Manifold regularization in structured output space for semi-supervised structured output prediction

TL;DR

This paper introduces a semi-supervised structured output prediction method that leverages manifold regularization in the input space to improve predictions when output labels are missing for some data points.

Contribution

It proposes a novel approach combining manifold regularization with structured output prediction, unifying slack structured outputs and predictor learning in a single optimization framework.

Findings

Outperforms existing methods on benchmark datasets

Effectively utilizes unlabeled data in structured output prediction

Demonstrates robustness across different structured output types

Abstract

Structured output prediction aims to learn a predictor to predict a structured output from a input data vector. The structured outputs include vector, tree, sequence, etc. We usually assume that we have a training set of input-output pairs to train the predictor. However, in many real-world appli- cations, it is difficult to obtain the output for a input, thus for many training input data points, the structured outputs are missing. In this paper, we dis- cuss how to learn from a training set composed of some input-output pairs, and some input data points without outputs. This problem is called semi- supervised structured output prediction. We propose a novel method for this problem by constructing a nearest neighbor graph from the input space to present the manifold structure, and using it to regularize the structured out- put space directly. We define a slack structured output for each training data point, and proposed to predict it by learning a structured output predictor. The learning of both slack structured outputs and the predictor are unified within one single minimization problem. In this problem, we propose to mini- mize the structured loss between the slack structured outputs of neighboring data points, and the prediction error measured by the structured loss. The problem is optimized by an iterative algorithm. Experiment results over three benchmark data sets show its advantage.