21 research outputs found
Calibrated Simplex Mapping Classification
We propose a novel supervised multi-class/single-label classifier that maps
training data onto a linearly separable latent space with a simplex-like
geometry. This approach allows us to transform the classification problem into
a well-defined regression problem. For its solution we can choose suitable
distance metrics in feature space and regression models predicting latent space
coordinates. A benchmark on various artificial and real-world data sets is used
to demonstrate the calibration qualities and prediction performance of our
classifier.Comment: 24 pages, 8 figures, 7 table
Optimized data exploration applied to the simulation of a chemical process
In complex simulation environments, certain parameter space regions may
result in non-convergent or unphysical outcomes. All parameters can therefore
be labeled with a binary class describing whether or not they lead to valid
results. In general, it can be very difficult to determine feasible parameter
regions, especially without previous knowledge. We propose a novel algorithm to
explore such an unknown parameter space and improve its feasibility
classification in an iterative way. Moreover, we include an additional
optimization target in the algorithm to guide the exploration towards regions
of interest and to improve the classification therein. In our method we make
use of well-established concepts from the field of machine learning like kernel
support vector machines and kernel ridge regression. From a comparison with a
Kriging-based exploration approach based on recently published results we can
show the advantages of our algorithm in a binary feasibility classification
scenario with a discrete feasibility constraint violation. In this context, we
also propose an improvement of the Kriging-based exploration approach. We apply
our novel method to a fully realistic, industrially relevant chemical process
simulation to demonstrate its practical usability and find a comparably good
approximation of the data space topology from relatively few data points.Comment: 45 pages, 6 figure
Shapley Values with Uncertain Value Functions
We propose a novel definition of Shapley values with uncertain value
functions based on first principles using probability theory. Such uncertain
value functions can arise in the context of explainable machine learning as a
result of non-deterministic algorithms. We show that random effects can in fact
be absorbed into a Shapley value with a noiseless but shifted value function.
Hence, Shapley values with uncertain value functions can be used in analogy to
regular Shapley values. However, their reliable evaluation typically requires
more computational effort.Comment: 12 pages, 1 figure, 1 tabl
A Quantum Optimization Case Study for a Transport Robot Scheduling Problem
We present a comprehensive case study comparing the performance of D-Waves'
quantum-classical hybrid framework, Fujitsu's quantum-inspired digital
annealer, and Gurobi's state-of-the-art classical solver in solving a transport
robot scheduling problem. This problem originates from an industrially relevant
real-world scenario. We provide three different models for our problem
following different design philosophies. In our benchmark, we focus on the
solution quality and end-to-end runtime of different model and solver
combinations. We find promising results for the digital annealer and some
opportunities for the hybrid quantum annealer in direct comparison with Gurobi.
Our study provides insights into the workflow for solving an
application-oriented optimization problem with different strategies, and can be
useful for evaluating the strengths and weaknesses of different approaches