Multivariate Latent Recalibration for Conditional Normalizing Flows

TL;DR

This paper introduces a novel latent recalibration method for conditional normalizing flows that improves multivariate distribution calibration and provides explicit density functions, enhancing predictive reliability.

Contribution

It proposes latent recalibration (LR), a new post-hoc method that learns transformations in the latent space with finite-sample calibration guarantees, filling a gap in multivariate model calibration.

Findings

LR improves latent calibration error.

LR reduces negative log-likelihood.

Method is computationally efficient.

Abstract

Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor approximation of the joint distribution of the response variables, leading to unreliable predictions and suboptimal decisions. Furthermore, standard recalibration methods are primarily limited to univariate settings, while conformal prediction techniques, despite generating multivariate prediction regions with coverage guarantees, do not provide a full probability density function. We address this gap by first introducing a novel notion of latent calibration, which assesses probabilistic calibration in the latent space of a conditional normalizing flow. Second, we propose latent recalibration (LR), a novel post-hoc model recalibration method that learns a transformation of the latent space with finite-sample bounds on latent calibration. Unlike existing methods, LR produces a recalibrated distribution with an explicit multivariate density function while remaining computationally efficient. Extensive experiments on both tabular and image datasets show that LR consistently improves latent calibration error and the negative log-likelihood of the recalibrated models.