Model Agreement via Anchoring

Eric Eaton, Surbhi Goel, Marcel Hussing, Michael Kearns, Aaron Roth, Sikata Bela Sengupta, Jessica Sorrell

Keywords: model agreement, stacking, gradient boosting, neural networks, regression trees

TL;DR: We develop a simple general technique for proving bounds on independent model disagreement based on anchoring to the average of two models within the analysis.

Abstract:

Numerous lines of aim to control *model disagreement* --- the extent to which two machine learning models disagree in their predictions. We adopt a simple and standard notion of model disagreement in real-valued prediction problems, namely the expected squared difference in predictions between two models trained on independent samples, without any coordination of the training processes.
We would like to be able to drive disagreement to zero with some natural parameter(s) of the training procedure using analyses that can be
applied to existing training methodologies.

We develop a simple general technique for proving bounds on independent model disagreement
based on *anchoring* to the average of two models within the analysis. We then apply this technique to prove disagreement bounds for four commonly used machine learning algorithms: (1) stacked aggregation over an arbitrary model class (where disagreement is driven to 0 with the number of models $k$ being stacked) (2) gradient boosting (where disagreement is driven to 0 with the number of iterations $k$) (3) neural network training with architecture search (where disagreement is driven to 0 with the size $n$ of the architecture being optimized over) and (4) regression tree training over all regression trees of fixed depth (where disagreement is driven to 0 with the depth $d$ of the tree architecture). For clarity, we work out our initial bounds in the setting of one-dimensional regression with squared error loss --- but then show that all of our results generalize to multi-dimensional regression with any strongly convex loss.

Email Sharing: We authorize the sharing of all author emails with Program Chairs.

Data Release: We authorize the release of our submission and author names to the public in the event of acceptance.

Submission Number: 66