Related papers: Exemplar or Matching: Modeling DCJ Problems with U…
The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…
Distance-based tests, also called "energy statistics", are leading methods for two-sample and independence tests from the statistics community. Kernel-based tests, developed from "kernel mean embeddings", are leading methods for two-sample…
Assessing the extent of human edits on texts generated by Large Language Models (LLMs) is crucial to understanding the human-AI interactions and improving the quality of automated text generation systems. Existing edit distance metrics,…
During the course of evolution, an organism's genome can undergo changes that affect the large-scale structure of the genome. These changes include gene gain, loss, duplication, chromosome fusion, fission, and rearrangement. When gene gain…
We study complexity of rearrangement problems in the generalized breakpoint model and settle several open questions. The model was introduced by Tannier et al. (2009) who showed that the median problem is solvable in polynomial time in the…
Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and…
Overlapping frequently occurs in paired texts in natural language processing tasks like text editing and semantic similarity evaluation. Better evaluation of the semantic distance between the overlapped sentences benefits the language…
When estimating a phylogeny from a multiple sequence alignment, researchers often assume the absence of recombination. However, if recombination is present, then tree estimation and all downstream analyses will be impacted, because…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
Synthetic DNA can in principle be used for the archival storage of arbitrary data. Because errors are introduced during DNA synthesis, storage, and sequencing, an error-correcting code (ECC) is necessary for error-free recovery of the data.…
The Earth Mover's Distance (EMD) is a state-of-the art metric for comparing discrete probability distributions, but its high distinguishability comes at a high cost in computational complexity. Even though linear-complexity approximation…
We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual…
We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…
Building on the remarkable achievements in generative sampling of natural images, we propose an innovative challenge, potentially overly ambitious, which involves generating samples of entire multivariate time series that resemble images.…
The edit distance (a.k.a. the Levenshtein distance) between two strings is defined as the minimum number of insertions, deletions or substitutions of symbols needed to transform one string into another. The problem of computing the edit…
The graph edit distance is used for comparing graphs in various domains. Due to its high computational complexity it is primarily approximated. Widely-used heuristics search for an optimal assignment of vertices based on the distance…
Considering a pair of genomes, the goal of rearrangement distance problems is to estimate how distant these genomes are from each other based on genome rearrangements. Seminal works in genome rearrangements assumed that both genomes being…
In the era of high throughput DNA sequencing (HTS) technologies, calculating the edit distance (i.e., the minimum number of substitutions, insertions, and deletions between a pair of sequences) for billions of genomic sequences is the…
We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…
Are two sets of observations drawn from the same distribution? This problem is a two-sample test. Kernel methods lead to many appealing properties. Indeed state-of-the-art approaches use the $L^2$ distance between kernel-based distribution…