Normalized mutual information sensitiveness

I would like to know how to conduct sensitivity analysis of three or more parameter variables through mutual information？because NMI or MI can assesses the level of interdependence between variables and reflects the correlation stength between variables

Answer 1

[Nithin Kumar]

Hi Wentong,

I understand that you want to know the process of sensitivity analysis of three or more parameter variables through mutual information. To perform this analysis in MATLAB, kindly refer to the following steps:

1. Prepare Your Data: First, make sure you have your dataset ready with three or more parameter variables which you want to analyze. Additionally, ensure that the data is properly formatted.

2. Calculate Mutual Information: Use the “mutualinfo” function from Statistics and Machine Learning Toolbox to calculate MI or NMI between pairs of variables. If you have three variables, you will need to calculate MI for each pair (variable1-variable2, variable1-variable3, variable2-variable3).

Kindly refer to the following code snippet -

    MI_12 = mutualinfo(variable1, variable2);
    MI_13 = mutualinfo(variable1, variable3);
    MI_23 = mutualinfo(variable2, variable3);

3. Visualize the Results: Use data visualization techniques such as heatmap to show the MI values between pairs of variables. This can help you identify which pairs have the highest interdependence.

4. Analyze the Results: Based on the MI values, you can determine the level of interdependence between your variables. Variables with high MI are more strongly correlated, while those with low MI are less correlated.

5. Perform Sensitivity Analysis: To conduct sensitivity analysis, you can vary the values of one variable while keeping the others constant and observe how it affects MI with the other variables. Use a loop to systematically vary the parameter values and calculate MI at each step.

Kindly refer to the following code snippet -

sensitivity_values  = linspace(min_value, max_value, num_points); % Define a range of values to test
sensitivity_results = zeros(size(sensitivity_values));
for i = 1:length(sensitivity_values)
    variable1_modified = sensitivity_values(i);
    MI_modified = mutualinfo(variable1_modified, variable2); % Calculate MI with the modified variable1
    sensitivity_results(i) = MI_modified;
end
% Plot the sensitivity analysis results
plot(sensitivity_values, sensitivity_results);
xlabel('Variable1 Values');
ylabel('Mutual Information with Variables');
title('Sensitivity Analysis of Variable1');

For more information regarding "mutualinfo" function of MATLAB, kindly refer to the following documentation:

https://in.mathworks.com/matlabcentral/fileexchange/12858-mutualinfo

I hope this provides you with the required information regarding your query.

Regards,

Nithin Kumar.

Answer 2

[wentong]

Thank you very much for your answer. Your reply is very valuable to me