[Neural Networks and Deep Learning] 2주차

Linear Regression

 

Logistic Regression

 

Logistic Regression cost function

 

Gradient Descent

 

Logistic Regression Gradient Descent

 

Logistic Regression Gradient Descent on m examples

 

Vectorization

import numpy as np
import time

a = np.random.rand(1000000)
b = np.random.rand(1000000)

tic = time.time()
c = 0
for i in range(1000000) :
    c += a[i] * b[i]
toc = time.time()

print('for loop :' + str(1000 * (toc - tic)) + 'ms')
print(c)

tic = time.time()
c = np.dot(a, b)
toc = time.time()

print('vectorization :' + str(1000 * (toc - tic)) + 'ms')
print(c)

>>> for loop :339.0049934387207ms
    249929.39667635385
    vectorization :1.4219284057617188ms
    249929.39667634486

 

Python Broadcasting

import numpy as np

A = np.array([[56.0, 0.0, 4.4, 68.0],
               [1.2, 104.0, 52.0, 8.0],
               [1.8, 135.0, 99.0, 0.9]])

summ = A.sum(axis = 0)

percent = 100 * A / summ
print(percent)

B = np.array([[1],
             [2],
             [3],
             [4]])
print(B + 100)

C = np.array([[1, 2, 3],
             [4, 5, 6]])

D = np.array([[100, 200, 300]])
print(C + D)

E = np.array([[100],
             [200]])
print(C + E)

>>> [[94.91525424  0.          2.83140283 88.42652796]
     [ 2.03389831 43.51464435 33.46203346 10.40312094]
     [ 3.05084746 56.48535565 63.70656371  1.17035111]]
    [[101]
     [102]
     [103]
     [104]]
    [[101 202 303]
     [104 205 306]]
    [[101 102 103]
     [204 205 206]]

 

Python-Numpy vectors

import numpy as np

a = np.random.randn(3).reshape(1, 3) # 행벡터인지 열벡터인지 반드시 명시
print(np.dot(a, a.T))
print(np.dot(a.T, a))

>>> [[1.45552316]]
    [[ 0.82748124  0.70883268 -0.131336  ]
     [ 0.70883268  0.60719656 -0.11250436]
     [-0.131336   -0.11250436  0.02084536]]

 

Vectorizing Logistic Regression