Udacity机器学习进阶—监督学习之神经网络迷你项目

1.创建感知

def activate(self,inputs):
"""
Takes in @param inputs, a list of numbers equal to length of weights.
@return the output of a threshold perceptron with given inputs based on
perceptron weights and threshold.
"""

# The strength with which the perceptron fires.
strength = np.dot(self.weights, inputs)
# TODO: return 0 or 1 based on the threshold
if strength <= self.threshold :
self.result = 0# TODO
else:
self.result = 1# TODO
return self.result

3.在哪儿训练感知

我们希望建立一个感知机，那么在建立模型的过程中，我们需要修改的是以下哪些值？

阈值

权重

4.感知输入

人工神经网络是由感知机单元构成的，人工神经网络的输入应该是什么格式的呢？

每行带有标签的数值型矩阵

5.神经网络输出

我们能从神经网络的输出中得到什么信息？

一个有向图（神经网络本身）

一个标量

用向量表示的分类信息

每个输入向量都对应一个输出向量

6.感知更新规则

def update(self, values, train, eta=.1):
"""
Takes in a 2D array @param values consisting of a LIST of inputs and a
1D array @param train, consisting of a corresponding list of expected
outputs. Updates internal weights according to the perceptron training
rule using these values and an optional learning rate, @param eta.
"""

# For each data point:
for data_point in xrange(len(values)):
# TODO: Obtain the neuron's prediction for the data_point --> values[data_point]
prediction = self.activate(values[data_point])
# Get the prediction accuracy calculated as (expected value - predicted value)
# expected value = train[data_point], predicted value = prediction
error = trai
4000
n[data_point] - prediction
# TODO: update self.weights based on the multiplication of:
# - prediction accuracy(error)
# - learning rate(eta)
# - input value(values[data_point])
weight_update =  eta*error*values[data_point]# TODO
self.weights += weight_update

7.多层网络示例



8.线性表征能力



9.创建XOR网络

# Part 1: Set up the perceptron network
Network = [
# input layer, declare input layer perceptrons here
[ input1,input2], \
# output node, declare output layer perceptron here
[ output ]
]

# Part 2: Define a procedure to compute the output of the network, given inputs
def EvalNetwork(inputValues, Network):
"""
Takes in @param inputValues, a list of input values, and @param Network
that specifies a perceptron network. @return the output of the Network for
the given set of inputs.
"""

# YOUR CODE HERE
input=[]
for net in Network[0]:
input.append(net.activate(inputValues))
OutputValue = output.activate(input)
# Be sure your output value is a single number
return OutputValue

10.离散测验

人工神经网络的一个问题是他只能输出离散值，这就使得他不能有效的处理回归问题，并且处理负责问题的时候需要更多的单元。

例如： 给定一个结构为 [2,2,1]（输入层两个单元，隐藏层两个单元，输出层一个单元）的神经网络，最多可以预测几种房屋的价格？



2*2=4

13.激活函数 测验

我们已经决定使用一个连续(避免离散问题)并且非线性(允许我们表示非线性)的方程，以下哪个方程满足我们的需求？

Logistic function

其实就是阶跃函数和sigmoid函数

14.Perceptron Vs Sigmoid

单个感知机和一个 Sigmoid 单元在二分类问题上有什么区别？

后者给出了更多的信息，但是两者的结果会相同

15.Sigmoid Learning

我们需要像训练感知机一样来训练 Sigmoid 单元。该怎么定义更新规则呢？

运用微积分

16.Gradient Descent Issues

运用微积分，梯度下降算法可以给我们提供一个求极值的方法。但是也会产生很多问题，你认为会产生下列哪些问题？

局部的极值

运行太耗时

会产生无限次循环

无法收敛

17.

# ----------
#
# As with the previous perceptron exercises, you will complete some of the core
# methods of a sigmoid unit class.
#
# There are two functions for you to finish:
# First, in activate(), write the sigmoid activation function.
# Second, in update(), write the gradient descent update rule. Updates should be
#   performed online, revising the weights after each data point.
#
# ----------

import numpy as np

class Sigmoid:
"""
This class models an artificial neuron with sigmoid activation function.
"""

def __init__(self, weights = np.array([1])):
"""
Initialize weights based on input arguments. Note that no type-checking
is being performed here for simplicity of code.
"""
self.weights = weights

# NOTE: You do not need to worry about these two attribues for this
# programming quiz, but these will be useful for if you want to create
# a network out of these sigmoid units!

self.last_input = 0 # strength of last input
self.delta      = 0 # error signal

def activate(self, values):
"""
Takes in @param values, a list of numbers equal to length of weights.
@return the output of a sigmoid unit with given inputs based on unit
weights.
"""

# YOUR CODE HERE

# First calculate the strength of the input signal.
strength = np.dot(values, self.weights)
self.last_input = strength

# TODO: Modify strength using the sigmoid activation function and
# return as output signal.
# HINT: You may want to create a helper function to compute the
#   logistic function since you will need it for the update function.

result=self.logistic(strength)

return result

def logistic(self,x):
return 1.0/(1+np.exp(-x))

def update(self, values, train, eta=.1):
"""
Takes in a 2D array @param values consisting of a LIST of inputs and a
1D array @param train, consisting of a corresponding list of expected
outputs. Updates internal weights according to gradient descent using
these values and an optional learning rate, @param eta.
"""

# TODO: for each data point...
for X, y_true in zip(values, train):
# obtain the output signal for that point
y_pred = self.activate(X)

# YOUR CODE HERE
error  = y_true - y_pred
# TODO: compute derivative of logistic function at input strength
# Recall: d/dx logistic(x) = logistic(x)*(1-logistic(x))
from scipy.special import expit
de_logistic = self.logistic(self.last_input)* (1 -self.logistic(self.last_input))
# TODO: update self.weights based on learning rate, signal accuracy,
# function slope (derivative) and input value
weight_update=X*de_logistic*eta*error
self.weights += weight_update

def test():
"""
A few tests to make sure that the perceptron class performs as expected.
Nothing should show up in the output if all the assertions pass.
"""
def sum_almost_equal(array1, array2, tol = 1e-5):
return sum(abs(array1 - array2)) < tol

u1 = Sigmoid(weights=[3,-2,1])
assert abs(u1.activate(np.array([1,2,3])) - 0.880797) < 1e-5

u1.update(np.array([[1,2,3]]),np.array([0]))
assert sum_almost_equal(u1.weights, np.array([2.990752, -2.018496, 0.972257]))

u2 = Sigmoid(weights=[0,3,-1])
u2.update(np.array([[-3,-1,2],[2,1,2]]),np.array([1,0]))
assert sum_almost_equal(u2.weights, np.array([-0.030739, 2.984961, -1.027437]))

if __name__ == "__main__":
test()