• python实现代码 # -*- coding: utf-8 -*- import math def get_average(records): &quot;&quot;&quot; 平均值 &quot;&quot;&quot; return sum(records) / len(records) def get_...
缩写英文中文RMSRRoot Mean Squared Error均方根误差MAEMean Absolute Error平均绝对误差
python实现代码
# -*- coding: utf-8 -*-

import math

def get_average(records):
"""
平均值
"""
return sum(records) / len(records)

def get_variance(records):
"""
方差 反映一个数据集的离散程度
"""
average = get_average(records)
return sum([(x - average) ** 2 for x in records]) / len(records)

def get_standard_deviation(records):
"""
标准差 == 均方差 反映一个数据集的离散程度
"""
variance = get_variance(records)
return math.sqrt(variance)

def get_rms(records):
"""
均方根值 反映的是有效值而不是平均值
"""
return math.sqrt(sum([x ** 2 for x in records]) / len(records))

def get_mse(records_real, records_predict):
"""
均方误差 估计值与真值 偏差
"""
if len(records_real) == len(records_predict):
return sum([(x - y) ** 2 for x, y in zip(records_real, records_predict)]) / len(records_real)
else:
return None

def get_rmse(records_real, records_predict):
"""
均方根误差：是均方误差的算术平方根
"""
mse = get_mse(records_real, records_predict)
if mse:
return math.sqrt(mse)
else:
return None

def get_mae(records_real, records_predict):
"""
平均绝对误差
"""
if len(records_real) == len(records_predict):
return sum([abs(x - y) for x, y in zip(records_real, records_predict)]) / len(records_real)
else:
return None

if __name__ == '__main__':
records1 = [3, 4, 5]
records2 = [2, 4, 6]

# 平均值
average1 = get_average(records1)  # 4.0
average2 = get_average(records2)  # 4.0

# 方差
variance1 = get_variance(records1)  # 0.66
variance2 = get_variance(records2)  # 2.66

# 标准差
std_deviation1 = get_standard_deviation(records1)  # 0.81
std_deviation2 = get_standard_deviation(records2)  # 1.63

# 均方根
rms1 = get_rms(records1)  # 4.08
rms2 = get_rms(records2)  # 4.32

# 均方误差
mse = get_mse(records1, records2)  # 0.66

# 均方根误差
rmse = get_rmse(records1, records2)  # 0.81

# 平均绝对误差
mae = get_mae(records1, records2)  # 0.66



公式参考： 方差（variance）、标准差（Standard Deviation）、均方差、均方根值（RMS）、均方误差（MSE）、均方根误差（RMSE）

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• 在机器学习中，当我们要查看模型的准确性时，我们用数学上的平均值来计算测试值和预测值之间出现的误差均方根： For a single value: 对于单个值： Let a= (predicted value- actual value) ^2 Let b= mean of a ...

Hello learners, welcome to yet another article on machine learning. Today we would be looking at one of the methods to determine the accuracy of our model in predicting the target values. All of you reading this article must have heard about the term RMS i.e. Root Mean Square and you might have also used RMS values in statistics as well. In machine Learning when we want to look at the accuracy of our model we take the root mean square of the error that has occurred between the test values and the predicted values mathematically:
大家好，欢迎阅读关于机器学习的另一篇文章。 今天，我们将研究确定模型预测目标值准确性的方法之一。 阅读本文的所有人都必须听说过RMS(即均方根)一词，并且您可能在统计数据中也使用过RMS值。 在机器学习中，当我们要查看模型的准确性时，我们用数学上的平均值来计算测试值和预测值之间出现的误差的均方根：
For a single value:
对于单个值：
    Let a= (predicted value- actual value) ^2
Let b= mean of a = a (for single value)
Then RMSE= square root of b


For a wide set of values RMSE is defined as follows:
对于广泛的值，RMSE定义如下：

Graphically:
图形化：

As you can see in this scattered graph the red dots are the actual values and the blue line is the set of predicted values drawn by our model. Here X represents the distance between the actual value and the predicted line this line represents the error, similarly, we can draw straight lines from each red dot to the blue line. Taking mean of all those distances and squaring them and finally taking the root will give us RMSE of our model.
正如您在此分散图中所看到的，红点是实际值，蓝线是我们的模型绘制的一组预测值。 这里的X表示实际值与预测线之间的距离，该线表示误差，类似地，我们可以绘制从每个红点到蓝线的直线。 取所有这些距离的平均值并平方，最后求根将为我们提供模型的RMSE。
Let us write a python code to find out RMSE values of our model. We would be predicting the brain weight of the users. We would be using linear regression to train our model, the data set used in my code can be downloaded from here: headbrain6
Python code:
Python代码：
# -*- coding: utf-8 -*-
"""
Created on Sun Jul 29 22:21:12 2018

@author: Raunak Goswami
"""
import time
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

"""
here the directory of my code and the headbrain6.csv file
is same make sure both the files are stored in same folder or directory
"""
x=data.iloc[:,2:3].values
y=data.iloc[:,3:4].values

#splitting the data into training and test
from sklearn.cross_validation import train_test_split
x_train,x_test,y_train,y_test=train_test_split(x,y,test_size=1/4,random_state=0)

#fitting simple linear regression to the training set
from sklearn.linear_model import LinearRegression
regressor=LinearRegression()
regressor.fit(x_train,y_train)

#predict the test result
y_pred=regressor.predict(x_test)

#to see the relationship between the training data values
plt.scatter(x_train,y_train,c='red')
plt.show()

#to see the relationship between the predicted
#brain weight values using scattered graph
plt.plot(x_test,y_pred)
plt.scatter(x_test,y_test,c='red')
plt.ylabel('brain weight')

#errorin each value
for i in range(0,60):
print("Error in value number",i,(y_test[i]-y_pred[i]))
time.sleep(1)

#combined rmse value
mse=np.mean((y_test-y_pred)**2)
print("Final rmse value is =",np.sqrt(np.mean((y_test-y_pred)**2)))


.minHeight{
min-height: 250px;
}
@media (min-width: 1025px){
.minHeight{
min-height: 90px;
}
}

.minHeight{
min-height: 250px;
}
@media (min-width: 1025px){
.minHeight{
min-height: 90px;
}
}

Outputs:
输出：

The RMSE value of our is coming out to be approximately 73 which is not bad. A good model should have an RMSE value less than 180. In case you have a higher RMSE value, this would mean that you probably need to change your feature or probably you need to tweak your hyperparameters. In case you want to know how did the model predicted the values, just have a look at my previous article on linear regression.
我们的RMSE值约为73，这还不错。 好的模型的RMSE值应小于180。如果您具有较高的RMSE值，则意味着您可能需要更改功能或调整超参数。 如果您想了解模型如何预测值，请看一下我以前关于线性回归的文章。

翻译自: https://www.includehelp.com/ml-ai/root-mean-square error-rmse.aspx


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• """ 均方根误差：是均方误差的算术平方根 """ mse = get_mse(records_real, records_predict) if mse: return math.sqrt(mse) else: return None def get_mae(records_real, records_predict): """ 平均绝对误差 "...
# -*- coding: utf-8 -*-

import math

def get_average(records):
"""
平均值
"""
return sum(records) / len(records)

def get_variance(records):
"""
方差 反映一个数据集的离散程度
"""
average = get_average(records)
return sum([(x - average) ** 2 for x in records]) / len(records)

def get_standard_deviation(records):
"""
标准差 == 均方差 反映一个数据集的离散程度
"""
variance = get_variance(records)
return math.sqrt(variance)

def get_rms(records):
"""
均方根值 反映的是有效值而不是平均值
"""
return math.sqrt(sum([x ** 2 for x in records]) / len(records))

def get_mse(records_real, records_predict):
"""
均方误差 估计值与真值 偏差
"""
if len(records_real) == len(records_predict):
return sum([(x - y) ** 2 for x, y in zip(records_real, records_predict)]) / len(records_real)
else:
return None

def get_rmse(records_real, records_predict):
"""
均方根误差：是均方误差的算术平方根
"""
mse = get_mse(records_real, records_predict)
if mse:
return math.sqrt(mse)
else:
return None

def get_mae(records_real, records_predict):
"""
平均绝对误差
"""
if len(records_real) == len(records_predict):
return sum([abs(x - y) for x, y in zip(records_real, records_predict)]) / len(records_real)
else:
return None

if __name__ == '__main__':
records1 = [3, 4, 5]
records2 = [2, 4, 6]

