Target customers for a vehicle insurance using machine learning

An insurance company has provided health insurance to its customers and now they want to predict whether the customers from past years will also be interested in a vehicle insurance provided by the company.

Customer targeting consists of identifying those persons that are more prone to a specific product or service.

Contents:

  1. Application type.
  2. Data set.
  3. Neural network.
  4. Training strategy.
  5. Model selection.
  6. Testing analysis.
  7. Model deployment.
  8. Tutorial video.

This example is solved with Neural Designer. In order to follow this example step by step, you can use the free trial.

1. Application type

This is a classification project, since the variable to predict is binary (interested or not interested).

The goal here is to create a model to obtain the probability of being interested as a function of customer features.

2. Data set

The data set contains information to create our model. We need to configure three things:

The data file used for this example is vehicle-insurances.csv, which contains 9 features about 381109 customers of the insurance company.

The data set includes the following variables:

On the other hand, the instances are divided randomly into training, selection and testing subsets, containing 60%, 20% and 20% of the instances, respectively.

Our target variable is response. We can calculate the data distributions and plot a pie chart with the percentage of instances for each class.

As we can see, the target variable is very unbalanced since there are many customers that are not interested on the vehicle insurance, almost 88%, while only 12% are interested, we could say that around 1 out of 10 customers are interested on the vehicle insurance.

Furthermore, we can also compute the inputs-targets correlations, which might indicate which factors have the greatest influence on being interested on the vehicle insurance.

In this example, vehicle_damage and previously_insured are the two variables with the highest correlation, vehicle_damage has a positive correlation while previously_insured has a negative correlation.

3. Neural network

The next step is to set the neural network parameters. For classification problems, it is composed of:

For the scaling layer, the mean and standard deviation scaling method has been set.

We set one perceptron layer with 3 neurons having the logistic activation function. This layer has 7 inputs and since the target variable is binary, only one output.

The neural network for this example can be represented with the following diagram:

4. Training strategy

The fourth step is to set the training strategy, which defines what the neural network will learn. A general training strategy for classification is composed of two terms:

The loss index chosen for this problem is the normalized squared error between the outputs from the neural network and the targets in the data set with L1 regularization.

The selected optimization algorithm is the adaptative linear momentum.

The following chart shows how the training and selection errors develop with the epochs during the training process. The final values are training error = 0.593 NSE and selection error = 0.598 NSE.

5. Model selection

The objective of model selection is to find the network architecture with the best generalization properties, that means to find the one which minimizes the error on the selected instances of the data set.

More specifically, we want to find a neural network with a selection error of less than 0.598 NSE, which is the value that we have achieved so far.

Order selection algorithms train several network architectures with a different number of neurons and select the one with the smallest selection error.

The incremental order method starts with a small number of neurons and increases the complexity at each iteration.

The final selection error achieved is 0.5873 for an optimal number of neurons of 6.

The graph above represents the architecture of the final neural network.

6. Testing analysis

The objective of the testing analysis is to validate the generalization performance of the trained neural network. To validate a classification technique, we need to compare the values provided by this technique to the observed values. We can use the ROC curve as it is the standard testing method for binary classification projects.

The AUC value for this example is 0.8342.

The following table contains the elements of the confusion matrix. This matrix contains the true positives, false positives, false negatives and true negatives for the variable response.

Predicted positive Predicted negative
Real positive 9.1 ∙ 103 (11%) 205 (0%)
Real negative 2.75 ∙ 104 (36%) 3.94 ∙ 104 (51%)

The total number of testing samples is 76221. The number of correctly classified samples is 48519 (63%) and the number of misclassified samples is 27702 (36%).

We are interested in the customers classified as positive (first column), these would be the customers that we would contact to offer the vehicle insurance, and now, the ratio is around 1 out of every 5 customers are interested, which is double of the previous one (1 out of 10). Moreover, the number of true positives classified as negative (customers that are interested but we would not contact) is very low, 205 out of 76221 (0.27%).

We can also observe this results in the positive rates chart:

The initial positive rate was around 12% and now, after applying our model, it is 25%. This means that with this model, we would be able to duplicate the vehicle insurance's sales.

We can also perform the cumulative gain analysis which is a visual aid that shows the advantage of using a predictive model as opposed to randomness. It consists of three lines.

The baseline represents the results that would be obtained without using a model. The positive cumulative gain shows in the y-axis the percentage of positive instances found against the percentage of the population represented in the x-axis. Similarly, the negative cumulative gain shows the percentage of the negative instances found against the population percentage.

