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In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the precision. We present a systematic recurrence for a martingale…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
Model-driven engineering is the automatic production of software artefacts from abstract models of structure and functionality. By targeting a specific class of system, it is possible to automate aspects of the development process, using…
Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models…
Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the…
Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…
Modern computer architectures support low-precision arithmetic, which present opportunities for the adoption of mixed-precision algorithms to achieve high computational throughput and reduce energy consumption. As a growing number of…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…
Establishing bounds on the accuracy achievable by localization techniques represents a fundamental technical issue. Bounds on localization accuracy have been derived for cases in which the position of an agent is estimated on the basis of a…
A robot can invoke heterogeneous computation resources such as CPUs, cloud GPU servers, or even human computation for achieving a high-level goal. The problem of invoking an appropriate computation model so that it will successfully…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
Approximate computing is a computation domain which can be used to trade time and energy with quality and therefore is useful in embedded systems. Energy is the prime resource in battery-driven embedded systems, like robots. Approximate…
In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…
Accuracy and Availability computations for a GNSS System - or combination of Systems - through Service Volume Simulations take considerable time. Therefore, the computation of the accuracy in 2D and 3D are often simplified by an approximate…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…
Many techniques for handling missing data have been proposed in the literature. Most of these techniques are overly complex. This paper explores an imputation technique based on rough set computations. In this paper, characteristic…