DL Intro
熟悉sckit learn
import pandas as pd
from sklearn import linear_model
import matplotlib.pyplot as plt
#read data
dataframe = pd.read_fwf('brain_body.txt')
x_values = dataframe[['Brain']]
y_values = dataframe[['Body']]
#train model on data
body_reg = linear_model.LinearRegression()
body_reg.fit(x_values, y_values)
#visualize results
plt.scatter(x_values, y_values)
plt.plot(x_values, body_reg.predict(x_values))
plt.show()
gradient descent
- 一种寻找 local minimum 的方法;
- 对各维度求偏导数,顺着偏导数的方向(local minimum 方向)跑,跑的幅度(即learning rate);
- 几个概念类比:
- 偏导数的方向: 人脑学习技能时的学习“方向”;
- learning rate: 人脑学习技能时候的细致程度;学得太细,完成学习的时间就长;学得太粗,可能最后没法子“收敛”(即完不成学习),把握好learning rate的度。。。
#The optimal values of m and b can be actually calculated with way less effort than doing a linear regression.
#this is just to demonstrate gradient descent
from numpy import *
# y = mx + b
# m is slope, b is y-intercept
def compute_error_for_line_given_points(b, m, points):
totalError = 0
for i in range(0, len(points)):
x = points[i, 0]
y = points[i, 1]
totalError += (y - (m * x + b)) ** 2
return totalError / float(len(points))
def step_gradient(b_current, m_current, points, learningRate):
b_gradient = 0
m_gradient = 0
N = float(len(points))
for i in range(0, len(points)):
x = points[i, 0]
y = points[i, 1]
b_gradient += -(2/N) * (y - ((m_current * x) + b_current))
m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))
new_b = b_current - (learningRate * b_gradient)
new_m = m_current - (learningRate * m_gradient)
return [new_b, new_m]
def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):
b = starting_b
m = starting_m
for i in range(num_iterations):
b, m = step_gradient(b, m, array(points), learning_rate)
return [b, m]
def run():
points = genfromtxt("data.csv", delimiter=",")
learning_rate = 0.0001
initial_b = 0 # initial y-intercept guess
initial_m = 0 # initial slope guess
num_iterations = 1000
print "Starting gradient descent at b = {0}, m = {1}, error = {2}".format(initial_b, initial_m, compute_error_for_line_given_points(initial_b, initial_m, points))
print "Running..."
[b, m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)
print "After {0} iterations b = {1}, m = {2}, error = {3}".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points))
if __name__ == '__main__':
run()
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