DL00 Intro

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()