Related papers: Distance Estimation Between Unknown Matrices Using…
We show how to compute any symmetric Boolean function on $n$ variables over any field (as well as the integers) with a probabilistic polynomial of degree $O(\sqrt{n \log(1/\epsilon)})$ and error at most $\epsilon$. The degree dependence on…
We give a $(1+\epsilon)$-approximate distance oracle with $O(1)$ query time for an undirected planar graph $G$ with $n$ vertices and non-negative edge lengths. For $\epsilon>0$ and any two vertices $u$ and $v$ in $G$, our oracle gives a…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem ($\mathsf{GHD}^n_{L, U}$): Alice and Bob are given binary string of length $n$ and they are guaranteed that Hamming distance between their…
We present new and improved data structures that answer exact node-to-node distance queries in planar graphs. Such data structures are also known as distance oracles. For any directed planar graph on n nodes with non-negative lengths we…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
Markov Chain Monte Carlo (MCMC) algorithms play an important role in statistical inference problems dealing with intractable probability distributions. Recently, many MCMC algorithms such as Hamiltonian Monte Carlo (HMC) and Riemannian…
We give a practical random mapping that takes any set of documents represented as vectors in Euclidean space and then maps them to a sparse subset of the Hamming cube while retaining ordering of inter-vector inner products. Once represented…
We study metric data structures for curves in doubling spaces, such as trajectories of moving objects in Euclidean $\mathbb{R}^d$, where the distance between two curves is measured using the discrete Fr\'echet distance. We design data…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
A well-defined distance on the parameter space is key to evaluating estimators, ensuring consistency, and building confidence sets. While there are typically standard distances to adopt in a continuous space, this is not the case for…
Weighted Hamming distance, as a similarity measure between binary codes and binary queries, provides superior accuracy in search tasks than Hamming distance. However, how to efficiently and accurately find $K$ binary codes that have the…
Similarity search is essential to many important applications and often involves searching at scale on high-dimensional data based on their similarity to a query. In biometric applications, recent vulnerability studies have shown that…
A (1 + eps)-approximate distance oracle for a graph is a data structure that supports approximate point-to-point shortest-path-distance queries. The most relevant measures for a distance-oracle construction are: space, query time, and…
We present a path planning framework that takes into account the human's safety perception in the presence of a flying robot. The framework addresses two objectives: (i) estimation of the uncertain parameters of the proposed safety…
We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While powerful probabilistic models such as Gaussian Processes…
Statistical analysis of massive datasets very often implies expensive linear algebra operations with large dense matrices. Typical tasks are an estimation of unknown parameters of the underlying statistical model and prediction of missing…