Business Scenario: A diamond merchant has come to you for help. They want to create an automated system to predict the apt price of a diamond based on its shape/size/color etc.
They have shared the shape/size/color data of 53940 diamonds.
Your task is to create a machine learning model which can predict the price of a diamond based on its characteristics.
In below case study I will discuss the step by step approach to create a Machine Learning predictive model in such scenarios.
You can use this flow as a template to solve any supervised ML Regression problem!
The flow of the case study is as below:
- Reading the data in python
- Defining the problem statement
- Identifying the Target variable
- Looking at the distribution of Target variable
- Basic Data exploration
- Visual Exploratory Data Analysis for data distribution (Histogram and Barcharts)
- Feature Selection based on data distribution
- Outlier treatment
- Missing Values treatment
- Visual correlation analysis
- Statistical correlation analysis (Feature Selection)
- Converting data to numeric for ML
- Sampling and K-fold cross validation
- Trying multiple Regression algorithms
- Selecting the best Model
- Deploying the best model in production
I know its a long list!! Take a deep breath... and let us get started!
Reading the data into python¶
This is one of the most important steps in machine learning! You must understand the data and the domain well before trying to apply any machine learning algorithm.
The data has one file "DiamondpricesData.csv". This file contains 53940 diamond details.
Data description¶
The business meaning of each column in the data is as below
- price: The price of the Diamond
- carat: The carat value of the Diamond
- cut: The cut type of the Diamond, it determines the shine
- color: The color value of the Diamond
- clarity: The carat type of the Diamond
- depth: The depth value of the Diamond
- table: Flat facet on its surface — the large, flat surface facet that you can see when you look at the diamond from above.
- x: Width of the diamond
- y: Length of the diamond
- z: Height of the diamond
# Supressing the warning messages
import warnings
warnings.filterwarnings('ignore')
# Reading the dataset
import pandas as pd
import numpy as np
DiamondpricesData=pd.read_csv('/Users/farukh/Python Case Studies/DiamondpricesData.csv', encoding='latin')
print('Shape before deleting duplicate values:', DiamondpricesData.shape)
# Removing duplicate rows if any
DiamondpricesData=DiamondpricesData.drop_duplicates()
print('Shape After deleting duplicate values:', DiamondpricesData.shape)
# Printing sample data
# Start observing the Quantitative/Categorical/Qualitative variables
DiamondpricesData.head(10)
Determining the type of Machine Learning¶
Based on the problem statement you can understand that we need to create a supervised ML Regression model, as the target variable is Continuous.
Looking at the distribution of Target variable¶
- If target variable's distribution is too skewed then the predictive modeling will not be possible.
- Bell curve is desirable but slightly positive skew or negative skew is also fine
- When performing Regression, make sure the histogram looks like a bell curve or slight skewed version of it. Otherwise it impacts the Machine Learning algorithms ability to learn all the scenarios.
%matplotlib inline
# Creating Bar chart as the Target variable is Continuous
DiamondpricesData['price'].hist()
The data distribution of the target variable is satisfactory to proceed further. There are sufficient number of rows for each type of values to learn from. It is slightly positively skewed. which is acceptable.
Basic Data Exploration¶
This step is performed to guage the overall data. The volume of data, the types of columns present in the data. Initial assessment of the data should be done to identify which columns are Quantitative, Categorical or Qualitative.
This step helps to start the column rejection process. You must look at each column carefully and ask, does this column affect the values of the Target variable? For example in this case study, you will ask, does this column affect the price of the diamond? If the answer is a clear "No", then remove the column immediately from the data, otherwise keep the column for further analysis.
There are four commands which are used for Basic data exploration in Python
- head() : This helps to see a few sample rows of the data
- info() : This provides the summarized information of the data
- describe() : This provides the descriptive statistical details of the data
- nunique(): This helps us to identify if a column is categorical or continuous
# Looking at sample rows in the data
DiamondpricesData.head()
# Observing the summarized information of data
# Data types, Missing values based on number of non-null values Vs total rows etc.
# Remove those variables from data which have too many missing values (Missing Values > 30%)
# Remove Qualitative variables which cannot be used in Machine Learning
DiamondpricesData.info()
# Looking at the descriptive statistics of the data
DiamondpricesData.describe(include='all')
# Finging unique values for each column
# TO understand which column is categorical and which one is Continuous
# Typically if the numer of unique values are < 20 then the variable is likely to be a category otherwise continuous
DiamondpricesData.nunique()
Basic Data Exploration Results¶
Based on the basic exploration above, you can now create a simple report of the data, noting down your observations regaring each column. Hence, creating a initial roadmap for further analysis.
The selected columns in this step are not final, further study will be done and then a final list will be created
- price: Continuous. Selected. This is the Target Variable!
- carat: Continuous. Selected.
- cut: Categorical. Selected.
- color: Categorical. Selected.
- clarity: Categorical. Selected.
- depth: Continuous. Selected.
- table: Continuous. Selected.
- x: Continuous. Selected.
- y: Continuous. Selected.
- z: Continuous. Selected.
Visual Exploratory Data Analysis¶
- Categorical variables: Bar plot
- Continuous variables: Histogram
Visualize distribution of all the Categorical Predictor variables in the data using bar plots¶
We can spot a categorical variable in the data by looking at the unique values in them. Typically a categorical variable contains less than 20 Unique values AND there is repetition of values, which means the data can be grouped by those unique values.
Based on the Basic Data Exploration above, we have spotted three categorical predictors in the data
Categorical Predictors: 'cut', 'color', 'clarity'
We use bar charts to see how the data is distributed for these categorical columns.
