Related papers: The monoids of the patience sorting algorithm
Large Language Models (LLMs) have shown exciting performance in listwise passage ranking. Due to the limited input length, existing methods often adopt the sliding window strategy. Such a strategy, though effective, is inefficient as it…
Rank-based zeroth-order (ZO) optimization -- which relies only on the ordering of function evaluations -- offers strong robustness to noise and monotone transformations, and underlies many successful algorithms such as CMA-ES, natural…
In this master thesis we analyze the complexity of sorting a set of strings. It was shown that the complexity of sorting strings can be naturally expressed in terms of the prefix trie induced by the set of strings. The model of computation…
Online Contention Resolution Schemes (OCRS's) represent a modern tool for selecting a subset of elements, subject to resource constraints, when the elements are presented to the algorithm sequentially. OCRS's have led to some of the…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
Multi-label ranking maps instances to a ranked set of predicted labels from multiple possible classes. The ranking approach for multi-label learning problems received attention for its success in multi-label classification, with one of the…
We introduce the problem of ranking with slot constraints, which can be used to model a wide range of application problems -- from college admission with limited slots for different majors, to composing a stratified cohort of eligible…
The Bulk-Synchronous Parallel model of computation has been used for the architecture independent design and analysis of parallel algorithms whose performance is expressed not only in terms of problem size n but also in terms of parallel…
We consider a natural generalization of braids which we call shrinking braids. We state the relations of shrinking braids and use them to define algebraically the monoid $R$. We endow a subset of $R$ with a \emph{left distributive monoid}…
Unsupervised aggregation of independently built univariate predictors is explored as an alternative regularization approach for noisy, sparse datasets. Bipartite ranking algorithm Smooth Rank implementing this approach is introduced. The…
In information retrieval, learning to rank constructs a machine-based ranking model which given a query, sorts the search results by their degree of relevance or importance to the query. Neural networks have been successfully applied to…
Load forecasting is a fundamental task in smart grid. Many techniques have been applied to developing load forecasting models. Due to the challenges such as the Curse of Dimensionality, overfitting, and limited computing resources,…
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
We study stochastic object assignment problems in which objects may have minimum and maximum requirements, such as with classes with upper and lower enrollment bounds. We construct a new random assignment mechanism, the minimums…
Right (and left) coherency and right (and left) weak coherency are natural finitary conditions for monoids. Determining whether or not a given monoid has any of these properties is historically a difficult problem. This paper has several…
Non-dominated sorting is a computational bottleneck in Pareto-based multi-objective evolutionary algorithms (MOEAs) due to the runtime-intensive comparison operations involved in establishing dominance relationships between solution…
In this article, we consider the monoid of all monotone and order-decreasing partial transformations denoted as $\mathcal{DORP}_{n}$ on an $n$ ordered chain $[n]=\{1, \ldots,n\}$, its two-sided ideal $I(n,p)= \{\rho \in \mathcal{DORP}_{n} :…
The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected…
In this article the notion of the nondecreasing (ND) rank of a matrix or tensor is introduced. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each vector satisfying a monotonicity…
Given a sequence of $n$ numbers and $k$ parallel First-in-First-Out (FIFO) queues, how close can one bring the sequence to sorted order? It is known that $k$ queues suffice to sort the sequence if the Longest Decreasing Subsequence (LDS) of…