Related papers: Distances Between Partial Preference Orderings
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
The quality of consequences in a decision making problem under (severe) uncertainty must often be compared among different targets (goals, objectives) simultaneously. In addition, the evaluations of a consequence's performance under the…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
Preference are central to decision making by both machines and humans. Representing, learning, and reasoning with preferences is an important area of study both within computer science and across the sciences. When working with preferences…
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…
When solving the Hamiltonian path problem it seems natural to be given additional precedence constraints for the order in which the vertices are visited. For example one could decide whether a Hamiltonian path exists for a fixed starting…
Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their limitations, for the three classic second…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
Linearizing two partial orders to maximize the number of adjacencies and minimize the number of breakpoints is APX-hard. This holds even if one of the two partial orders is already a linear order and the other is an interval order, or if…
The problem of finding the distance from a given $n \times n$ matrix polynomial of degree $k$ to the set of matrix polynomials having the elementary divisor $(\lambda-\lambda_0)^j, \, j \geqslant r,$ for a fixed scalar $\lambda_0$ and $2…
In this paper, an evidential distance measure is proposed which can measure the difference or dissimilarity between complex basic belief assignments (CBBAs), in which the CBBAs are composed of complex numbers. When the CBBAs are degenerated…
We unveil an alluring alternative to parametric search that applies to both the non-geodesic and geodesic Fr\'echet optimization problems. This randomized approach is based on a variant of red-blue intersections and is appealing due to its…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…
For a given Markov chain Monte Carlo algorithm we introduce a distance between two configurations that quantifies the difficulty of transition from one configuration to the other configuration. We argue that the distance takes a universal…
Differential logical relations are a method to measure distances between higher-order programs. They differ from standard methods based on program metrics in that differences between functional programs are themselves functions, relating…
We consider a classical problem in choice theory -- vote aggregation -- using novel distance measures between permutations that arise in several practical applications. The distance measures are derived through an axiomatic approach, taking…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
Applications in machine learning and data mining require computing pairwise Lp distances in a data matrix A. For massive high-dimensional data, computing all pairwise distances of A can be infeasible. In fact, even storing A or all pairwise…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…