Exercise 9: How to run D-VARS for a set of given input-output data

Objective:

This notebook runs a sensitivity analysis on a set of input-output data, however sampled. The data set may follow any multi-variate distributional and correlational properties.

Example research question 1: Suppose there is a model that you don’t have access to run, but your colleague has already run it and taken a set of input-output sets with some unknown sampling strategy. How can you run a sensitivity analysis on this given data and identify the most important and the least important inputs and rank them?

Example research question 2: Suppose you need to develop a machine-learning model based on a set of given input-output data. The number of potential inputs to the model is large, and you like to do ‘input variable selection’ (also called ‘feature selection’) to possibly reduce the model size for parsimonious reasons. Which inputs may have the most predictive power and which ones do the least?

Example research question 3: Suppose you have collected data on a set of natural variables over some time. These variables might follow any distribution and might be related to each other in complex and unknown ways. What is the strength of possible relationship of each variable to every other variable?