Structured Conformal Inference for Matrix Completion with Applications to Group Recommender Systems

TL;DR

This paper introduces a model-agnostic conformal inference method for constructing joint confidence regions for groups of missing entries in matrices, enhancing uncertainty quantification in group recommender systems.

Contribution

It proposes a structured conformal inference framework that provides reliable group-level uncertainty estimates, addressing dependencies and computational challenges in matrix completion.

Findings

Method achieves accurate group-level confidence regions.

Demonstrates effectiveness on MovieLens 100K dataset.

Compatible with any matrix completion algorithm.

Abstract

We develop a conformal inference method to construct a joint confidence region for a given group of missing entries within a sparsely observed matrix, focusing primarily on entries from the same column. Our method is model-agnostic and can be combined with any ``black-box'' matrix completion algorithm to provide reliable uncertainty estimation for group-level recommendations. For example, in the context of movie recommendations, it is useful to quantify the uncertainty in the ratings assigned by all members of a group to the same movie, enabling more informed decision-making when individual preferences may conflict. Unlike existing conformal techniques, which estimate uncertainty for one individual at a time, our method provides stronger group-level guarantees by assembling a structured calibration dataset that mimics the dependencies expected in the test group. To achieve this, we introduce a generalized weighted conformalization framework that addresses the lack of exchangeability arising from structured calibration, introducing several innovations to overcome associated computational challenges. We demonstrate the practicality and effectiveness of our approach through extensive numerical experiments and an analysis of the MovieLens 100K dataset.