Abstract
Currently, the theory and methods of machine learning (ML) are rapidly developing and are increasingly used in various fields of science and technology, in particular in manufacturing, education and medicine. Weakly supervised learning is a subset of machine learning research that aims to develop models and methods for analyzing various types of information. When formulating a weakly supervised learning problem, it is assumed that some objects in the model are not defined correctly. This inaccuracy can be understood in different ways. Weakly supervised learning is a type of machine learning method in which a model is trained using incomplete, inaccurate, or imprecise observation signals rather than using fully validated data. Weakly supervised learning often occurs in real-world problems for various reasons. This may be due to the high cost of the data labeling process, low sensor accuracy, lack of expert experience, or human error. For example, labeling of poor control is carried out in cases obtained by crowdsourcing methods: for each object there is a set of different assessments, the quality of which depends on the skill of the performers. Another example is the problem of object detection in an image. Boundary lines are a common way to indicate the location and size of objects detected in an image in object detection tasks. The article presents an algorithm for solving a multi-objective weakly supervised regression problem using the Wasserstein metric, various regularizations and a co-association matrix as a similarity matrix. The work also improved the algorithm for calculating the weighted average co-association matrix. We compare the proposed algorithm with existing supervised learning and unsupervised learning algorithms on synthetic and real data.