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mlp_numpy.py
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mlp_numpy.py
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import numpy as np
from scipy.special import expit
import copy
def tanh(x):
return np.tanh(x)
def tanh_prime(x):
return 1.0 - np.tanh(x)**2.0
def linear(x):
return x
def linear_prime(x):
return 1.0
def relu(x):
y = copy.deepcopy(x)
y[y<=0] = 0.0
return y
def relu_prime(x):
y = copy.deepcopy(x)
y[y>0] = 1.0
y[y<=0] = 0.0
return y
def logistic(x):
return 1.0/(1+np.exp(-x))
def logistic_prime(x):
ex=expit(-x)
return ex/(1+ex)**2
def identity(x):
return x
def identity_prime(x):
return 1
class NeuralNetwork(object):
def __init__(self, X, y, parameters):
#Input data
self.X=X
#Output data
self.y=y
#Expect parameters to be a tuple of the form:
# ((n_input,0,0), (n_hidden_layer_1, f_1, f_1'), ...,
# (n_hidden_layer_k, f_k, f_k'), (n_output, f_o, f_o'))
self.n_layers = len(parameters)
#Counts number of neurons without bias neurons in each layer.
self.sizes = [layer[0] for layer in parameters]
#Activation functions for each layer.
self.fs =[layer[1] for layer in parameters]
#Derivatives of activation functions for each layer.
self.fprimes = [layer[2] for layer in parameters]
self.build_network()
def build_network(self):
#List of weight matrices taking the output of one layer to the input of the next.
self.weights=[]
#Bias vector for each layer.
self.biases=[]
#Input vector for each layer.
self.inputs=[]
#Output vector for each layer.
self.outputs=[]
#Vector of errors at each layer.
self.errors=[]
#We initialise the weights randomly, and fill the other vectors with 1s.
for layer in range(self.n_layers-1):
n = self.sizes[layer]
m = self.sizes[layer+1]
self.weights.append(np.random.normal(0,0.1, (m,n)))
self.biases.append(np.random.normal(0,0.1,(m,1)))
self.inputs.append(np.zeros((n,1)))
self.outputs.append(np.zeros((n,1)))
self.errors.append(np.zeros((n,1)))
#There are only n-1 weight matrices, so we do the last case separately.
n = self.sizes[-1]
self.inputs.append(np.zeros((n,1)))
self.outputs.append(np.zeros((n,1)))
self.errors.append(np.zeros((n,1)))
def feedforward(self, x):
#Propagates the input from the input layer to the output layer.
#k=len(x)
#x.shape=(k,1)
self.inputs[0]=x
self.outputs[0]=x
for i in range(1,self.n_layers):
self.inputs[i]=self.weights[i-1].dot(self.outputs[i-1])+self.biases[i-1]
self.outputs[i]=self.fs[i](self.inputs[i])
return self.outputs[-1]
def feedforwardnoisy(self, x):
#Propagates the input from the input layer to the output layer.
#k=len(x)
#x.shape=(k,1)
self.inputs[0]=x
self.outputs[0]=x
for i in range(1,self.n_layers):
self.outputs[i-1]=copy.deepcopy(self.outputs[i-1]+np.random.normal(0, 0.1, self.outputs[i-1].shape))
self.inputs[i]=self.weights[i-1].dot(self.outputs[i-1])+self.biases[i-1]
self.outputs[i]=self.fs[i](self.inputs[i])
return self.outputs[-1]
def update_weights(self,x,y):
#Update the weight matrices for each layer based on a single input x and target y.
output = self.feedforward(x)
self.errors[-1]=self.fprimes[-1](self.outputs[-1])*(output-y)
n=self.n_layers-2
for i in xrange(n,0,-1):
self.errors[i] = self.fprimes[i](self.inputs[i])*self.weights[i].T.dot(self.errors[i+1])
self.weights[i] = self.weights[i]-self.learning_rate*np.outer(self.errors[i+1],self.outputs[i])
self.biases[i] = self.biases[i] - self.learning_rate*self.errors[i+1]
self.weights[0] = self.weights[0]-self.learning_rate*np.outer(self.errors[1],self.outputs[0])
self.biases[0] = self.biases[0] - self.learning_rate*self.errors[1]
def update_weights_batch(self,x,y):
#Update the weight matrices for each layer based on a single input x and target y.
output = self.feedforwardnoisy(x)
self.errors[-1]=self.fprimes[-1](self.outputs[-1])*(output-y)
n=self.n_layers-2
for i in xrange(n,0,-1):
self.errors[i] = self.fprimes[i](self.inputs[i])*self.weights[i].T.dot(self.errors[i+1])
self.weights[i] = self.weights[i]-self.learning_rate*np.outer(self.errors[i+1],self.outputs[i])
self.biases[i] = self.biases[i] - self.learning_rate*self.errors[i+1]
self.weights[0] = self.weights[0]-self.learning_rate*np.outer(self.errors[1],self.outputs[0])
self.biases[0] = self.biases[0] - self.learning_rate*self.errors[1]
def train(self, X, Y, n_iter, learning_rate=1):
#Updates the weights after comparing each input in X with y
#repeats this process n_iter times.
self.X = X
self . y= Y
self.learning_rate=learning_rate
n=self.X.shape[0]
for repeat in range(n_iter):
#We shuffle the order in which we go through the inputs on each iter.
index=list(range(n))
np.random.shuffle(index)
for row in index:
x=self.X[row:row+1,:]
y=self.y[row:row+1,:]
self.update_weights(x.T,y.T)
def train_sgd(self, X, Y, n_iter, learning_rate=1):
#Updates the weights after comparing each input in X with y
#repeats this process n_iter times.
self.X = X
self . y= Y
self.learning_rate=learning_rate
n=self.X.shape[0]
for repeat in range(n_iter):
#We shuffle the order in which we go through the inputs on each iter.
index=list(range(n))
np.random.shuffle(index)
for row in index:
x=self.X[row:row+1,:]
y=self.y[row:row+1,:]
self.update_weights(x.T,y.T)
def predict_x(self, x):
return self.feedforward(x)
def predict(self, X):
n = len(X)
m = self.sizes[-1]
ret = np.ones((n,m))
for i in range(len(X)):
ret[i,:] = self.feedforward(X[i:i+1,:].T).reshape((m))
return ret
#expit is a fast way to compute logistic using precomputed exp.
def test_regression(plots=False):
#First create the data.
n=200
X=np.linspace(0,3*np.pi,num=n)
X.shape=(n,1)
y=np.sin(X)
#We make a neural net with 2 hidden layers, 20 neurons in each, using logistic activation
#functions.
param=((1,0,0),(20, expit, logistic_prime),(20, expit, logistic_prime),(1,identity, identity_prime))
#Set learning rate.
rates=[0.05]
predictions=[]
for rate in rates:
N=NeuralNetwork(X,y,param)
N.train(40, learning_rate=rate)
predictions.append([rate,N.predict(X)])
import matplotlib.pyplot as plt
fig, ax=plt.subplots(1,1)
if plots:
ax.plot(X,y, label='Sine', linewidth=2, color='black')
for data in predictions:
ax.plot(X,data[1],label="Learning Rate: "+str(data[0]))
ax.legend()
plt.show()
if __name__ == "__main__":
test_regression(True)