# Plotting multiple bar charts at once for categorical variables
# Since there is no default function which can plot bar charts for multiple columns at once
# we are defining our own function for the same
def PlotBarCharts(inpData, colsToPlot):
%matplotlib inline
import matplotlib.pyplot as plt
# Generating multiple subplots
fig, subPlot=plt.subplots(nrows=1, ncols=len(colsToPlot), figsize=(20,5))
fig.suptitle('Bar charts of: '+ str(colsToPlot))
for colName, plotNumber in zip(colsToPlot, range(len(colsToPlot))):
inpData.groupby(colName).size().plot(kind='bar',ax=subPlot[plotNumber])
#####################################################################
# Calling the function
PlotBarCharts(inpData=DiamondpricesData, colsToPlot=['cut', 'color', 'clarity'])
Bar Charts Interpretation¶
These bar charts represent the frequencies of each category in the Y-axis and the category names in the X-axis.
In the ideal bar chart each category has comparable frequency. Hence, there are enough rows for each category in the data for the ML algorithm to learn.
If there is a column which shows too skewed distribution where there is only one dominant bar and the other categories are present in very low numbers. These kind of columns may not be very helpful in machine learning. We confirm this in the correlation analysis section and take a final call to select or reject the column.
If the bars are too skewed, like there is just one bar which is dominating and other categories have very less rows or there is just one value only. Such columns are not correlated with the target variable because there is no information to learn. The algorithms cannot find any rule like when the value is this then the target variable is that.
Selected Categorical Variables: In this data, all three categorical variables are selected for further analysis.
'cut', 'color', 'clarity'
Visualize distribution of all the Continuous Predictor variables in the data using histograms¶
Based on the Basic Data Exploration, Three continuous predictor variables 'ApplicantIncome', 'CoapplicantIncome',and 'LoanAmount'.
# Plotting histograms of multiple columns together
DiamondpricesData.hist(['carat', 'depth', 'table', 'x','y','z'], figsize=(18,10))
Histogram Interpretation¶
Histograms shows us the data distribution for a single continuous variable.
The X-axis shows the range of values and Y-axis represent the number of values in that range. For example, in the above histogram of "carat", there are around 25000 rows in data that has a value between 0 to 0.5.
The ideal outcome for histogram is a bell curve or slightly skewed bell curve. If there is too much skewness, then outlier treatment should be done and the column should be re-examined, if that also does not solve the problem then only reject the column.
Selected Continuous Variables:
- carat : Selected. The distribution is good.
- table: Selected. The distribution is good.
- depth: Selected. The distribution is good.
- x: Selected. Outliers seen near 0, need to treat them.
- y: Selected. Outliers seen beyond 20, need to treat them.
- z: Selected. Outliers seen beyond 10, need to treat them.
Outlier treatment¶
Outliers are extreme values in the data which are far away from most of the values. You can see them as the tails in the histogram.
Outlier must be treated one column at a time. As the treatment will be slightly different for each column.
Why I should treat the outliers?
Outliers bias the training of machine learning models. As the algorithm tries to fit the extreme value, it goes away from majority of the data.
There are below two options to treat outliers in the data.
- Option-1: Delete the outlier Records. Only if there are just few rows lost.
- Option-2: Impute the outlier values with a logical business value
Below we are finding out the most logical value to be replaced in place of outliers by looking at the histogram.
Replacing outliers for 'x'¶
# Finding nearest values to 2 mark
DiamondpricesData['x'][DiamondpricesData['x']>2].sort_values(ascending=True)
The above result shows that the nearest logical value is 3.73, hence replacing any values less than that with it.
# Replacing outliers with nearest possibe value
DiamondpricesData['x'][DiamondpricesData['x']<3.73] =3.73
Replacing outliers for 'y'¶
# Finding nearest values to 20 mark
DiamondpricesData['y'][DiamondpricesData['y']<20].sort_values(ascending=False)
Above result shows the nearest logical value is 10.54, hence, replacing any value above 20 with it.
# Replacing outliers with nearest possibe value
DiamondpricesData['y'][DiamondpricesData['y']>20] =10.54
Replacing outliers for 'z'¶
# Finding nearest values to 10 mark
DiamondpricesData['z'][DiamondpricesData['z']<10].sort_values(ascending=False)
Above result shows the nearest logical value is 6.98, hence, replacing any value above 8 with it.
# Replacing outliers with nearest possibe value
DiamondpricesData['z'][DiamondpricesData['z']>8] =6.98
Visualizing distribution after outlier treatment¶
The distribution has improved after the outlier treatment. There is still a tail but it is thick, that means there are many values in that range, hence, it is acceptable.
# Plotting the histogram
DiamondpricesData.hist(['x','y', 'z'], figsize=(18,8))
Outliers seen on the left hand side near zero! Need to treat them as well.
Replacing outliers for 'y' on the left side¶
# Finding nearest value beyond 2
DiamondpricesData['y'][DiamondpricesData['y']>2].sort_values(ascending=True)
Above result shows the nearest logical value is 3.68, hence, replacing any value below 2 with it.
# Replacing outliers with nearest possibe value
DiamondpricesData['y'][DiamondpricesData['y']<2] =3.68
Replacing outliers for 'z' on the left side¶
# Finding nearest value beyond 2
DiamondpricesData['z'][DiamondpricesData['z']>2].sort_values(ascending=True)
Above result shows the nearest logical value is 2.06, hence, replacing any value below 2 with it.
# Replacing outliers with nearest possibe value
DiamondpricesData['z'][DiamondpricesData['z']<2] =2.06
Visualizing distribution again after outlier treatment¶
The distribution has improved after the outlier treatment. The outliers on the left side are treated.
# Plotting the histogram
DiamondpricesData.hist(['x','y', 'z'], figsize=(18,8))
Missing values treatment¶
Missing values are treated for each column separately.
If a column has more than 30% data missing, then missing value treatment cannot be done. That column must be rejected because too much information is missing.
There are below options for treating missing values in data.
