Related papers: Differentiable Ranks and Sorting using Optimal Tra…
Learning to Rank (LTR) is one of the most widely used machine learning applications. It is a key component in platforms with profound societal impacts, including job search, healthcare information retrieval, and social media content feeds.…
Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
We present a framework wherein the trajectory optimization problem (or a problem involving calculus of variations) is formulated as a search problem in a discrete space. A distinctive feature of our work is the treatment of discretization…
The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…
Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…
We introduce a sorting machine consisting of $k+1$ stacks in series: the first $k$ stacks can only contain elements in decreasing order from top to bottom, while the last one has the opposite restriction. This device generalizes \cite{SM},…
In this research paper, we address the Distinct Elements estimation problem in the context of streaming algorithms. The problem involves estimating the number of distinct elements in a given data stream $\mathcal{A} = (a_1, a_2,\ldots,…
Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…
One approach for reducing run time and improving efficiency of machine learning is to reduce the convergence rate of the optimization algorithm used. Shuffling is an algorithm technique that is widely used in machine learning, but it only…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important…
Inspired by the great success of machine learning in the past decade, people have been thinking about the possibility of improving the theoretical results by exploring data distribution. In this paper, we revisit a fundamental problem…
Selecting prototypical examples from a source distribution to represent a target data distribution is a fundamental problem in machine learning. Existing subset selection methods often rely on implicit importance scores, which can be skewed…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
Clustering is a fundamental task in the computer vision and machine learning community. Although various methods have been proposed, the performance of existing approaches drops dramatically when handling incomplete high-dimensional data…
Scheduling is an important task allowing parallel systems to perform efficiently and reliably. For modern computation systems, divisible load is a special type of data which can be divided into arbitrary sizes and independently processed in…
The selection problem, where one wishes to locate the $k^{th}$ smallest element in an unsorted array of size $n$, is one of the basic problems studied in computer science. The main focus of this work is designing algorithms for solving the…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
We discuss a relationship between rate-distortion and optimal transport (OT) theory, even though they seem to be unrelated at first glance. In particular, we show that a function defined via an extremal entropic OT distance is equivalent to…