相关论文: Recovery from Non-Decomposable Distance Oracles
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
We introduce an improved structure of distance sensitivity oracle (DSO). The task is to pre-process a non-negatively weighted graph so that a data structure can quickly answer replacement path length for every triple of source, terminal and…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
The sequence reconstruction problem was proposed by Levenshtein in 2001. In this model, a sequence from a code is transmitted over several channels, and the decoder receives the distinct outputs from each channel. The main problem is to…
In the trace reconstruction problem our goal is to learn an unknown string $x\in \{0,1\}^n$ given independent traces of $x$. A trace is obtained by independently deleting each bit of $x$ with some probability $\delta$ and concatenating the…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations by considering the number of oscillations. This is a function version of the difference hierarchy for…
In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…
We study the query complexity of exactly reconstructing a string from adaptive queries, such as substring, subsequence, and jumbled-index queries. Such problems have applications, e.g., in computational biology. We provide a number of new…
We provide a static data structure for distance estimation which supports {\it adaptive} queries. Concretely, given a dataset $X = \{x_i\}_{i = 1}^n$ of $n$ points in $\mathbb{R}^d$ and $0 < p \leq 2$, we construct a randomized data…
We consider the problem of privately answering queries defined on databases which are collections of points belonging to some metric space. We give simple, computationally efficient algorithms for answering distance queries defined over an…
The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysis-of-variance dimensional…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
Non-line-of-sight reconstruction (NLoS) is a novel indirect imaging modality that aims to recover objects or scene parts outside the field of view from measurements of light that is indirectly scattered off a directly visible, diffuse wall.…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
In the $(k,m)$-mappability problem, for a given sequence $T$ of length $n$, the goal is to compute a table whose $i$th entry is the number of indices $j \ne i$ such that the length-$m$ substrings of $T$ starting at positions $i$ and $j$…
We present an approximate distance oracle for a point set S with n points and doubling dimension {\lambda}. For every {\epsilon}>0, the oracle supports (1+{\epsilon})-approximate distance queries in (universal) constant time, occupies space…
The orthogonal beltway problem is the problem of recovering the $\mathrm{O}(n)$-orbit of a $\delta$-function supported at a finite number of points in $\r^n$ from its auto-correlation or, equivalently, second moment. It was introduced as a…
Methods for reconstructing the topology of complex networks from time-resolved observations of node dynamics are gaining relevance across scientific disciplines. Of biggest practical interest are methods that make no assumptions about…