- Delete the missing value rows if there are only few records
- Impute the missing values with MEDIAN value for continuous variables
- Impute the missing values with MODE value for categorical variables
- Interpolate the values based on nearby values
- Interpolate the values based on business logic
# Finding how many missing values are there for each column
DiamondpricesData.isnull().sum()
I am choosing to replace missing values using Median and Mode values
# Replacing missing value for categorical data using MODE value
DiamondpricesData['color'].fillna(value=DiamondpricesData['color'].mode()[0], inplace=True)
# Replacing missing value for continuous data using median value
DiamondpricesData['depth'].fillna(value=DiamondpricesData['depth'].median(), inplace=True)
# Checking missing values again after treatment
DiamondpricesData.isnull().sum()
Feature Selection¶
Now its time to finally choose the best columns(Features) which are correlated to the Target variable. This can be done directly by measuring the correlation values or ANOVA/Chi-Square tests. However, it is always helpful to visualize the relation between the Target variable and each of the predictors to get a better sense of data.
I have listed below the techniques used for visualizing relationship between two variables as well as measuring the strength statistically.
Visual exploration of relationship between variables¶
- Continuous Vs Continuous ---- Scatter Plot
- Categorical Vs Continuous---- Box Plot
- Categorical Vs Categorical---- Grouped Bar Plots
Statistical measurement of relationship strength between variables¶
- Continuous Vs Continuous ---- Correlation matrix
- Categorical Vs Continuous---- ANOVA test
- Categorical Vs Categorical--- Chi-Square test
In this case study the Target variable is Continuous, hence below two scenarios will be present
- Continuous Target Variable Vs Continuous Predictor
- Continuous Target Variable Vs Categorical Predictor
Relationship exploration: Continuous Vs Continuous -- Scatter Charts¶
When the Target variable is continuous and the predictor is also continuous, we can visualize the relationship between the two variables using scatter plot and measure the strength of relation using pearson's correlation value.
ContinuousCols=['carat', 'depth', 'table', 'x','y','z']
# Plotting scatter chart for each predictor vs the target variable
for predictor in ContinuousCols:
DiamondpricesData.plot.scatter(x=predictor, y='price', figsize=(10,5), title=predictor+" VS "+ 'price')
Scatter charts interpretation¶
What should you look for in these scatter charts?
Trend. You should try to see if there is a visible trend or not. There could be three scenarios
Increasing Trend: This means both variables are positively correlated. In simpler terms, they are directly proportional to each other, if one value increases, other also increases. This is good for ML!
Decreasing Trend: This means both variables are negatively correlated. In simpler terms, they are inversely proportional to each other, if one value increases, other decreases. This is also good for ML!
No Trend: You cannot see any clear increasing or decreasing trend. This means there is no correlation between the variables. Hence the predictor cannot be used for ML.
Based on this chart you can get a good idea about the predictor, if it will be useful or not. You confirm this by looking at the correlation value.
Outliers seen in the scatter charts¶
In the above scatter charts you can observe some of the points in x, y and z columns, which are in the lower range. There is a straight line on the left side.
These points will interfere with the model fit.
Hence they must be removed from the data.
# Creating a data filter to remove outliers from data
DataFilter=(DiamondpricesData['z']>2.06) & (DiamondpricesData['z']<6.5)
DiamondpricesData=DiamondpricesData[DataFilter]
Looking at the scatter charts again after outlier removal¶
ContinuousCols=['carat', 'depth', 'table', 'x','y','z']
# Plotting scatter chart for each predictor vs the target variable
for predictor in ContinuousCols:
DiamondpricesData.plot.scatter(x=predictor, y='price', figsize=(10,5), title=predictor+" VS "+ 'price')
Statistical Feature Selection (Continuous Vs Continuous) using Correlation value¶
Pearson's correlation coefficient can simply be calculated as the covariance between two features $x$ and $y$ (numerator) divided by the product of their standard deviations (denominator):
- This value can be calculated only between two numeric columns
- Correlation between [-1,0) means inversely proportional, the scatter plot will show a downward trend
- Correlation between (0,1] means directly proportional, the scatter plot will show a upward trend
- Correlation near {0} means No relationship, the scatter plot will show no clear trend.
- If Correlation value between two variables is > 0.5 in magnitude, it indicates good relationship the sign does not matter
- We observe the correlations between Target variable and all other predictor variables(s) to check which columns/features/predictors are actually related to the target variable in question
# Calculating correlation matrix
ContinuousCols=['price','carat', 'depth', 'table', 'x','y','z']
# Creating the correlation matrix
CorrelationData=DiamondpricesData[ContinuousCols].corr()
CorrelationData
# Filtering only those columns where absolute correlation > 0.5 with Target Variable
# reduce the 0.5 threshold if no variable is selected like in this case
CorrelationData['price'][abs(CorrelationData['price']) > 0.2 ]
Final selected Continuous columns:
'carat', 'x','y','z'
Relationship exploration: Categorical Vs Continuous -- Box Plots¶
When the target variable is Continuous and the predictor variable is Categorical we analyze the relation using Boxplots and measure the strength of relation using Anova test
# Box plots for Categorical Target Variable "price" and continuous predictors
CategoricalColsList=['cut', 'color', 'clarity']
import matplotlib.pyplot as plt
fig, PlotCanvas=plt.subplots(nrows=1, ncols=len(CategoricalColsList), figsize=(18,5))
# Creating box plots for each continuous predictor against the Target Variable "price"
for PredictorCol , i in zip(CategoricalColsList, range(len(CategoricalColsList))):
DiamondpricesData.boxplot(column='price', by=PredictorCol, figsize=(5,5), vert=True, ax=PlotCanvas[i])
Box-Plots interpretation¶
What should you look for in these box plots?
These plots gives an idea about the data distribution of continuous predictor in the Y-axis for each of the category in the X-Axis.
