Problem Statement : This problem and the datasets are given in Kaggle and we can download the dataset from here. The dataset comprises of the time stamped weather conditions recorded at different places during the year 1940-1945. The dataset is further decomposed into two sub datasets that are :

• Stations_info.csv
• Weather_Report.csv

Dataset Stations_info.csv:Description of the columns are :

• Station_ID : denotes the id numbers of different places where weather conditions were recorded.
• NAME : names of the corresponding places.
• STATE/COUNTRY ID: state/country codes of the corresponding places.
• LAT: information regarding latitudes in direction format.
• LON: information regarding longitudes in direction format.
• ELEV: elevation of the corresponding place from sea level.
• Latitude: information regarding latitudes in numerical format.
• Longitude: information regarding longitudes in numerical format.

Dataset Weather_Report.csv: Description of the columns are:

• Station_ID : denotes the id numbers of different places where weather conditions were recorded.
• DATE : Timestamps of the reports.
• Precip : Precipitation count in mm.
• MaxTemp : Maximum Temperature in degree Celsius.
• MinTemp : Minimum Temperature in degree Celsius.
• Snowfall : Snowfall count in mm.
• DA : Dates of month.

The challenge is to study some correlations between the given dataset and train a machine learning model to predict the Minimum Temperature when other features are provided. As Minimum Temperature is target variable and it has continuous values so this is Regression problem.

## Solution:

#### Importing Libraries:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

#for implementing Backward Elimination.
import statsmodels.api as sm
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error, r2_score
#for model fitting
from sklearn.linear_model import LinearRegression
from sklearn.svm import SVR
from sklearn.ensemble import RandomForestRegressor
#For implementing k fold cross validation
from sklearn.model_selection import cross_val_score
#For finding the best parameters in the algorithm
from sklearn.model_selection import GridSearchCV


df1 = pd.read_csv('Weather_Report.csv')
df2.head(15)

#### Data Preprocessing:

It can be observed that both the dataframes df1 and df2 have some features which can be useful to predict the Minimum Temperatures. Hence it is a good practice to merge the dataframes and then proceed.

Pandas merge() method provides such functionality.

Merging the data frames on the basis of common feature ie. Station_ID

df_merge = pd.merge(df1,df2,on = 'Station_ID')

df_merge.head(5)

Not all features are relevant in the above dataframe. Some of them are redundant and some of them are absurd to use while predicting the MinTemp feature.

Using drop() method to eliminate.

Here as of now we are removing the features ‘Station_ID’, ‘Date’, ‘NAME’, ‘STATE/COUNTRY ID’, ‘LAT’, ‘LON’, ‘DA’ features.
(Here axis=1 for columns and axis=0 for rows)

final_dataset = df_merge.drop(['Station_ID','Date','NAME','STATE/COUNTRY ID','LAT','LON','DA'],axis=1)
#It can have the assignments to keep LAT, LON and DA columns to prepare the model and please message us in case you get better results. 

#### Checking Nulls:

Pandas isnull().sum() method can be used for finding the null values in each of the features and count() function to display all non null records.
print(final_dataset.isnull().sum())
print(final_dataset.count())

It can be observed that all features are having 102287 entries except Snowfall. Hence Snowfall column has some missing values. Moreover it has some faulty values as ‘#Value!’. Let us see how to deal with these cases.

tf_value = final_dataset[final_dataset['Snowfall']=='#VALUE!']
print(tf_value.shape[0])

#Output:
23

There are 23 faulty values in Snowfall column which are very less in number as compared to total entries. Hence dropping these rows via slicing.

final_dataset = final_dataset[final_dataset['Snowfall']!='#VALUE!']

#Now filling up the null values via padding ie. using previous non null values #and converting all the values to float values as some values might be stored #as string format in the dataset.

final_dataset['Snowfall'].fillna(method = 'ffill',inplace=True)
print(final_dataset.count())
final_dataset = final_dataset.astype(float)


#### EDA (Exploratory Data Analysis):

Using heatmap from seaborn library to visualize correlations amongst different variables.

correlation = final_dataset.corr()
sns.heatmap(correlation,annot=True)
plt.show()

We can observe that dark colored cells are very less correlated with corresponding features and light colored cells are highly correlated with the corresponding features. MaxTemp is found to have very high correlation (0.87) with MinTemp.

Next, plotting Implots from seaborn library to study correlations between MinTemp and other features.

# Correlation between MinTemp and other features

features=['Precip','MaxTemp','Snowfall','ELEV','Latitude','Longitude']
for i in features:
sns.lmplot(x=i, y="MinTemp", data=final_dataset,line_kws={'color': 'red'})
text="Relation between MinTemp and " + i
plt.title(text)
plt.show()

Here we can observe the scattering as well as correlation between the MinTemp and other features. From the second plot we can observe that MaxTeam closely correlates with MinTemp.

