Practice Lab: Linear Regression
Exercise 1
Complete the compute_cost below to:
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Iterate over the training examples, and for each example, compute:
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The prediction of the model for that example
f w b ( x ( i ) ) = w x ( i ) + b f_{wb}(x^{(i)}) = wx^{(i)} + b fwb?(x(i))=wx(i)+b -
The cost for that example c o s t ( i ) = ( f w b ? y ( i ) ) 2 cost^{(i)} = (f_{wb} - y^{(i)})^2 cost(i)=(fwb??y(i))2
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Return the total cost over all examples
J ( w , b ) = 1 2 m ∑ i = 0 m ? 1 c o s t ( i ) J(\mathbf{w},b) = \frac{1}{2m} \sum\limits_{i = 0}^{m-1} cost^{(i)} J(w,b)=2m1?i=0∑m?1?cost(i)- Here, m m m is the number of training examples and ∑ \sum ∑ is the summation operator
If you get stuck, you can check out the hints presented after the cell below to help you with the implementation.文章來源地址http://www.zghlxwxcb.cn/news/detail-709262.html
# UNQ_C1
# GRADED FUNCTION: compute_cost
def compute_cost(x, y, w, b):
# number of training examples
m = x.shape[0]
# You need to return this variable correctly
total_cost = 0
### START CODE HERE ###
for i in range(m):
total_cost+=((x[i]*w+b)-y[i])**2
total_cost=total_cost/(2*m)
### END CODE HERE ###
return total_cost
Exercise 2
Please complete the compute_gradient function to:
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Iterate over the training examples, and for each example, compute:
-
The prediction of the model for that example
f w b ( x ( i ) ) = w x ( i ) + b f_{wb}(x^{(i)}) = wx^{(i)} + b fwb?(x(i))=wx(i)+b -
The gradient for the parameters w , b w, b w,b from that example
? J ( w , b ) ? b ( i ) = ( f w , b ( x ( i ) ) ? y ( i ) ) \frac{\partial J(w,b)}{\partial b}^{(i)} = (f_{w,b}(x^{(i)}) - y^{(i)}) ?b?J(w,b)?(i)=(fw,b?(x(i))?y(i))
? J ( w , b ) ? w ( i ) = ( f w , b ( x ( i ) ) ? y ( i ) ) x ( i ) \frac{\partial J(w,b)}{\partial w}^{(i)} = (f_{w,b}(x^{(i)}) -y^{(i)})x^{(i)} ?w?J(w,b)?(i)=(fw,b?(x(i))?y(i))x(i)
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Return the total gradient update from all the examples
? J ( w , b ) ? b = 1 m ∑ i = 0 m ? 1 ? J ( w , b ) ? b ( i ) \frac{\partial J(w,b)}{\partial b} = \frac{1}{m} \sum\limits_{i = 0}^{m-1} \frac{\partial J(w,b)}{\partial b}^{(i)} ?b?J(w,b)?=m1?i=0∑m?1??b?J(w,b)?(i)? J ( w , b ) ? w = 1 m ∑ i = 0 m ? 1 ? J ( w , b ) ? w ( i ) \frac{\partial J(w,b)}{\partial w} = \frac{1}{m} \sum\limits_{i = 0}^{m-1} \frac{\partial J(w,b)}{\partial w}^{(i)} ?w?J(w,b)?=m1?i=0∑m?1??w?J(w,b)?(i)文章來源：http://www.zghlxwxcb.cn/news/detail-709262.html
- Here, m m m is the number of training examples and ∑ \sum ∑ is the summation operator
If you get stuck, you can check out the hints presented after the cell below to help you with the implementation.
# UNQ_C2
# GRADED FUNCTION: compute_gradient
def compute_gradient(x, y, w, b):
# Number of training examples
m = x.shape[0]
# You need to return the following variables correctly
dj_dw = 0
dj_db = 0
### START CODE HERE ###
for i in range(m):
f_wb=w*x[i]+b
dj_dw_i=(f_wb-y[i])*x[i]
dj_db_i=f_wb-y[i]
dj_dw+=dj_dw_i
dj_db+=dj_db_i
dj_dw=dj_dw/m
dj_db=dj_db/m
### END CODE HERE ###
return dj_dw, dj_db
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