相关论文: New upper bounds for trace reconstruction

This paper considers the problem of recovering a one or two dimensional discrete signal which is approximately sparse in its discrete gradient from an incomplete subset of its discrete Fourier coefficients which have been corrupted with…

We consider the problem of recovering polynomials that are sparse with respect to the basis of Legendre polynomials from a small number of random samples. In particular, we show that a Legendre s-sparse polynomial of maximal degree N can be…

We estimate the minimum number of distance queries that is sufficient to reconstruct the binomial random graph $G(n,p)$ with constant diameter with high probability. We get a tight (up to a constant factor) answer for all $p>n^{-1+o(1)}$…

The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable…

Repeat finding in strings has important applications in subfields such as computational biology. Surprisingly, all prior work on repeat finding did not consider the constraint on the locality of repeats. In this paper, we propose and study…

This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…

We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…

We study here the so called subsequence pattern matching also known as hidden pattern matching in which one searches for a given pattern $w$ of length $m$ as a subsequence in a random text of length $n$. The quantity of interest is the…

Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…

This paper studies reconstruction of strings based upon their substrings spectrum. Under this paradigm, it is assumed that all substrings of some fixed length are received and the goal is to reconstruct the string. While many existing works…

We give a randomized online algorithm that guarantees near-optimal $\widetilde O(\sqrt T)$ expected swap regret against any sequence of $T$ adaptively chosen Lipschitz convex losses on the unit interval. This improves the previous best…

Markov random fields are used to model high dimensional distributions in a number of applied areas. Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random…

Let $V$ be a set of $n$ points in $\mathbb{R}^d$, and suppose that the distance between each pair of points is revealed independently with probability $p$. We study when this information is sufficient to reconstruct large subsets of $V$, up…

In the trace reconstruction problem, one attempts to reconstruct a fixed but unknown string $x$ of length $n$ from a given number of traces $\tilde{x}$ drawn iid from the application of a noisy process (such as the deletion channel) to $x$.…

We revisit the classical problem of universal prediction of stochastic sequences with a finite time horizon $T$ known to the learner. The question we investigate is whether it is possible to derive vanishing regret bounds that hold with…

Let $G$ be a $3$-connected ordered graph with $n$ vertices and $m$ edges. Let $\mathbf{p}$ be a randomly chosen mapping of these $n$ vertices to the integer range $\{1, 2,3, \ldots, 2^b\}$ for $b\ge m^2$. Let $\ell$ be the vector of $m$…

A matrix is given in ``shredded'' form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matrix is reconstructible if it is uniquely determined by this…

We study high-probability regret bounds for adversarial $K$-armed bandits with time-varying feedback graphs over $T$ rounds. For general strongly observable graphs, we develop an algorithm that achieves the optimal regret…

We propose a penalized pseudo-likelihood criterion to estimate the graph of conditional dependencies in a discrete Markov random field that can be partially observed. We prove the convergence of the estimator in the case of a finite or…

Following (Kolpakov et al., 2013; Gawrychowski and Manea, 2015), we continue the study of {\em $\alpha$-gapped repeats} in strings, defined as factors $uvu$ with $|uv|\leq \alpha |u|$. Our main result is the $O(\alpha n)$ bound on the…