Next, we can plot the histograms to observe the outliers and experiment with the model by removing the outliers by certain ratio. (Preferably if they are less than 1% of the whole dataset.)

plt.hist(final_dataset['Precip'])
plt.show()
plt.hist(final_dataset['MaxTemp'])
plt.show()
plt.hist(final_dataset['Snowfall'])
plt.show()
plt.hist(final_dataset['ELEV'])
plt.show()
plt.hist(final_dataset['Latitude'])
plt.show()
plt.hist(final_dataset['Longitude'])
plt.show()
plt.hist(final_dataset['MinTemp'])
plt.show()

We can observe that there are some outliers present here. But currently we are keep the outliers as it is.

Now splitting the dataset into training and testing datasets using 'train_test_split' and rescaling the data using 'StandardScaler'.
X = final_dataset.iloc[:,[0,1,3,4,5,6]]
y = final_dataset.iloc[:,2:3]

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 42)

sc_X = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)
sc_y = StandardScaler()
y_train = sc_y.fit_transform(y_train)

#### Model Training:

We will train the model using different regression algorithm to get a high R-squared value and low Mean Squared Error.

1- Using Linear Regression model to fit the training dataset.

regressor = LinearRegression()
regressor.fit(X_train,y_train)
y_pred = sc_y.inverse_transform(regressor.predict(X_test))
mse_linear = mean_squared_error(y_test,y_pred)
r2_linear= r2_score(y_test, y_pred)
print('Mean Squared Error : ' + str(mse_linear) + '\nR-squared score : ' + str(r2_linear) )

#Output
Mean Squared Error : 13.278779162798093
R-squared score : 0.8062624058591776



2- Using Support Vector Regression to fit the training dataset.

regressor = SVR(kernel = 'linear')
regressor.fit(X_train, y_train)
y_pred = sc_y.inverse_transform(regressor.predict(X_test))
mse_svr = mean_squared_error(y_test,y_pred)
r2_svr= r2_score(y_test, y_pred)
print('Mean Squared Error : ' + str(mse_svr) + '\nR-squared score : ' + str(r2_svr) )

#Output
Mean Squared Error : 13.49954689681221
R-squared score : 0.8030414011924503


3- Using Random forest Regression to fit the training dataset.

regressor = RandomForestRegressor(n_estimators = 100, random_state = 0,verbose = 1)
regressor.fit(X_train,y_train)
y_pred = sc_y.inverse_transform(regressor.predict(X_test))
mse_forest = mean_squared_error(y_test,y_pred)
r2_forest = r2_score(y_test, y_pred)
print('Mean Squared Error : ' + str(mse_forest) + '\nR-squared score : ' + str(r2_forest) )

#Output
Mean Squared Error : 5.088068983374495
R-squared score : 0.9257649945393174


Since a High R-squared value and low Mean Squared Error is desired for a model to be a Good Fit one, it can be concluded that Random Forest Regression outperforms SVR and Linear Regression models.

#### Feature Selection:

Now let us see what all features can be remove and train the model again to get better results. This steps can be merged after EDA also. Here we are using OLS Regression from statsmodels.api library to select features based on p value.

In general we can set a threshold value of p value as 5% ie 0.005. Any feature with p value less than 0.005 should be retained and the features with p values greater than 0.005 must be rejected.

This process should be sequential one ie. first the feature with highest p value should be removed then model should be tested again and in the next turn the other feature with largest p value should be rejected and so on until all features are having p values less than the threshold value.

X = np.append(arr = np.ones((X.shape[0],1)).astype(int),values = X,axis = 1)

X_opt = X[:,[0,1,2,3,4,5,6]]
regressor_OLS = sm.OLS(endog = y,exog = X_opt).fit()
regressor_OLS.summary()

We can observe that in P>|t| column, no value is greater than the set threshold value. Hence all features are relevant and reducing the number of features will only reduce the model’s performance.

#### k-fold cross validation:

Cross-validation is a resampling procedure used to evaluate machine learning models on a limited data sample.

The procedure has a single parameter called k that refers to the number of groups that a given data sample is to be split into. As such, the procedure is often called k-fold cross-validation. When a specific value for k is chosen, it may be used in place of k in the reference to the model, such as k=10 becoming 10-fold cross-validation.

score = cross_val_score(estimator = regressor,X = X_train, y = y_train, cv=10,n_jobs=-1)

mean = score.mean()
std = score.std()

print('Mean score : ' + str(mean) + '\nStandard Deviation : ' + str(std))

#Output
Mean score : 0.9200122114054985
Standard Deviation : 0.003825567902797884


#### Grid Search :

Using Grid search to optimize the n_estimators and min_impurity split of the Random Forest Regression. You can optimize any parameter by listing them in paramters dictionary.

