如何将深度学习梯度下降方程式转换为python [英] How to convert deep learning gradient descent equation into python

问题描述

我一直在关注有关深度学习的在线教程.它有一个关于梯度下降和成本计算的实际问题，在将其转换为python代码后，我一直在努力获得给定的答案.希望您能帮助我获得正确答案

I've been following an online tutorial on deep learning. It has a practical question on gradient descent and cost calculations where I been struggling to get the given answers once it was converted to python code. Hope you can kindly help me get the correct answer please

使用的方程式请参见以下链接 点击此处查看用于计算的方程式

Please see the following link for the equations used Click here to see the equations used for the calculations

以下是用于计算梯度下降，成本等的函数.无需使用for循环而是使用矩阵操作运算即可找到这些值

Following is the function given to calculate the gradient descent,cost etc. The values need to be found without using for loops but using matrix manipulation operations

import numpy as np

def propagate(w, b, X, Y):
"""
Arguments:
w -- weights, a numpy array of size (num_px * num_px * 3, 1)
b -- bias, a scalar
X -- data of size (num_px * num_px * 3, number of examples)
Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size
  (1, number of examples)

Return:
cost -- negative log-likelihood cost for logistic regression
dw -- gradient of the loss with respect to w, thus same shape as w
db -- gradient of the loss with respect to b, thus same shape as b

Tips:
- Write your code step by step for the propagation. np.log(), np.dot()
"""

m = X.shape[1]


# FORWARD PROPAGATION (FROM X TO COST)
### START CODE HERE ### (≈ 2 lines of code)
A =                                      # compute activation
cost =                                   # compute cost
### END CODE HERE ###


# BACKWARD PROPAGATION (TO FIND GRAD)
### START CODE HERE ### (≈ 2 lines of code)
dw = 
db = 
### END CODE HERE ###


assert(dw.shape == w.shape)
assert(db.dtype == float)
cost = np.squeeze(cost)
assert(cost.shape == ())

grads = {"dw": dw,
         "db": db}

return grads, cost

以下是测试上述功能的数据

Following are the data given to test the above function

w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), 
np.array([[1,0]])
grads, cost = propagate(w, b, X, Y)
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print ("cost = " + str(cost))

以下是上述内容的预期输出

Following is the expected output of the above

Expected Output:
dw  [[ 0.99993216] [ 1.99980262]]
db  0.499935230625
cost    6.000064773192205

对于上面的传播函数，我使用了以下替换，但是输出不是预期的.请提供有关如何获得预期输出的帮助

For the above propagate function I have used the below replacements, but the output is not what is expected. Please kindly help on how to get the expected output

A = sigmoid(X)
cost = -1*((np.sum(np.dot(Y,np.log(A))+np.dot((1-Y),(np.log(1-A))),axis=0))/m)
dw = (np.dot(X,((A-Y).T)))/m
db = np.sum((A-Y),axis=0)/m

以下是用于计算激活的S型函数:

Following is the sigmoid function used to calculate the Activation:

def sigmoid(z):
  """
  Compute the sigmoid of z

  Arguments:
  z -- A scalar or numpy array of any size.

  Return:
  s -- sigmoid(z)
  """

  ### START CODE HERE ### (≈ 1 line of code)
  s = 1 / (1+np.exp(-z))
  ### END CODE HERE ###

return s

希望有人可以帮助我了解如何解决此问题，因为如果不了解这一点，我将无法继续本教程的其余部分.非常感谢

Hope someone could help me understand how to solve this as I couldn't continue with rest of the tutorials without understanding this. Many thanks

推荐答案

您可以按以下方式计算A，cost，dw，db:

You can calculate A,cost,dw,db as the following:

A = sigmoid(np.dot(w.T,X) + b)     
cost = -1 / m * np.sum(Y*np.log(A)+(1-Y)*np.log(1-A)) 

dw = 1/m * np.dot(X,(A-Y).T)
db = 1/m * np.sum(A-Y)

sigmoid是:

def sigmoid(z):
    s = 1 / (1 + np.exp(-z))    
    return s

这篇关于如何将深度学习梯度下降方程式转换为python的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！