# 平均值
average1 = get_average(records1)  # 4.0
average2 = get_average(records2)  # 4.0

# 方差
variance1 = get_variance(records1)  # 0.66
variance2 = get_variance(records2)  # 2.66

# 标准差
std_deviation1 = get_standard_deviation(records1)  # 0.81
std_deviation2 = get_standard_deviation(records2)  # 1.63

# 均方根
rms1 = get_rms(records1)  # 4.08
rms2 = get_rms(records2)  # 4.32

# 均方误差
mse = get_mse(records1, records2)  # 0.66

# 均方根误差
rmse = get_rmse(records1, records2)  # 0.81

# 平均绝对误差
mae = get_mae(records1, records2)  # 0.66

具体对某组数据操作可参考下例：
#导入math包
import math
#定义点的函数
class Point:
def __init__(self,x=0,y=0):
self.x=x
self.y=y
def getx(self):
return self.x
def gety(self):
return self.y
#定义直线函数
class Getlen:
def __init__(self,p1,p2):
self.x=p1.getx()-p2.getx()
self.y=p1.gety()-p2.gety()
#用math.sqrt（）求平方根
self.len= math.sqrt((self.x**2)+(self.y**2))
#定义得到直线长度的函数
def getlen(self):
return self.len

#设置点p1的坐标为（0,0）
p1=Point(0,0)
#设置点p2的坐标为（3,4）
p2=Point(3,4)
#定义对象
l=Getlen(p1,p2)
#获取两点之间直线的长度
d=l.getlen())

或者
    import numpy as np
import math
p1=np.array([0,0])
p2=np.array([1000,2000])
p3=p2-p1
p4=math.hypot(p3[0],p3[1])
print(p4)

