# Discrete-Continuous ADMM for Transductive Inference in Higher-Order MRFs

## TL;DR

This paper presents a new ADMM-based algorithm for transductive inference in higher-order MRFs that jointly optimizes continuous classifier parameters and discrete labels, ensuring global convergence and integrality.

## Contribution

It introduces a decoupled optimization method combining discrete and continuous subproblems with ADMM, improving inference in higher-order MRFs over prior relaxations.

## Key findings

- Effective in video object segmentation on DAVIS dataset
- Preserves label integrality and guarantees convergence
- Outperforms existing relaxation-based methods

## Abstract

This paper introduces a novel algorithm for transductive inference in higher-order MRFs, where the unary energies are parameterized by a variable classifier. The considered task is posed as a joint optimization problem in the continuous classifier parameters and the discrete label variables. In contrast to prior approaches such as convex relaxations, we propose an advantageous decoupling of the objective function into discrete and continuous subproblems and a novel, efficient optimization method related to ADMM. This approach preserves integrality of the discrete label variables and guarantees global convergence to a critical point. We demonstrate the advantages of our approach in several experiments including video object segmentation on the DAVIS data set and interactive image segmentation.