What is it about?

In this paper, we consider the weakly supervised multi-target regression problem where the observed data is partially or imprecisely labelled. The model of the multivariate normal distribution over the target vectors represents the uncertainty arising from the labelling process. The proposed solution is based on the combination of a manifold regularisation method, the use of the Wasserstein distance between multivariate distributions, and a cluster ensemble technique. The method uses a low-rank representation of the similarity matrix. An algorithm for constructing a co-association matrix with calculation of the optimal number of clusters in a partition is presented. To increase the stability and quality of the ensemble clustering, we use k-means with different distance metrics. The experimental part presents the results of numerical experiments with the proposed method on artificially generated data and real data sets. The results show the advantages of the proposed method over existing solutions.

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Why is it important?

Weakly supervised learning is a popular approach for training machine learning models in resource-constrained settings. Instead of requiring high-quality but costly human annotations, it allows models to be trained with noisy annotations from a variety of weak sources.


There are many uncertainties in the observational data and labels. The proposed method can improve the accuracy of the multidimensional weakly supervised regression problem.

Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen

Read the Original

This page is a summary of: Multi-target Weakly Supervised Regression Using Manifold Regularization and Wasserstein Metric, January 2023, Springer Science + Business Media,
DOI: 10.1007/978-3-031-43257-6_27.
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