) for (x, y) in test_results) #gets incorrect amount
    
    def get_first_incorrect(): #we're gonna use this to print the incorrect images
        return 0

    def cost_derivative(self, output_activations, y):
        """Return the vector of partial derivatives \partial C_x /
        \partial a for the output activations."""
        return (output_activations-y)

#### Miscellaneous functions
def sigmoid(z):
    """The sigmoid function."""
    return 1.0/(1.0+np.exp(-z))

def sigmoid_prime(z):
    """Derivative of the sigmoid function."""
    return sigmoid(z)*(1-sigmoid(z))