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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…
Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…
The seminal work of Dwork {\em et al.} [ITCS 2012] introduced a metric-based notion of individual fairness. Given a task-specific similarity metric, their notion required that every pair of similar individuals should be treated similarly.…
We study the properties of several proximity measures for the vertices of weighted multigraphs and multidigraphs. Unlike the classical distance for the vertices of connected graphs, these proximity measures are applicable to weighted…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
In this paper we propose a class of weighted rank correlation coefficients extending the Spearman's rho. The proposed class constructed by giving suitable weights to the distance between two sets of ranks to place more emphasis on items…
We study a revenue maximization problem in the context of social networks. Namely, we consider a model introduced by Alon, Mansour, and Tennenholtz (EC 2013) that captures inequity aversion, i.e., prices offered to neighboring vertices…
Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Learning how to aggregate ranking lists has been an active research area for many years and its advances have played a vital role in many applications ranging from bioinformatics to internet commerce. The problem of discerning reliability…
A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically…
The Kemeny aggregation problem consists of computing the consensus rankings of an election with respect to the well-known Kemeny-Young voting method. These consensus rankings satisfy various fundamental properties and are the geometric…
Proximal Policy Optimization (PPO) is among the most widely used deep reinforcement learning algorithms, yet its theoretical foundations remain incomplete. Most importantly, convergence and understanding of fundamental PPO advantages remain…
Many popular policy gradient methods for reinforcement learning follow a biased approximation of the policy gradient known as the discounted approximation. While it has been shown that the discounted approximation of the policy gradient is…
We focus on two research issues in entity search: scoring a document or snippet that potentially supports a candidate entity, and aggregating scores from different snippets into an entity score. Proximity scoring has been studied in IR…
In this work, we investigate the problem of learning distance functions within the query-based learning framework, where a learner is able to pose triplet queries of the form: ``Is $x_i$ closer to $x_j$ or $x_k$?'' We establish formal…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…