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• 利用Python计算Excel表里多个sheet的均方根误差（RMSE）。前提是在已经知晓你的Excel表中有多少个Sheet，使用for循环，快速计算每个sheet的均方根误差
• print("RMSE = ", sqrt(sum(squaredError) / len(squaredError)))#均方根误差RMSE print("MAE = ", sum(absError) / len(absError))#平均绝对误差MAE aDeviation = [] aMean = sum(a) / len(a)#a平均值 for val...
from scipy.stats import pearsonr a=[2187,1817.5,1696.5,2217,2208.7,2305,2205.7,2299,2414,2109,1695.5,2277.5,2227,1989.5,2183.5,2142,2125,2018.5,2182.1,2124.5,1954,1930.3,1995.5,2329,2003.5,2282.5,2042,2503.5,2128,2123.5,2081.5,1883,1973.5,1876.5,1823.5,1754.5,2004.5,2000.5,1741.5,1680,1703,1735.5,1923.5,1668.4,2086,1485.5,1462,1342,2133.5,2039,1999.7,2005.5,1974,1927.6,2091,2034.5,1948.5,1926.1,2338,2265.5,2178.5,2075.5,2265] b=[2006,1917,1740,2595,2595,2595,2595,2290,2290,2290,2101,2101,2193,2101,2193,2193,2188,2188,2188,2188,2042,1942,2042,2309,2247,2351,2351,2467,2247,2247,2247,2142,2142,2028,2042,1917,2101,1942,1942,1820,1820,1820,1947,1853,1947,1814,1738,1738,2054,2054,2054,2054,2153,2187,2187,2538,2153,2153,2497,2497,2538,2538,2537] print(pearsonr(a, b))
error = [] for i in range(len(a)): error.append(a[i] - b[i])
print("Errors: ", error) print(error)
squaredError = [] absError = [] for val in error: squaredError.append(val * val)#a-b之差平方 absError.append(abs(val))#误差绝对值
print("Square Error: ", squaredError) print("Absolute Value of Error: ", absError) print("MSE = ", sum(squaredError) / len(squaredError))#均方误差MSE
from math import sqrt print("RMSE = ", sqrt(sum(squaredError) / len(squaredError)))#均方根误差RMSE print("MAE = ", sum(absError) / len(absError))#平均绝对误差MAE
aDeviation = [] aMean = sum(a) / len(a)#a平均值 for val in a: aDeviation.append((val - aMean) * (val - aMean)) print("a efficiency = ", 1-sum(squaredError) / sum(aDeviation))#效率系数E
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• 用于机器学习回归问题的两个最常见的性能评价指标是均方根误差（RMSE）和皮尔逊相关系数（R2） import numpy as np import pandas as pd y_true = np.array([0, 0, 0, 1, 1, 1, 1, 1, 1, 1]) y_pred = np.array([0,...
• Root Mean Square Error, 均方根误差 是观测值与真值偏差的平方和与观测次数 m 比值的平方根。 是用来衡量观测值同真值之间的偏差 MAE Mean Absolute Error ，平均绝对误差 是绝对误差的平均值 能更好地反映预测值...
• python实现回归相关系数计算的几种方法 #计算回归相关系数的方法 确定Ok #第一种 def calc_corr(a,b): a_avg = sum(a)/len(a) b_avg = sum(b)/len(b) cov_ab = sum([(x - a_avg)*(y - b_avg) for x,y in zip(a, ...
• ", sqrt(sum(squaredError) / len(squaredError)))#均方根误差RMSE print("MAE = ", sum(absError) / len(absError))#平均绝对误差MAE aDeviation = [] aMean = sum(a) / len(a)#a平均值 for val in a: aDeviation....
• 用作主要误差标准的根差百分比 (PRD)。
• RMSE（Root Mean Square Error）均方根误差 均方根误差是预测值与真实值偏差的平方与观测次数n比值的平方根。 衡量的是预测值与真实值之间的偏差，并且对数据中的异常值较为敏感。 RMSE与其他指标的对比： ...
• MSE: Mean Squared Error 均方误差是指参数估计...均方根误差:均方根误差是均方误差的算术平方根 MAE :Mean Absolute Error 平均绝对误差是绝对误差的平均值 平均绝对误差能更好地反映预测值误差的实际情况. fi...
• import numpy as np from sklearn import metrics # 定义MAPE def mape(y_true, y_pred): return np.mean(np.abs((y_pred - y_true) / y_true)) * 100 # MSE print(metrics.mean_squared_error(y_true, y_pred)...
• 均方根误差在图像的质量评价中相当于一个中间的评价指标，很多后续的评价指标都是沿用均方根误差均方根误差主要是评价已知图像和退化图像之间误差大小。其实这个指标跟最小二乘的原理多少有些类似，也跟统计知识的...
• python的Scipy.optimize中有函数可以用来拟合函数，可以用来求参数和误差。需要有一组二维数据X和Y样本，根据数据假设函数的形式，然后根基最函数值与样本数据Y的差的平方的和来判定合适的参数，然后再求得误差。...
• 我们要编程计算所选直线的平均平方误差(MSE), 即数据集中每个点到直线的Y方向距离的平方的平均数，表达式如下： MSE=1n∑i=1n(yi−mxi−b)2 最初麻烦的写法 # TODO 实现以下函数并输出所选直线的MSE def ...
• %均方根误差MSE PSNR = 10*log10(255^2/MSE);%峰值信噪比 MAE=mean(mean(abs(D)));%平均绝对误差 w = fspecial('gaussian', 11, 1.5); %window 加窗 K(1) = 0.01; K(2) = 0.03; L = 255; Z = double(Z); X = ...
• slam 轨迹误差
• 2019独角兽企业重金招聘Python工程师标准>>> ...
• import open3d as o3d import numpy as np #--------------------读取点云数据------------------- source = o3d.io.read_point_cloud("C1.pcd") target = o3d.io.read_point_cloud(...print("均方根误差 RMSE=",rmse)
• 方差（variance)：衡量随机变量或一组数据时离散程度的度量。概率论中方差用来度量随机变量和其数学期望（即均值）之间的偏离程度。统计中的方差（样本方差）是每个样本值与全体样本值的平均数之差的平方值的平均数...
• 我们通常采用MSE、RMSE、MAE、R2来评价回归预测算法。 1、均方误差：MSE（Mean Squared Error） 其中，为测试集上真实值-预测值。...2、均方根误差：RMSE（Root Mean Squard Error） 可以看出，RMSE=sqrt（MS...
• 内容较多，如有错误之处请评论区留言以便更正，内容仅供参考。 文章目录期望（Expected value）意义定义离散型连续型期望与平均值的...square error, MSE）python实现代码均方根误差（root mean squared error，RMS.
• 2019独角兽企业重金招聘Python工程师标准>>> ...

...

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