[Paper Review] Predictive Multiplicity in Classification

Charles T. Marx, Flávio P. Calmon+1 more|arXiv (Cornell University)|Sep 14, 2019

Bayesian Modeling and Causal Inference52 references34 citations

TL;DR

This paper defines predictive multiplicity in classification, introduces ambiguity and discrepancy metrics, and develops integer programming tools to compute them exactly for linear classifiers, revealing substantial multiplicity in recidivism datasets.

ABSTRACT

Prediction problems often admit competing models that perform almost equally well. This effect challenges key assumptions in machine learning when competing models assign conflicting predictions. In this paper, we define predictive multiplicity as the ability of a prediction problem to admit competing models with conflicting predictions. We introduce formal measures to evaluate the severity of predictive multiplicity and develop integer programming tools to compute them exactly for linear classification problems. We apply our tools to measure predictive multiplicity in recidivism prediction problems. Our results show that real-world datasets may admit competing models that assign wildly conflicting predictions, and motivate the need to measure and report predictive multiplicity in model development.

Motivation & Objective

• Define predictive multiplicity and motivate its practical relevance in classification tasks.
• Introduce formal measures (ambiguity and discrepancy) to quantify multiplicity.
• Develop integer programming methods to compute these measures exactly for linear classifiers.
• Empirically evaluate predictive multiplicity on recidivism prediction datasets (e.g., COMPAS).

Proposed method

• Define the epsilon-level set around a baseline classifier to capture near-optimal models.
• Formulate DiscMIP to compute maximum disagreement (discrepancy) with the baseline under the epsilon constraint.
• Develop a path algorithm to compute discrepancy across multiple epsilon values efficiently.
• Formulate FlipMIP to construct classifiers that flip a specific data point’s prediction for ambiguity.
• Use mixed-integer programming solvers to obtain exact or bounded solutions for the multiplicity measures.

Experimental results

Research questions

• RQ1 How can predictive multiplicity be formally defined for binary classification?
• RQ2 How can we quantify the severity of multiplicity via ambiguity and discrepancy?
• RQ3 Can we compute these measures exactly for linear classifiers using optimization techniques?
• RQ4 What is the extent of predictive multiplicity in real-world datasets such as recidivism prediction?
• RQ5 How do multiplicity measures relate to baseline model accuracy and deployment decisions?

Key findings

• Competing models with near-equal accuracy can assign highly conflicting predictions on the same data.
• In the ProPublica COMPAS dataset, a competing model 1% less accurate than the best model can assign conflicting predictions to over 17% of individuals, and 44% of individuals’ predictions are affected by model choice.