If the distribution looks similar for each category(Boxes are in the same line), that means the the continuous variable has NO effect on the target variable. Hence, the variables are not correlated to each other.
On the other hand if the distribution is different for each category(the boxes are not in same line!). It hints that these variables might be correlated with price.
In this data, all three categorical predictors looks correlated with the Target variable.
We confirm this by looking at the results of ANOVA test below
Statistical Feature Selection (Categorical Vs Continuous) using ANOVA test¶
Analysis of variance(ANOVA) is performed to check if there is any relationship between the given continuous and categorical variable
- Assumption(H0): There is NO relation between the given variables (i.e. The average(mean) values of the numeric Target variable is same for all the groups in the categorical Predictor variable)
- ANOVA Test result: Probability of H0 being true
# Defining a function to find the statistical relationship with all the categorical variables
def FunctionAnova(inpData, TargetVariable, CategoricalPredictorList):
from scipy.stats import f_oneway
# Creating an empty list of final selected predictors
SelectedPredictors=[]
print('##### ANOVA Results ##### \n')
for predictor in CategoricalPredictorList:
CategoryGroupLists=inpData.groupby(predictor)[TargetVariable].apply(list)
AnovaResults = f_oneway(*CategoryGroupLists)
# If the ANOVA P-Value is <0.05, that means we reject H0
if (AnovaResults[1] < 0.05):
print(predictor, 'is correlated with', TargetVariable, '| P-Value:', AnovaResults[1])
SelectedPredictors.append(predictor)
else:
print(predictor, 'is NOT correlated with', TargetVariable, '| P-Value:', AnovaResults[1])
return(SelectedPredictors)
# Calling the function to check which categorical variables are correlated with target
CategoricalPredictorList=['cut', 'color', 'clarity']
FunctionAnova(inpData=DiamondpricesData,
TargetVariable='price',
CategoricalPredictorList=CategoricalPredictorList)
The results of ANOVA confirm our visual analysis using box plots above.
All categorical variables are correlated with the Target variable. This is something we guessed by looking at the box plots!
Final selected Categorical columns:
'cut', 'color', 'clarity'
Selecting final predictors for Machine Learning¶
Based on the above tests, selecting the final columns for machine learning
SelectedColumns=['carat', 'x','y','z','cut', 'color', 'clarity']
# Selecting final columns
DataForML=DiamondpricesData[SelectedColumns]
DataForML.head()
# Saving this final data for reference during deployment
DataForML.to_pickle('DataForML.pkl')
Data Pre-processing for Machine Learning¶
List of steps performed on predictor variables before data can be used for machine learning
- Converting each Ordinal Categorical columns to numeric
- Converting Binary nominal Categorical columns to numeric using 1/0 mapping
- Converting all other nominal categorical columns to numeric using pd.get_dummies()
- Data Transformation (Optional): Standardization/Normalization/log/sqrt. Important if you are using distance based algorithms like KNN, or Neural Networks
Converting the ordinal variable to numeric using mapping¶
# Looking at unique values of ordinal column
DataForML['cut'].unique()
# Replacing the ordinal values
DataForML['cut'].replace({'Good':1,
'Very Good':2,
'Fair':3,
'Ideal':4,
'Premium':5
}, inplace=True)
# Looking at unique values of ordinal column
DataForML['color'].unique()
# Replacing the ordinal values
DataForML['color'].replace({'J':1,
'I':2,
'H':3,
'G':4,
'F':5,
'E':6,
'D':7
}, inplace=True)
# Looking at unique values of ordinal column
DataForML['clarity'].unique()
# Replacing the ordinal values
DataForML['clarity'].replace({'I1':1,
'SI1':2,
'SI2':3,
'VS1':4,
'VS2':5,
'VVS1':6,
'VVS2':7,
'IF':8
}, inplace=True)
Converting the binary nominal variable to numeric using 1/0 mapping¶
No Binary nominal variables in this data
Converting the nominal variable to numeric using get_dummies()¶
# Treating all the nominal variables at once using dummy variables
DataForML_Numeric=pd.get_dummies(DataForML)
# Adding Target Variable to the data
DataForML_Numeric['price']=DiamondpricesData['price']
# Printing sample rows
DataForML_Numeric.head()
Machine Learning: Splitting the data into Training and Testing sample¶
We dont use the full data for creating the model. Some data is randomly selected and kept aside for checking how good the model is. This is known as Testing Data and the remaining data is called Training data on which the model is built. Typically 70% of data is used as Training data and the rest 30% is used as Tesing data.
# Printing all the column names for our reference
DataForML_Numeric.columns
# Separate Target Variable and Predictor Variables
TargetVariable='price'
Predictors=['carat', 'x', 'y', 'z', 'cut', 'color', 'clarity']
X=DataForML_Numeric[Predictors].values
y=DataForML_Numeric[TargetVariable].values
# Split the data into training and testing set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=428)
Standardization/Normalization of data¶
You can choose not to run this step if you want to compare the resultant accuracy of this transformation with the accuracy of raw data.
However, if you are using KNN or Neural Networks, then this step becomes necessary.
