# -*- coding: utf-8 -*-
# @Time : 2020/3/7 23:19
# @Author : zhoujianwen
# @Email : [email protected]
# @File : gd.py
# @Describe: 采用梯度下降的方法求解二元一次方程组
import numpy as np
# y = wx + b
# MSE均方误差(1/n)∑(f(x_i)-y_i)^2，预测值f(x_i)与真实值y_i之差的平方和的平均值，
# MSE可用来作为衡量预测的一个指标。
# 计算出loss值
def compute_error_for_line_given_points(b, w, points):
totalError = 0
for i in range(0, len(points)):
x = points[i, 0]
y = points[i, 1]
totalError += (y - (w * x + b)) ** 2
return totalError / float(len(points))
# 梯度下降(gradient descent)
# loss = (w_current*x + b_current-y)^2
# (Δw,Δb) = (∂L/∂w,∂L/∂b)
# new_w = w_current - lr * Δw
# new_b = w_current - lr * Δb
def step_gradient(b_current, w_current, points, learningRate):
b_gradient = 0
w_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 - ((w_current * x) + b_current)) # 把所有点的梯度信息（偏导数的值）累加起来
w_gradient += -(2 / N) * x * (y - ((w_current * x) + b_current))
new_b = b_current - (learningRate * b_gradient) # 更新参数（权值和偏置）
new_w = w_current - (learningRate * w_gradient)
return [new_b, new_w]
# 反复迭代梯度信息获取最优参数值
def gradient_descent_runner(points, starting_b, starting_w, learning_rate, num_iterations):
b = starting_b
w = starting_w
for i in range(num_iterations):
print("num_iterations:{0},current_w:{1},current_b:{2}".format(i, w, b))
b, w = step_gradient(b, w, np.array(points), learning_rate)
return [b, w]
"""
梯度下降的batch、epoch、iteration的含义，现在用的优化器SGD是stochastic gradient descent的缩写，
但不代表一个样本就更新一回，还是基于mini-batch的。
batchsize：批大小。在深度学习中，一般采用SGD训练，即每次训练在训练集中取batchsize个样本训练；
iteration：1个iteration等于使用batchsize个样本训练一次；
epoch：1个epoch等于使用训练集中的全部样本训练一次，通俗的讲epoch的值就是整个数据集被轮几次。
比如训练集有500个样本，batchsize = 10 ，那么训练完整个样本集：iteration=50，epoch=1.
batch: 深度学习每一次参数的更新所需要损失函数并不是由一个数据获得的，而是由一组数据加权得到的，这一组数据的数量就是batchsize。
batchsize最大是样本总数N，此时就是Full batch learning；最小是1，即每次只训练一个样本，这就是在线学习（Online Learning）。
当我们分批学习时，每次使用过全部训练数据完成一次Forword运算以及一次BP运算，成为完成了一次epoch。
"""
def run():
# 一次性读取训练集的100个样本点，batchsize=1，iteration= 100，epoch = 1，也就定义了每个epoch读取100个样本点
points = np.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()
写于2020.03.08 11:45:50
复制样本数据保存为.csv文件
32.502345269453031,31.70700584656992
53.426804033275019,68.77759598163891
61.530358025636438,62.562382297945803
47.475639634786098,71.546632233567777
59.813207869512318,87.230925133687393
55.142188413943821,78.211518270799232
52.211796692214001,79.64197304980874
39.299566694317065,59.171489321869508
48.10504169176825,75.331242297063056
52.550014442733818,71.300879886850353
45.419730144973755,55.165677145959123
54.351634881228918,82.478846757497919
44.164049496773352,62.008923245725825
58.16847071685779,75.392870425994957
56.727208057096611,81.43619215887864
48.955888566093719,60.723602440673965
44.687196231480904,82.892503731453715
60.297326851333466,97.379896862166078
45.618643772955828,48.847153317355072
38.816817537445637,56.877213186268506
66.189816606752601,83.878564664602763
65.41605174513407,118.59121730252249
47.48120860786787,57.251819462268969
41.57564261748702,51.391744079832307
51.84518690563943,75.380651665312357
59.370822011089523,74.765564032151374
57.31000343834809,95.455052922574737
63.615561251453308,95.229366017555307
46.737619407976972,79.052406169565586
50.556760148547767,83.432071421323712
52.223996085553047,63.358790317497878
35.567830047746632,41.412885303700563
42.436476944055642,76.617341280074044
58.16454011019286,96.769566426108199
57.504447615341789,74.084130116602523
45.440530725319981,66.588144414228594
61.89622268029126,77.768482417793024
33.093831736163963,50.719588912312084
36.436009511386871,62.124570818071781
37.675654860850742,60.810246649902211
44.555608383275356,52.682983366387781
43.318282631865721,58.569824717692867
50.073145632289034,82.905981485070512
43.870612645218372,61.424709804339123
62.997480747553091,115.24415280079529
32.669043763467187,45.570588823376085
40.166899008703702,54.084054796223612
53.575077531673656,87.994452758110413
33.864214971778239,52.725494375900425
64.707138666121296,93.576118692658241
38.119824026822805,80.166275447370964
44.502538064645101,65.101711570560326
40.599538384552318,65.562301260400375
41.720676356341293,65.280886920822823
51.088634678336796,73.434641546324301
55.078095904923202,71.13972785861894
41.377726534895203,79.102829683549857
62.494697427269791,86.520538440347153
49.203887540826003,84.742697807826218
41.102685187349664,59.358850248624933
41.182016105169822,61.684037524833627
50.186389494880601,69.847604158249183
52.378446219236217,86.098291205774103
50.135485486286122,59.108839267699643
33.644706006191782,69.89968164362763
39.557901222906828,44.862490711164398
56.130388816875467,85.498067778840223
57.362052133238237,95.536686846467219
60.269214393997906,70.251934419771587
35.678093889410732,52.721734964774988
31.588116998132829,50.392670135079896
53.66093226167304,63.642398775657753
46.682228649471917,72.247251068662365
43.107820219102464,57.812512976181402
70.34607561504933,104.25710158543822
44.492855880854073,86.642020318822006
57.50453330326841,91.486778000110135
36.930076609191808,55.231660886212836
55.805733357942742,79.550436678507609
38.954769073377065,44.847124242467601
56.901214702247074,80.207523139682763
56.868900661384046,83.14274979204346
34.33312470421609,55.723489260543914
59.04974121466681,77.634182511677864
57.788223993230673,99.051414841748269
54.282328705967409,79.120646274680027
51.088719898979143,69.588897851118475
50.282836348230731,69.510503311494389
44.211741752090113,73.687564318317285
38.005488008060688,61.366904537240131
32.940479942618296,67.170655768995118
53.691639571070056,85.668203145001542
68.76573426962166,114.85387123391394
46.230966498310252,90.123572069967423
68.319360818255362,97.919821035242848
50.030174340312143,81.536990783015028
49.239765342753763,72.111832469615663
50.039575939875988,85.232007342325673
48.149858891028863,66.224957888054632
25.128484647772304,53.454394214850524
