Data Envelopment Analysis using Decision making Units, an Analytical Approach
In my last article, I had described on how to calculate feature importances using:
- Convex Optimization
- Lagrangian Minimization
- Shap Library
The plots for Shap values are ordered by its Shap features as described in How to calculate feature importances from a DEA model. They work based on turning off and turning on some features.
Some insights on direct weights obtained from Convex Optimization have been plotted here to enable more discussion on the topic.
In DEA, the problem value denotes the efficiency. Here’s a plot of all features put together.
The size of the bubbles denote the problem value or efficiency of the entire list of sets iterated by switching on and switching off certain features (weights). The graph is represented by “rows x blob weights x efficiency”.

The size of the bubbles denote the feature importances calculated using convex optimization and y axis denotes the efficiency of DEA model of the entire list of sets iterated by switching on and switching off certain features (weights). The graph is represented by “rows x efficiency x blob weights”.

To illustrate, the four large bubbles in the first bubble plot have moved to the top in the second bubble plot. The first plot oscillates from high problem value to low problem value until it finishes the iteration.
DEA method is used in the domain of economics such as analysing the maximization of fuel efficiency based on its input parameters such as driving distance, terrain, traffic, etc. In those cases the decision making units are real world values and the outputs make sense.