### Sandardization of data ###
from sklearn.preprocessing import StandardScaler, MinMaxScaler
# Choose either standardization or Normalization
# On this data Min Max Normalization produced better results
# Choose between standardization and MinMAx normalization
#PredictorScaler=StandardScaler()
PredictorScaler=MinMaxScaler()
# Storing the fit object for later reference
PredictorScalerFit=PredictorScaler.fit(X)
# Generating the standardized values of X
X=PredictorScalerFit.transform(X)
# Split the data into training and testing set
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
# Sanity check for the sampled data
print(X_train.shape)
print(y_train.shape)
print(X_test.shape)
print(y_test.shape)
Multiple Linear Regression¶
# Multiple Linear Regression
from sklearn.linear_model import LinearRegression
RegModel = LinearRegression()
# Printing all the parameters of Linear regression
print(RegModel)
# Creating the model on Training Data
LREG=RegModel.fit(X_train,y_train)
prediction=LREG.predict(X_test)
# Taking the standardized values to original scale
from sklearn import metrics
# Measuring Goodness of fit in Training data
print('R2 Value:',metrics.r2_score(y_train, LREG.predict(X_train)))
###########################################################################
print('\n##### Model Validation and Accuracy Calculations ##########')
# Printing some sample values of prediction
TestingDataResults=pd.DataFrame(data=X_test, columns=Predictors)
TestingDataResults[TargetVariable]=y_test
TestingDataResults[('Predicted'+TargetVariable)]=np.round(prediction)
# Printing sample prediction values
print(TestingDataResults[[TargetVariable,'Predicted'+TargetVariable]].head())
# Calculating the error for each row
TestingDataResults['APE']=100 * ((abs(
TestingDataResults['price']-TestingDataResults['Predictedprice']))/TestingDataResults['price'])
MAPE=np.mean(TestingDataResults['APE'])
MedianMAPE=np.median(TestingDataResults['APE'])
Accuracy =100 - MAPE
MedianAccuracy=100- MedianMAPE
print('Mean Accuracy on test data:', Accuracy) # Can be negative sometimes due to outlier
print('Median Accuracy on test data:', MedianAccuracy)
# Defining a custom function to calculate accuracy
# Make sure there are no zeros in the Target variable if you are using MAPE
def Accuracy_Score(orig,pred):
MAPE = np.mean(100 * (np.abs(orig-pred)/orig))
#print('#'*70,'Accuracy:', 100-MAPE)
return(100-MAPE)
# Custom Scoring MAPE calculation
from sklearn.metrics import make_scorer
custom_Scoring=make_scorer(Accuracy_Score, greater_is_better=True)
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(RegModel, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Decision Trees¶
# Decision Trees (Multiple if-else statements!)
from sklearn.tree import DecisionTreeRegressor
RegModel = DecisionTreeRegressor(max_depth=10,criterion='mse')
# Good Range of Max_depth = 2 to 20
# Printing all the parameters of Decision Tree
print(RegModel)
# Creating the model on Training Data
DT=RegModel.fit(X_train,y_train)
prediction=DT.predict(X_test)
from sklearn import metrics
# Measuring Goodness of fit in Training data
print('R2 Value:',metrics.r2_score(y_train, DT.predict(X_train)))
# Plotting the feature importance for Top 10 most important columns
%matplotlib inline
feature_importances = pd.Series(DT.feature_importances_, index=Predictors)
feature_importances.nlargest(10).plot(kind='barh')
###########################################################################
print('\n##### Model Validation and Accuracy Calculations ##########')
# Printing some sample values of prediction
TestingDataResults=pd.DataFrame(data=X_test, columns=Predictors)
TestingDataResults[TargetVariable]=y_test
TestingDataResults[('Predicted'+TargetVariable)]=np.round(prediction)
# Printing sample prediction values
print(TestingDataResults[[TargetVariable,'Predicted'+TargetVariable]].head())
# Calculating the error for each row
TestingDataResults['APE']=100 * ((abs(
TestingDataResults['price']-TestingDataResults['Predictedprice']))/TestingDataResults['price'])
MAPE=np.mean(TestingDataResults['APE'])
MedianMAPE=np.median(TestingDataResults['APE'])
Accuracy =100 - MAPE
MedianAccuracy=100- MedianMAPE
print('Mean Accuracy on test data:', Accuracy) # Can be negative sometimes due to outlier
print('Median Accuracy on test data:', MedianAccuracy)
# Defining a custom function to calculate accuracy
# Make sure there are no zeros in the Target variable if you are using MAPE
def Accuracy_Score(orig,pred):
MAPE = np.mean(100 * (np.abs(orig-pred)/orig))
#print('#'*70,'Accuracy:', 100-MAPE)
return(100-MAPE)
# Custom Scoring MAPE calculation
from sklearn.metrics import make_scorer
custom_Scoring=make_scorer(Accuracy_Score, greater_is_better=True)
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(RegModel, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Plotting a Decision Tree¶
# Installing the required library for plotting the decision tree
# Make sure to run all three commands
# 1. Open anaconda Prompt
# pip install graphviz
# conda install graphviz
# pip install pydotplus
# Adding graphviz path to the PATH env variable
# Try to find "dot.exe" in your system and provide the path of that folder
import os
os.environ["PATH"] += os.pathsep + 'C:\\Users\\fhashmi\\AppData\\Local\\Continuum\\Anaconda3\\Library\\bin\\graphviz'
# max_depth=10 is too large to plot here
# Load libraries
#from IPython.display import Image
#from sklearn import tree
#import pydotplus
# Create DOT data
#dot_data = tree.export_graphviz(RegModel, out_file=None,
# feature_names=Predictors, class_names=TargetVariable)
# printing the rules
#print(dot_data)
# Draw graph
#graph = pydotplus.graph_from_dot_data(dot_data)
# Show graph
#Image(graph.create_png(), width=5000,height=5000)
