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Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If $f(\boldsymbol{x})$ is the loss function, and $C$ is the constraint set in a constrained minimization problem, then…
We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this…
The Two Alternative Forced Choice (2AFC) paradigm offers advantages over the Mean Opinion Score (MOS) paradigm in psychophysics (PF), such as simplicity and robustness. However, when evaluating perceptual distance models, MOS enables direct…
We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x…
Pareto front learning is a technique that introduces preference vectors in a neural network to approximate the Pareto front. Previous Pareto front learning methods have demonstrated high performance in approximating simple Pareto fronts.…
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…
Borgs et al. [2016] investigated essential requirements for communities in preference networks. They defined six axioms on community functions, i.e., community detection rules. Though having elegant properties, the practicality of this…
This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters…
This paper studies best finitely supported approximations of one-dimensional probability measures with respect to the $L^r$-Kantorovich (or transport) distance, where either the locations or the weights of the approximations' atoms are…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…
We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, {\em Phys. Rev. E} (2003)], the concept of network random walking is introduced and a distance measure defined. Here we…
We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is…
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
Two aspects of neural networks that have been extensively studied in the recent literature are their function approximation properties and their training by gradient descent methods. The approximation problem seeks accurate approximations…
Rankings of people and items are at the heart of selection-making, match-making, and recommender systems, ranging from employment sites to sharing economy platforms. As ranking positions influence the amount of attention the ranked subjects…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…