Feature Selection by a Mechanism Design

TL;DR

This paper introduces a novel feature selection method based on a coalitional game mechanism design, which evaluates feature relevance through a hypothesis test of zero mean contribution, leading to improved accuracy in model construction.

Contribution

The paper proposes a new feature selection approach using mechanism design and game theory, providing a theoretically grounded and robust method that outperforms existing techniques.

Findings

Significantly outperforms popular existing methods in simulations

Robust accuracy regardless of payoff function choice

Effectively identifies irrelevant features through valuation testing

Abstract

In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a performance measurement in all possible modeling scenarios. Thus, in theory, an irrelevant feature is equivalent to a dummy player in the game, which contributes nothing to all modeling situations. The hypothesis test of zero mean contribution is the rule to decide a feature is irrelevant or not. In our mechanism design, the end goal perfectly matches the expected model performance with the expected sum of individual marginal effects. Within a class of noninformative likelihood among all modeling opportunities, the matching equation results in a specific valuation for each feature. After estimating the valuation and its standard deviation, we drop any candidate feature if its valuation is not significantly different from zero. In the simulation studies, our new approach significantly outperforms several popular methods used in practice, and its accuracy is robust to the choice of the payoff function.