# Double click on the graph to zoom in
# This graph with max_depth=10 is too large to plot!!
Random Forest¶
# Random Forest (Bagging of multiple Decision Trees)
from sklearn.ensemble import RandomForestRegressor
RegModel = RandomForestRegressor(max_depth=5, n_estimators=100,criterion='mse')
# Good range for max_depth: 2-10 and n_estimators: 100-1000
# Printing all the parameters of Random Forest
print(RegModel)
# Creating the model on Training Data
RF=RegModel.fit(X_train,y_train)
prediction=RF.predict(X_test)
from sklearn import metrics
# Measuring Goodness of fit in Training data
print('R2 Value:',metrics.r2_score(y_train, RF.predict(X_train)))
# Plotting the feature importance for Top 10 most important columns
%matplotlib inline
feature_importances = pd.Series(RF.feature_importances_, index=Predictors)
feature_importances.nlargest(10).plot(kind='barh')
###########################################################################
print('\n##### Model Validation and Accuracy Calculations ##########')
# Printing some sample values of prediction
TestingDataResults=pd.DataFrame(data=X_test, columns=Predictors)
TestingDataResults[TargetVariable]=y_test
TestingDataResults[('Predicted'+TargetVariable)]=np.round(prediction)
# Printing sample prediction values
print(TestingDataResults[[TargetVariable,'Predicted'+TargetVariable]].head())
# Calculating the error for each row
TestingDataResults['APE']=100 * ((abs(
TestingDataResults['price']-TestingDataResults['Predictedprice']))/TestingDataResults['price'])
MAPE=np.mean(TestingDataResults['APE'])
MedianMAPE=np.median(TestingDataResults['APE'])
Accuracy =100 - MAPE
MedianAccuracy=100- MedianMAPE
print('Mean Accuracy on test data:', Accuracy) # Can be negative sometimes due to outlier
print('Median Accuracy on test data:', MedianAccuracy)
# Defining a custom function to calculate accuracy
# Make sure there are no zeros in the Target variable if you are using MAPE
def Accuracy_Score(orig,pred):
MAPE = np.mean(100 * (np.abs(orig-pred)/orig))
#print('#'*70,'Accuracy:', 100-MAPE)
return(100-MAPE)
# Custom Scoring MAPE calculation
from sklearn.metrics import make_scorer
custom_Scoring=make_scorer(Accuracy_Score, greater_is_better=True)
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(RegModel, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Plotting one of the Decision Trees in Random Forest¶
#max_depth=5 is too large to plot here
# Plotting a single Decision Tree from Random Forest
# Load libraries
#from IPython.display import Image
#from sklearn import tree
#import pydotplus
# Create DOT data for the 6th Decision Tree in Random Forest
#dot_data = tree.export_graphviz(RegModel.estimators_[5] , out_file=None, feature_names=Predictors, class_names=TargetVariable)
# Draw graph
#graph = pydotplus.graph_from_dot_data(dot_data)
# Show graph
#Image(graph.create_png(), width=500,height=500)
# Double click on the graph to zoom in
AdaBoost¶
# Adaboost (Boosting of multiple Decision Trees)
from sklearn.ensemble import AdaBoostRegressor
from sklearn.tree import DecisionTreeRegressor
# Choosing Decision Tree with 1 level as the weak learner
DTR=DecisionTreeRegressor(max_depth=10)
RegModel = AdaBoostRegressor(n_estimators=100, base_estimator=DTR ,learning_rate=0.01)
# Printing all the parameters of Adaboost
print(RegModel)
# Creating the model on Training Data
AB=RegModel.fit(X_train,y_train)
prediction=AB.predict(X_test)
from sklearn import metrics
# Measuring Goodness of fit in Training data
print('R2 Value:',metrics.r2_score(y_train, AB.predict(X_train)))
# Plotting the feature importance for Top 10 most important columns
%matplotlib inline
feature_importances = pd.Series(AB.feature_importances_, index=Predictors)
feature_importances.nlargest(10).plot(kind='barh')
###########################################################################
print('\n##### Model Validation and Accuracy Calculations ##########')
# Printing some sample values of prediction
TestingDataResults=pd.DataFrame(data=X_test, columns=Predictors)
TestingDataResults[TargetVariable]=y_test
TestingDataResults[('Predicted'+TargetVariable)]=np.round(prediction)
# Printing sample prediction values
print(TestingDataResults[[TargetVariable,'Predicted'+TargetVariable]].head())
# Calculating the error for each row
TestingDataResults['APE']=100 * ((abs(
TestingDataResults['price']-TestingDataResults['Predictedprice']))/TestingDataResults['price'])
MAPE=np.mean(TestingDataResults['APE'])
MedianMAPE=np.median(TestingDataResults['APE'])
Accuracy =100 - MAPE
MedianAccuracy=100- MedianMAPE
print('Mean Accuracy on test data:', Accuracy) # Can be negative sometimes due to outlier
print('Median Accuracy on test data:', MedianAccuracy)
# Defining a custom function to calculate accuracy
# Make sure there are no zeros in the Target variable if you are using MAPE
def Accuracy_Score(orig,pred):
MAPE = np.mean(100 * (np.abs(orig-pred)/orig))
#print('#'*70,'Accuracy:', 100-MAPE)
return(100-MAPE)
# Custom Scoring MAPE calculation
from sklearn.metrics import make_scorer
custom_Scoring=make_scorer(Accuracy_Score, greater_is_better=True)
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(RegModel, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Plotting one of the Decision trees from Adaboost¶
# max_depth=10 is too large to plot here
# PLotting 5th single Decision Tree from Adaboost
# Load libraries
#from IPython.display import Image
#from sklearn import tree
#import pydotplus
# Create DOT data for the 6th Decision Tree in Random Forest
#dot_data = tree.export_graphviz(RegModel.estimators_[5] , out_file=None, feature_names=Predictors, class_names=TargetVariable)
# Draw graph
#graph = pydotplus.graph_from_dot_data(dot_data)
# Show graph
#Image(graph.create_png(), width=500,height=500)