For example here, best of 25,75,100,125,150 will be suggested as n_estimators value and best of 0.00000001 and 0.0000000001 will be suggested as min_impurity_split by the Grid Search process.

parameters = [{'n_estimators' : [25,75,100,125,150],'min_impurity_split':[0.00000001,0.0000000001.0.000000001]}]

grid_search = GridSearchCV(estimator = regressor, param_grid = parameters,cv=10,n_jobs = -1,verbose=1)

grid_search_ = grid_search.fit(X,y)
best_score = grid_search.best_score_
best_params = grid_search.best_params_

print('Best Score : ' + str(best_score) + '\nBest Parameters : ' + str(best_params))

#Output
Best Score : 0.5764613802083562
Best Parameters : {'min_impurity_split': 1e-08, 'n_estimators': 100}


Hence optimal choice of n_estimators is 100 and min_impurity_split is 1e-8 amongst the listed values for each of them.

Below is the complete code to solve this problem and It can download from here :

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

#for implementing Backward Elimination.
import statsmodels.api as sm
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error, r2_score
#for model fitting
from sklearn.linear_model import LinearRegression
from sklearn.svm import SVR
from sklearn.ensemble import RandomForestRegressor
#For implementing k fold cross validation
from sklearn.model_selection import cross_val_score
#For finding the best parameters in the algorithm
from sklearn.model_selection import GridSearchCV

#Merging the dataframes
df_merge = pd.merge(df1,df2,on = 'Station_ID')

#Drop few columns
final_dataset = df_merge.drop(['Station_ID','Date','NAME','STATE/COUNTRY ID','LAT','LON','DA'],axis=1)

#Checking the if columns have null or not.
print(final_dataset.isnull().sum())
print(final_dataset.count())

#Checking faulty values values
tf_value = final_dataset[final_dataset['Snowfall']=='#VALUE!']
print(tf_value.shape[0])

#Remove faulty values
final_dataset = final_dataset[final_dataset['Snowfall']!='#VALUE!']
#Now filling up the null values via padding ie. using previous non null values #and converting all the values to float values as some values might be stored #as string format in the dataset.
final_dataset['Snowfall'].fillna(method = 'ffill',inplace=True)
print(final_dataset.count())
final_dataset = final_dataset.astype(float)

#Analysing the relations
correlation = final_dataset.corr()
sns.heatmap(correlation,annot=True)
plt.show()

features=['Precip','MaxTemp','Snowfall','ELEV','Latitude','Longitude']
for i in features:
sns.lmplot(x=i, y="MinTemp", data=final_dataset,line_kws={'color': 'red'})
text="Relation between MinTemp and " + i
plt.title(text)
plt.show()

plt.hist(final_dataset['Precip'])
plt.show()
plt.hist(final_dataset['MaxTemp'])
plt.show()
plt.hist(final_dataset['Snowfall'])
plt.show()
plt.hist(final_dataset['ELEV'])
plt.show()
plt.hist(final_dataset['Latitude'])
plt.show()
plt.hist(final_dataset['Longitude'])
plt.show()
plt.hist(final_dataset['MinTemp'])
plt.show()

#Create the train and test dataset
X = final_dataset.iloc[:,[0,1,3,4,5,6]]
y = final_dataset.iloc[:,2:3]
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 42)
sc_X = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)
sc_y = StandardScaler()
y_train = sc_y.fit_transform(y_train)

regressor = RandomForestRegressor(n_estimators = 100, random_state = 0,verbose = 1)
regressor.fit(X_train,y_train)
y_pred = sc_y.inverse_transform(regressor.predict(X_test))
mse_forest = mean_squared_error(y_test,y_pred)
r2_forest = r2_score(y_test, y_pred)
print('Mean Squared Error : ' + str(mse_forest) + '\nR-squared score : ' + str(r2_forest) )
#Output
Mean Squared Error : 5.088068983374495
R-squared score : 0.9257649945393174

#GridSearch CV
parameters = [{'n_estimators' : [25,75,100,125,150],'min_impurity_split':[0.00000001,0.0000000001.0.000000001]}]
grid_search = GridSearchCV(estimator = regressor, param_grid = parameters,cv=10,n_jobs = -1,verbose=1)
grid_search_ = grid_search.fit(X,y)
best_score = grid_search.best_score_
best_params = grid_search.best_params_
print('Best Score : ' + str(best_score) + '\nBest Parameters : ' + str(best_params))



Thatâ€™s all I have and thanks a lot for reading. Please let me know if any corrections/suggestions. Please do share and comments if you like the post. Thanks in advanceâ€¦ đŸ˜‰

Thanks Sumit Rai for helping us to grow day by day. He is expert in Machine Learning and AI field and loves to solve the Kaggle problems.

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