Related papers: Algebraic characterization of equivalence between …
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
We investigate the convergence properties of a class of iterative algorithms designed to minimize a potentially non-smooth and noisy objective function, which may be algebraically intractable and whose values may be obtained as the output…
We propose a formalization of generic algorithms that includes analog algorithms. This is achieved by reformulating and extending the framework of abstract state machines to include continuous-time models of computation. We prove that every…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical…
Process mining offers techniques to exploit event data by providing insights and recommendations to improve business processes. The growing amount of algorithms for process discovery has raised the question of which algorithms perform best…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…
In this paper we present equivalence results for several types of unbounded operator functions. A generalization of the concept equivalence after extension is introduced and used to prove equivalence and linearization for classes of…
The evaluation of clustering algorithms can involve running them on a variety of benchmark problems, and comparing their outputs to the reference, ground-truth groupings provided by experts. Unfortunately, many research papers and graduate…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
Recent interest in codifying fairness in Automated Decision Systems (ADS) has resulted in a wide range of formulations of what it means for an algorithmic system to be fair. Most of these propositions are inspired by, but inadequately…
Symmetries of combinatorial objects are known to complicate search algorithms, but such obstacles can often be removed by detecting symmetries early and discarding symmetric subproblems. Canonical labeling of combinatorial objects…
Developing complex, real world graphics applications which leverage multiple GPUs and computers for interactive 3D rendering tasks is a complex task. It requires expertise in distributed systems and parallel rendering in addition to the…
We introduce a new workflow for unconstrained optimization whereby objective functions are mapped onto a physical domain to more easily design algorithms that are robust to hyperparameters and achieve fast convergence rates. Specifically,…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…
Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the…
Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…