# Use a smaller value of max_depth if you wish to plot it here!
XGBoost¶
# Xtreme Gradient Boosting (XGBoost)
from xgboost import XGBRegressor
RegModel=XGBRegressor(max_depth=2,
learning_rate=0.1,
n_estimators=1000,
objective='reg:linear',
booster='gbtree')
# Printing all the parameters of XGBoost
print(RegModel)
# Creating the model on Training Data
XGB=RegModel.fit(X_train,y_train)
prediction=XGB.predict(X_test)
from sklearn import metrics
# Measuring Goodness of fit in Training data
print('R2 Value:',metrics.r2_score(y_train, XGB.predict(X_train)))
# Plotting the feature importance for Top 10 most important columns
%matplotlib inline
feature_importances = pd.Series(XGB.feature_importances_, index=Predictors)
feature_importances.nlargest(10).plot(kind='barh')
###########################################################################
print('\n##### Model Validation and Accuracy Calculations ##########')
# Printing some sample values of prediction
TestingDataResults=pd.DataFrame(data=X_test, columns=Predictors)
TestingDataResults[TargetVariable]=y_test
TestingDataResults[('Predicted'+TargetVariable)]=np.round(prediction)
# Printing sample prediction values
print(TestingDataResults[[TargetVariable,'Predicted'+TargetVariable]].head())
# Calculating the error for each row
TestingDataResults['APE']=100 * ((abs(
TestingDataResults['price']-TestingDataResults['Predictedprice']))/TestingDataResults['price'])
MAPE=np.mean(TestingDataResults['APE'])
MedianMAPE=np.median(TestingDataResults['APE'])
Accuracy =100 - MAPE
MedianAccuracy=100- MedianMAPE
print('Mean Accuracy on test data:', Accuracy) # Can be negative sometimes due to outlier
print('Median Accuracy on test data:', MedianAccuracy)
# Defining a custom function to calculate accuracy
# Make sure there are no zeros in the Target variable if you are using MAPE
def Accuracy_Score(orig,pred):
MAPE = np.mean(100 * (np.abs(orig-pred)/orig))
#print('#'*70,'Accuracy:', 100-MAPE)
return(100-MAPE)
# Custom Scoring MAPE calculation
from sklearn.metrics import make_scorer
custom_Scoring=make_scorer(Accuracy_Score, greater_is_better=True)
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(RegModel, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Plotting a single Decision tree out of XGBoost¶
from xgboost import plot_tree
import matplotlib.pyplot as plt
fig, ax = plt.subplots(figsize=(20, 8))
plot_tree(XGB, num_trees=10, ax=ax)
KNN¶
# K-Nearest Neighbor(KNN)
from sklearn.neighbors import KNeighborsRegressor
RegModel = KNeighborsRegressor(n_neighbors=4)
# Printing all the parameters of KNN
print(RegModel)
# Creating the model on Training Data
KNN=RegModel.fit(X_train,y_train)
prediction=KNN.predict(X_test)
from sklearn import metrics
# Measuring Goodness of fit in Training data
print('R2 Value:',metrics.r2_score(y_train, KNN.predict(X_train)))
# Plotting the feature importance for Top 10 most important columns
# The variable importance chart is not available for KNN
###########################################################################
print('\n##### Model Validation and Accuracy Calculations ##########')
# Printing some sample values of prediction
TestingDataResults=pd.DataFrame(data=X_test, columns=Predictors)
TestingDataResults[TargetVariable]=y_test
TestingDataResults[('Predicted'+TargetVariable)]=np.round(prediction)
# Printing sample prediction values
print(TestingDataResults[[TargetVariable,'Predicted'+TargetVariable]].head())
# Calculating the error for each row
TestingDataResults['APE']=100 * ((abs(
TestingDataResults['price']-TestingDataResults['Predictedprice']))/TestingDataResults['price'])
MAPE=np.mean(TestingDataResults['APE'])
MedianMAPE=np.median(TestingDataResults['APE'])
Accuracy =100 - MAPE
MedianAccuracy=100- MedianMAPE
print('Mean Accuracy on test data:', Accuracy) # Can be negative sometimes due to outlier
print('Median Accuracy on test data:', MedianAccuracy)
# Defining a custom function to calculate accuracy
# Make sure there are no zeros in the Target variable if you are using MAPE
def Accuracy_Score(orig,pred):
MAPE = np.mean(100 * (np.abs(orig-pred)/orig))
#print('#'*70,'Accuracy:', 100-MAPE)
return(100-MAPE)
# Custom Scoring MAPE calculation
from sklearn.metrics import make_scorer
custom_Scoring=make_scorer(Accuracy_Score, greater_is_better=True)
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(RegModel, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Deployment of the Model¶
Based on the above trials you select that algorithm which produces the best average accuracy. In this case, multiple algorithms have produced similar kind of average accuracy. Hence, we can choose any one of them.
I am choosing KNN as the final model since it is very fast for this data!
In order to deploy the model we follow below steps
- Train the model using 100% data available
- Save the model as a serialized file which can be stored anywhere
- Create a python function which gets integrated with front-end(Tableau/Java Website etc.) to take all the inputs and returns the prediction
Choosing only the most important variables¶
Its beneficial to keep lesser number of predictors for the model while deploying it in production. The lesser predictors you keep, the better because, the model will be less dependent hence, more stable.
This is important specially when the data is high dimensional(too many predictor columns).
In this data, the most important predictor variables are 'carat','y', 'color' and 'clarity'
As these are consistently on top of the variable importance chart for every algorithm. Hence choosing these as final set of predictor variables.