In this case, by using the model, we see that by analyzing 50% of the clients with the higher probability of being interested on the vehicle insurance, we would reach almost 100% of clients that would take out the insurance.

Another testing method is the profit chart. This testing method shows the difference in profits from randomness and those using the model depending on the instance ratio.

The values of the previous plot are displayed below:

  • Unitary cost: 10 USD
  • Unitary income: 50 USD
  • Maximum profit: 125877 USD
  • Samples ratio: 0.35
  • In the graph we can observe that having an unitary cost of 10 USD and an unitary income of 50 USD, if we contact 35% of the customers that are most likely to be interested in the vehicle insurance, we would have the maximum benefict (125877 USD).

    7. Model deployment

    The model obtained after all the steps are not the best it could be achieved. Nevertheless, it is still better than guessing randomly.

    The next listing shows the mathematical expression of the predictive model.

    scaled_gender = gender*(1+1)/(1-(0))-0*(1+1)/(1-0)-1;
    scaled_age = age*(1+1)/(85-(20))-20*(1+1)/(85-20)-1;
    scaled_previously_insured = previously_insured*(1+1)/(1-(0))-0*(1+1)/(1-0)-1;
    scaled_vehicle_age = vehicle_age*(1+1)/(3-(1))-1*(1+1)/(3-1)-1;
    scaled_vehicle_damage = vehicle_damage*(1+1)/(1-(0))-0*(1+1)/(1-0)-1;
    scaled_annual_premium = annual_premium*(1+1)/(540165-(2630))-2630*(1+1)/(540165-2630)-1;
    scaled_vintage = vintage*(1+1)/(299-(10))-10*(1+1)/(299-10)-1;
    
    perceptron_layer_output_0 = tanh[ -0.233398 + (scaled_gender*-0.442383)+ (scaled_age*0.807861)+ (scaled_previously_insured*0.963257)+ (scaled_vehicle_age*-0.937439)+ (scaled_vehicle_damage*-0.78479)+ (scaled_annual_premium*-0.0365601)+ (scaled_vintage*-0.572449) ];
    perceptron_layer_output_1 = tanh[ -0.724854 + (scaled_gender*0.927185)+ (scaled_age*0.696899)+ (scaled_previously_insured*-0.251282)+ (scaled_vehicle_age*-0.990173)+ (scaled_vehicle_damage*0.47937)+ (scaled_annual_premium*-0.197021)+ (scaled_vintage*-0.838135) ];
    perceptron_layer_output_2 = tanh[ 0.452454 + (scaled_gender*0.517029)+ (scaled_age*0.893494)+ (scaled_previously_insured*-0.773743)+ (scaled_vehicle_age*0.477539)+ (scaled_vehicle_damage*-0.932251)+ (scaled_annual_premium*-0.0134888)+ (scaled_vintage*0.99707) ];
    perceptron_layer_output_3 = tanh[ -0.59967 + (scaled_gender*0.159912)+ (scaled_age*0.602417)+ (scaled_previously_insured*0.937988)+ (scaled_vehicle_age*-0.426086)+ (scaled_vehicle_damage*-0.157532)+ (scaled_annual_premium*0.194153)+ (scaled_vintage*-0.392334) ];
    perceptron_layer_output_4 = tanh[ -0.649536 + (scaled_gender*-0.85968)+ (scaled_age*0.686707)+ (scaled_previously_insured*0.222839)+ (scaled_vehicle_age*0.263245)+ (scaled_vehicle_damage*-0.328613)+ (scaled_annual_premium*-0.567871)+ (scaled_vintage*-0.525146) ];
    perceptron_layer_output_5 = tanh[ -0.581116 + (scaled_gender*0.530884)+ (scaled_age*-0.667358)+ (scaled_previously_insured*-0.549866)+ (scaled_vehicle_age*-0.768677)+ (scaled_vehicle_damage*-0.619324)+ (scaled_annual_premium*-0.226624)+ (scaled_vintage*-0.885376) ];
    
    	probabilistic_layer_combinations_0 = -0.593079 +0.960022*perceptron_layer_output_0 -0.123474*perceptron_layer_output_1 +0.800903*perceptron_layer_output_2 +0.802307*perceptron_layer_output_3 +0.0870361*perceptron_layer_output_4 +0.528748*perceptron_layer_output_5 
    	
    response = 1.0/(1.0 + exp(-probabilistic_layer_combinations_0);
    

    This formula can be also exported to the software tool required by the company.

    8. Video tutorial

    You can watch the step by step tutorial video below to help you complete this Machine Learning example for free using the powerful machine learning software, Neural Designer.

    References

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