# Joint Manifold Diffusion for Combining Predictions on Decoupled Observations

## TL;DR

This paper introduces a non-parametric manifold diffusion algorithm that enhances predictor combination by automatically aligning heterogeneous predictors across disjoint features, improving performance in ranking tasks.

## Contribution

The paper proposes a novel manifold diffusion-based method for estimating task dependence without parametric assumptions or shared datasets, enabling more flexible predictor combination.

## Key findings

- Outperforms existing predictor combination methods in ranking tasks
- Broadens application range to heterogeneous predictors across disjoint features
- Effectively refines predictor alignments and task dependence estimates

## Abstract

We present a new predictor combination algorithm that improves a given task predictor based on potentially relevant reference predictors. Existing approaches are limited in that, to discover the underlying task dependence, they either require known parametric forms of all predictors or access to a single fixed dataset on which all predictors are jointly evaluated. To overcome these limitations, we design a new non-parametric task dependence estimation procedure that automatically aligns evaluations of heterogeneous predictors across disjoint feature sets. Our algorithm is instantiated as a robust manifold diffusion process that jointly refines the estimated predictor alignments and the corresponding task dependence. We apply this algorithm to the relative attributes ranking problem and demonstrate that it not only broadens the application range of predictor combination approaches but also outperforms existing methods even when applied to classical predictor combination settings.