XTSC-Bench: Quantitative Benchmarking for Explainers on Time Series Classification

Despite the growing body of work on explainable machine learning in time series classification (TSC), it remains unclear how to evaluate different explainability methods. Resorting to qualitative assessment and user studies to evaluate explainers for TSC is difficult since humans have difficulties understanding the underlying information contained in time series data. Therefore, a systematic review and quantitative comparison of explanation methods to confirm their correctness becomes crucial. While steps to standardized evaluations were taken for tabular, image, and textual data, benchmarking explainability methods on time series is challenging due to a) traditional metrics not being directly applicable, b) implementation and adaption of traditional metrics for time series in the literature vary, and c) varying baseline implementations. This paper proposes XTSC-Bench, a benchmarking tool providing standardized datasets, models, and metrics for evaluating explanation methods on TSC. We analyze 3 perturbation-, 6 gradient- and 2 example-based explanation methods to TSC showing that improvements in the explainers' robustness and reliability are necessary, especially for multivariate data.Comment: Accepted at ICMLA 202

Stability of the B-spline basis via knot insertion

Abstract We derive the stability inequality C γ i c i b i for the B-splines b i from the formula for knot insertion. The key observation is that knot removal increases the norm of the B-spline coefficients C = {c i } i∈Z at most by a constant factor, which is independent of the knot sequence. As a consequence, stability for splines follows from the stability of the Bernstein basis

The Interaction of Trait Competitiveness and Leaderboard Design - An Experimental Analysis of Effects on Perceptions and Usage Intention

Gamification is a valuable approach to foster user engagement, raise motivation, and induce behavioral change. As a maturing field of research, the complex interactions of the various elements of gameful systems remain opaque. However, understanding these interactions, especially between user and gamified system, builds the foundation for the vast application of gamified systems. To advance our knowledge in this field, we employ an experimental research design with 192 participants. Thereby we show that users’ personal development competitiveness positively affects the perception and usage intention of a competitive gamified system in a work scenario. Further, this relationship is moderated by the system’s design. Focusing on a team-based rather than a player-based leaderboard supports the usage intentions and perceptions of individuals high in personal development competitiveness. Our study supports the need for individualized gameful systems rather than relying on one-system-fits-all approaches often found in business practice

Bouncing ball orbits and symmetry breaking effects in a three-dimensional chaotic billiard

We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only a few families of nongeneric periodic orbits. We introduce an analytic method for their treatment. The length spectrum can be understood in terms of the nongeneric and unstable periodic orbits. For unequal radii of the quarter cylinders the level statistics agree well with predictions from random matrix theory. For equal radii the billiard exhibits an additional symmetry. We investigated the effects of symmetry breaking on spectral properties. Moreover, for equal radii, we observe a small deviation of the level statistics from random matrix theory. This led to the discovery of stable and marginally stable orbits, which are absent for un equal radii.Comment: 11 pages, 10 eps figure

PetIGA: A framework for high-performance isogeometric analysis

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility of PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. We show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations