Kaiserslautern - Fachbereich Informatik
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Machine learning algorithms are widely applied to create powerful prediction models. With increasingly complex models, humans' ability to understand the decision function (that maps from a high-dimensional input space) is quickly exceeded. To explain a model's decisions, black-box methods have been proposed that provide either non-linear maps of the global topology of the decision boundary, or samples that allow approximating it locally. The former loses information about distances in input space, while the latter only provides statements about given samples, but lacks a focus on the underlying model for precise ‘What-If'-reasoning. In this paper, we integrate both approaches and propose an interactive exploration method using local linear maps of the decision space. We create the maps on high-dimensional hyperplanes—2D-slices of the high-dimensional parameter space—based on statistical and personal feature mutability and guided by feature importance. We complement the proposed workflow with established model inspection techniques to provide orientation and guidance. We demonstrate our approach on real-world datasets and illustrate that it allows identification of instance-based decision boundary structures and can answer multi-dimensional ‘What-If'-questions, thereby identifying counterfactual scenarios visually.
Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the construction of edit mappings for merge trees. Classic edit mappings match nodes or edges of two trees onto each other, and therefore have to either rely on branch decompositions of both trees or have to use auxiliary node properties to determine a matching. In contrast, branch mappings employ branch properties instead of node similarity information, and are independent of predetermined branch decompositions. Especially for topological features, which are typically based on branch properties, this allows a more intuitive distance measure which is also less susceptible to instabilities from small-scale perturbations. For trees with 𝒪(n) nodes, we describe an 𝒪(n4) algorithm for computing optimal branch mappings, which is faster than the only other branch decomposition-independent method in the literature by more than a linear factor. Furthermore, we compare the results of our method on synthetic and real-world examples to demonstrate its practicality and utility.
The development of algorithmic differentiation (AD) tools focuses mostly on handling floating point types in the target language. Taping optimizations in these tools mostly focus on specific operations like matrix vector products. Aggregated types like std::complex are usually handled by specifying the AD type as a template argument. This approach provides exact results, but prevents the use of expression templates. If AD tools are extended and specialized such that aggregated types can be added to the expression framework, then this will result in reduced memory utilization and improve the timing for applications where aggregated types such as complex number or matrix vector operations are used. Such an integration requires a reformulation of the stored data per expression and a rework of the tape evaluation process. We will demonstrate the overheads on a synthetic benchmark and show the improvement when aggregated types are handled properly by the expression framework of the AD tool.
Turbulence models, which are a means to fix the closure problem arising from Reynolds averaging of Navier-Stokes equations, are economical stop-gaps but suffer from accuracy issues. Modifying turbulence models by incorporating corrections in their functional form is one approach to improve their accuracy. We estimate correction functionals for the Spalart - Allmaras turbulence model, based on an inverse problem with PDE constraints emphasizing the issue of regularization.
Algorithmic decision-making (ADM) systems have come to support, pre-empt or substitute for human decisions in manifold areas, with potentially significant impacts on individuals' lives. Achieving transparency and accountability has been formulated as a general goal regarding the use of these systems. However, concrete applications differ widely in the degree of risk and the accountability problems they entail for data subjects. The present paper addresses this variation and presents a framework that differentiates regulatory requirements for a range of ADM system uses. It draws on agency theory to conceptualize accountability challenges from the point of view of data subjects with the purpose to systematize instruments for safeguarding algorithmic accountability. The paper furthermore shows how such instruments can be matched to applications of ADM based on a risk matrix. The resulting comprehensive framework can guide the evaluation of ADM systems and the choice of suitable regulatory provisions.
We describe a novel technique for the simultaneous visualization of multiple scalar fields, e.g. representing the members of an ensemble, based on their contour trees. Using tree alignments, a graph-theoretic concept similar to edit distance mappings, we identify commonalities across multiple contour trees and leverage these to obtain a layout that can represent all trees simultaneously in an easy-to-interpret, minimally-cluttered manner. We describe a heuristic algorithm to compute tree alignments for a given similarity metric, and give an algorithm to compute a joint layout of the resulting aligned contour trees. We apply our approach to the visualization of scalar field ensembles, discuss basic visualization and interaction possibilities, and demonstrate results on several analytic and real-world examples.
Editorial
(2021)
In order to discuss the kinds of reasoning a visualization supports and the conclusions that can be drawn within the analysiscontext, a theoretical framework is needed that enables a formal treatment of the reasoning process. Such a model needs toencompass three stages of the visualization pipeline: encoding, decoding and interpretation. The encoding details how dataare transformed into a visualization and what can be seen in the visualization. The decoding explains how humans constructgraphical contexts inside the depicted visualization and how they interpret them assigning meaning to displayed structuresaccording to a formal reasoning strategy. In the presented model, we adapt and combine theories for the different steps intoa unified formal framework such that the analysis process is modelled as an assignment of meaning to displayed structuresaccording to a formal reasoning strategy. Additionally, we propose the ConceptGraph, a combined graph-based representationof the finite-state transducers resulting from the three stages, that can be used to formalize and understand the reasoning process.We apply the new model to several visualization types and investigate reasoning strategies for various tasks.
Editorial
(2020)
Editorial
(2020)