Informed machine learning describes the injection of prior knowledge into learning systems. It can help to improve generalization, especially when training data is scarce. However, the field is so application-driven that general analyses about the effect of knowledge injection are rare. This makes it difficult to transfer existing approaches to new applications, or to estimate potential improvements. Therefore, in this paper, we present a framework for quantifying the value of prior knowledge in informed machine learning. Our main contributions are threefold. Firstly, we propose a set of relevant metrics for quantifying the benefits of knowledge injection, comprising in-distribution accuracy, out-of-distribution robustness, and knowledge conformity. We also introduce a metric that combines performance improvement and data reduction. Secondly, we present a theoretical framework that represents prior knowledge in a function space and relates it to data representations and a trained model. This suggests that the distances between knowledge and data influence potential model improvements. Thirdly, we perform a systematic experimental study with controllable toy problems. All in all, this helps to find general answers to the question how knowledge injection helps in informed machine learning.

Despite its great success, machine learning can have its limits when dealing with insufficient training data. A potential solution is the additional integration of prior knowledge into the training process which leads to the notion of informed machine learning. In this paper, we present a structured overview of various approaches in this field. We provide a definition and propose a concept for informed machine learning which illustrates its building blocks and distinguishes it from conventional machine learning. We introduce a taxonomy that serves as a classification framework for informed machine learning approaches. It considers the source of knowledge, its representation, and its integration into the machine learning pipeline. Based on this taxonomy, we survey related research and describe how different knowledge representations such as algebraic equations, logic rules, or simulation results can be used in learning systems. This evaluation of numerous papers on the basis of our taxonomy uncovers key methods in the field of informed machine learning.

Artificial intelligence for autonomous driving must meet strict requirements on safety and robustness, which motivates the thorough validation of learned models. However, current validation approaches mostly require ground truth data and are thus both cost-intensive and limited in their applicability. We propose to overcome these limitations by a model agnostic validation using a-priori knowledge from street maps. In particular, we show how to validate semantic segmentation masks and demonstrate the potential of our approach using OpenStreetMap. We introduce validation metrics that indicate false positive or negative road segments. Besides the validation approach, we present a method to correct the vehicle's GPS position so that a more accurate localization can be used for the street-map based validation. Lastly, we present quantitative results on the Cityscapes dataset indicating that our validation approach can indeed uncover errors in semantic segmentation masks.

In this paper, we describe the combination of machine learning and simulation towards a hybrid modelling approach. Such a combination of data-based and knowledge-based modelling is motivated by applications that are partly based on causal relationships, while other effects result from hidden dependencies that are represented in huge amounts of data. Our aim is to bridge the knowledge gap between the two individual communities from machine learning and simulation to promote the development of hybrid systems. We present a conceptual framework that helps to identify potential combined approaches and employ it to give a structured overview of different types of combinations using exemplary approaches of simulation-assisted machine learning and machine-learning assisted simulation. We also discuss an advanced pairing in the context of Industry 4.0 where we see particular further potential for hybrid systems.

In this work we address the problem of retrieving potentially interesting matrix views to support the exploration of networks. We introduce Matrix Diagnostics (or Magnostics), following in spirit related approaches for rating and ranking other visualization techniques, such as Scagnostics for scatter plots. Our approach ranks matrix views according to the appearance of specific visual patterns, such as blocks and lines, indicating the existence of topological motifs in the data, such as clusters, bi-graphs, or central nodes. Magnostics can be used to analyze, query, or search for visually similar matrices in large collections, or to assess the quality of matrix reordering algorithms. While many feature descriptors for image analyzes exist, there is no evidence how they perform for detecting patterns in matrices. In order to make an informed choice of feature descriptors for matrix diagnostics, we evaluate 30 feature descriptors-27 existing ones and three new descriptors that we designed specifically for MAGNOSTICS-with respect to four criteria: pattern response, pattern variability, pattern sensibility, and pattern discrimination. We conclude with an informed set of six descriptors as most appropriate for Magnostics and demonstrate their application in two scenarios; exploring a large collection of matrices and analyzing temporal networks.