# Separate Target Variable and Predictor Variables
TargetVariable='price'
# Selecting the final set of predictors for the deployment
# Based on the variable importance charts of multiple algorithms above
Predictors=['carat','y', 'color' , 'clarity']
X=DataForML_Numeric[Predictors].values
y=DataForML_Numeric[TargetVariable].values
### Sandardization of data ###
from sklearn.preprocessing import StandardScaler, MinMaxScaler
# Choose either standardization or Normalization
# On this data Min Max Normalization produced better results
# Choose between standardization and MinMAx normalization
#PredictorScaler=StandardScaler()
PredictorScaler=MinMaxScaler()
# Storing the fit object for later reference
PredictorScalerFit=PredictorScaler.fit(X)
# Generating the standardized values of X
X=PredictorScalerFit.transform(X)
print(X.shape)
print(y.shape)
Step 1. Retraining the model using 100% data¶
# K-Nearest Neighbor(KNN)
from sklearn.neighbors import KNeighborsRegressor
RegModel = KNeighborsRegressor(n_neighbors=4)
# Training the model on 100% Data available
Final_KNN_Model=RegModel.fit(X,y)
Cross validating the final model accuracy with less predictors¶
# Importing cross validation function from sklearn
from sklearn.model_selection import cross_val_score
# Running 10-Fold Cross validation on a given algorithm
# Passing full data X and y because the K-fold will split the data and automatically choose train/test
Accuracy_Values=cross_val_score(Final_KNN_Model, X , y, cv=10, scoring=custom_Scoring)
print('\nAccuracy values for 10-fold Cross Validation:\n',Accuracy_Values)
print('\nFinal Average Accuracy of the model:', round(Accuracy_Values.mean(),2))
Step 2. Save the model as a serialized file which can be stored anywhere¶
import pickle
import os
# Saving the Python objects as serialized files can be done using pickle library
# Here let us save the Final model
with open('Final_KNN_Model.pkl', 'wb') as fileWriteStream:
pickle.dump(Final_KNN_Model, fileWriteStream)
# Don't forget to close the filestream!
fileWriteStream.close()
print('pickle file of Predictive Model is saved at Location:',os.getcwd())
Step 3. Create a python function¶
# This Function can be called from any from any front end tool/website
def FunctionPredictResult(InputData):
import pandas as pd
Num_Inputs=InputData.shape[0]
# Making sure the input data has same columns as it was used for training the model
# Also, if standardization/normalization was done, then same must be done for new input
# Appending the new data with the Training data
DataForML=pd.read_pickle('DataForML.pkl')
InputData=InputData.append(DataForML)
# Treating ordinal variables
# Replacing the ordinal values of color
InputData['color'].replace({ 'J':1,
'I':2,
'H':3,
'G':4,
'F':5,
'E':6,
'D':7
}, inplace=True)
# Replacing the ordinal values for clarity
InputData['clarity'].replace({'I1':1,
'SI1':2,
'SI2':3,
'VS1':4,
'VS2':5,
'VVS1':6,
'VVS2':7,
'IF':8
}, inplace=True)
# Generating dummy variables for rest of the nominal variables
InputData=pd.get_dummies(InputData)
# Maintaining the same order of columns as it was during the model training
Predictors=['carat','y', 'color' , 'clarity']
# Generating the input values to the model
X=InputData[Predictors].values[0:Num_Inputs]
# Generating the standardized values of X since it was done while model training also
X=PredictorScalerFit.transform(X)
# Loading the Function from pickle file
import pickle
with open('Final_KNN_Model.pkl', 'rb') as fileReadStream:
PredictionModel=pickle.load(fileReadStream)
# Don't forget to close the filestream!
fileReadStream.close()
# Genprice Predictions
Prediction=PredictionModel.predict(X)
PredictionResult=pd.DataFrame(Prediction, columns=['Prediction'])
return(PredictionResult)
# Calling the function for new sample data
NewSampleData=pd.DataFrame(
data=[[0.23,3.98,'E','SI2'],
[0.29, 4.23,'I','VS2']],
columns=['carat','y', 'color' , 'clarity'])
print(NewSampleData)
# Calling the Function for prediction
FunctionPredictResult(InputData= NewSampleData)
The Function FunctionPredictResult() can be used to produce the predictions for one or more cases at a time. Hence, it can be scheduled using a batch job or cron job to run every night and generate predictions for all the loan applications available in the system.
Deploying a predictive model as an API¶
- Django and flask are two popular ways to deploy predictive models as a web service
- You can call your predictive models using a URL from any front end like tableau, java or angular js
Creating the model with few parameters¶
Function for predictions API¶
# Creating the function which can take inputs and return prediction
def FunctionGeneratePrediction(inp_carat, inp_y, inp_color, inp_clarity):
# Creating a data frame for the model input
SampleInputData=pd.DataFrame(
data=[[inp_carat , inp_y, inp_color, inp_clarity]],
columns=['carat','y', 'color', 'clarity'])
# Calling the function defined above using the input parameters
Predictions=FunctionPredictResult(InputData= SampleInputData)
# Returning the predicted value
return(Predictions.to_json())
# Function call
FunctionGeneratePrediction( inp_carat=0.29,
inp_y =4.23,
inp_color='I',
inp_clarity='VS2'
)
# Installing the flask library required to create the API
#!pip install flask
Creating Flask API¶
from flask import Flask, request, jsonify
import pickle
import pandas as pd
import numpy
app = Flask(__name__)
@app.route('/prediction_api', methods=["GET"])
def prediction_api():
try:
# Getting the paramters from API call
carat_value = float(request.args.get('carat'))
y_value=float(request.args.get('y'))
color_value=request.args.get('color')
clarity_value=request.args.get('clarity')
# Calling the funtion to get predictions
prediction_from_api=FunctionGeneratePrediction(
inp_carat=carat_value,
inp_y =y_value,
inp_color=color_value,
inp_clarity=clarity_value
)
return (prediction_from_api)
except Exception as e:
return('Something is not right!:'+str(e))
Starting the API engine¶
import os
if __name__ =="__main__":
# Hosting the API in localhost
app.run(host='127.0.0.1', port=8080, threaded=True, debug=True, use_reloader=False)
# Interrupt kernel to stop the API
Sample URL to call the API¶
Copy and paste below URL in the web browser¶
http://127.0.0.1:8080/prediction_api?carat=0.29&y=4.23&color=I&clarity=VS2
This URL can be called by any front end application like Java, Tableau etc. Once the parameters are passed to it, the predictions will be generated.