why im getting high MAE(mean absolute error) and MSE(mean square erro) compared to MAPE (mean absolute persentage error)?

Question

everyone I'm a newbie in data science. I'm working on a regression problem using support vector regression. After tunning SVM parameters using grid search I got 2.6% MAPE but my MAE and MSE are still very high.

I have used a user-defined function for mape.

from sklearn.metrics import mean_absolute_error 
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import Normalizer
import matplotlib.pyplot as plt
def mean_absolute_percentage_error(y_true, y_pred): 
    y_true, y_pred = np.array(y_true), np.array(y_pred)
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

import pandas as pd
from sklearn import preprocessing

features=pd.read_csv('selectedData.csv')
import numpy as np
from scipy import stats
print(features.shape)
features=features[(np.abs(stats.zscore(features)) < 3).all(axis=1)]
target = features['SYSLoad']
features= features.drop('SYSLoad', axis = 1)
names=list(features)

for i in names:
    x=features[[i]].values.astype(float)
    min_max_scaler = preprocessing.MinMaxScaler()
    x_scaled = min_max_scaler.fit_transform(x)
    features[i]=x_scaled

Selecting the target Variable which want to predict and for which we are

finding feature imps

import numpy as np
from sklearn.model_selection import train_test_split
train_input, test_input, train_target, test_target = 
train_test_split(features, target, test_size = 0.25, random_state = 42)
trans=Normalizer().fit(train_input);
train_input=Normalizer().fit_transform(train_input);
test_input=trans.fit_transform(test_input);

n=test_target.values;
test_targ=pd.DataFrame(n);

from sklearn.svm import SVR
svr_rbf = SVR(kernel='poly', C=10, epsilon=10,gamma=10)
y_rbf = svr_rbf.fit(train_input, train_target);
predicted=y_rbf.predict(test_input);
plt.figure
plt.xlim(20,100);
print('Total Days For training',len(train_input)); print('Total Days For 
Testing',len(test_input))
plt.ylabel('Load(MW) Prediction 3 '); plt.xlabel('Days'); 
plt.plot(test_targ,'-b',label='Actual'); plt.plot(predicted,'-r',label='RBF 
kernel ');
plt.gca().legend(('Actual','RBF'))
plt.title('SVM')
plt.show();



MAPE=mean_absolute_percentage_error(test_target,predicted);
print(MAPE);
mae=mean_absolute_error(test_targ,predicted)
mse=mean_squared_error(test_targ, predicted)
print(mae);
print(mse);

I'm getting MAPE = 2.56 , MAE =400 , MSE=437696. arent mae and mse are huge. and why they are? My target variable which is sysload contains values in range of 10 thousands

Answer 1

Since you have not provided data, we can not reproduce your example. Bu take a look at this

y_true = [3, -0.5, 2, 7]
y_pred = [2.5, 0.0, 2, 8]

Your code

def mean_absolute_percentage_error(y_true, y_pred): 
    y_true, y_pred = np.array(y_true), np.array(y_pred)
    return np.mean(np.abs((y_true - y_pred) / y_true)) * 100

Output

32.73809523809524

Let's compare

mean_squared_error(y_true, y_pred)
0.375

It is very close. Something is probably wrong with feature selection.