Recovery From Non-Decomposable Distance Oracles

arxiv(2023)

引用 1|浏览13
暂无评分
摘要
A line of work has looked at the problem of recovering an input from distance queries. In this setting, there is an unknown sequence $s \in \{0,1\}^{\leq n}$ , and one chooses a set of queries $y \in \{0,1\}^{ \mathcal {O}(n)}$ and receives $d(s,y)$ for a distance function $d$ . The goal is to make as few queries as possible to recover $s$ . Although this problem is well-studied for decomposable distances, i.e., distances of the form $d(s,y) = \sum _{i=1}^{n} f(s_{i}, y_{i})$ for some function $f$ , which includes the important cases of Hamming distance, $\ell _{p}$ -norms, and $M$ -estimators, to the best of our knowledge this problem has not been studied for non-decomposable distances, for which there are important instances including edit distance, dynamic time warping (DTW), Fréchet distance, earth mover’s distance, and others. We initiate the study and develop a general framework for such distances. Interestingly, for some distances such as DTW or Fréchet, exact recovery of the sequence $s$ is provably impossible, and so we show by allowing the characters in $y$ to be drawn from a slightly larger alphabet this then becomes possible. In a number of cases we obtain optimal or near-optimal query complexity. One motivation for understanding non-adaptivity is that the query sequence can be fixed and provide a non-linear embedding of the input, which can be used in downstream applications involving, e.g., neural networks for natural language processing.
更多
查看译文
关键词
Sequence recovery,edit distance,DTW distance,Fréchet distance
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要