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Learning-to-Rank (LTR) is a supervised machine learning approach that constructs models specifically designed to order a set of items or documents based on their relevance or importance to a given query or context. Despite significant…
We develop new tools in the theory of nonlinear random matrices and apply them to study the performance of the Sum of Squares (SoS) hierarchy on average-case problems. The SoS hierarchy is a powerful optimization technique that has achieved…
In search problems, a mobile searcher seeks to locate a target that hides in some unknown position of the environment. Such problems are typically considered to be of an on-line nature, in that the input is unknown to the searcher, and the…
We consider the problem of hitting sets online. The hypergraph (i.e., range-space consisting of points and ranges) is known in advance, and the ranges to be stabbed are input one-by-one in an online fashion. The online algorithm must stab…
Recently, Rendle has warned that the use of sampling-based top-$k$ metrics might not suffice. This throws a number of recent studies on deep learning-based recommendation algorithms, and classic non-deep-learning algorithms using such a…
Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical…
Google employs PageRank to rank web pages, determining the order in which search results are presented to users based on their queries. PageRank is primarily utilized for directed networks, although there are instances where it is also…
In this work author applies well known web search algorithm Hyperlink - Induced Topic Search (HITS) to problem of ranking football teams in English Premier League (EPL). The algorithm allows the ranking of the teams using the notions of…
Near an optimal learning point of a neural network, the learning performance of gradient descent dynamics is dictated by the Hessian matrix of the loss function with respect to the network parameters. We characterize the Hessian…
We analyze linkage strategies for a set I of webpages for which the webmaster wants to maximize the sum of Google's PageRank scores. The webmaster can only choose the hyperlinks starting from the webpages of I and has no control on the…
Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…
PageRank is arguably the most popular ranking algorithm which is being applied in real systems ranging from information to biological and infrastructure networks. Despite its outstanding popularity and broad use in different areas of…
The paper presents a comprehensive performance evaluation of some heuristic search algorithms in the context of autonomous systems and robotics. The objective of the study is to evaluate and compare the performance of different search…
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
Identifying the importance of nodes of complex networks is of interest to the research of Social Networks, Biological Networks etc.. Current researchers have proposed several measures or algorithms, such as betweenness, PageRank and HITS…
There has been significant success in designing highly efficient algorithms for distance and shortest-path queries in recent years; many of the state-of-the-art algorithms use the hub labeling framework. In this paper, we study the…
We study a general stochastic ranking problem where an algorithm needs to adaptively select a sequence of elements so as to "cover" a random scenario (drawn from a known distribution) at minimum expected cost. The coverage of each scenario…
Search engines intentionally influence user behavior by picking and ranking the list of results. Users engage with the highest results both because of their prominent placement and because they are typically the most relevant documents.…
Rank aggregation aims to combine the preference rankings of a number of alternatives from different voters into a single consensus ranking. As a useful model for a variety of practical applications, however, it is a computationally…
In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is important to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose…