Related papers: New upper bounds for trace reconstruction

We derive upper and lower bounds for the policy regret of $T$-round online learning problems with graph-structured feedback, where the adversary is nonoblivious but assumed to have a bounded memory. We obtain upper bounds of $\widetilde…

Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…

We propose a randomized algorithm with query access that given a graph $G$ with arboricity $\alpha$, and average degree $d$, makes $\widetilde{O}\left(\frac{\alpha}{\varepsilon^2d}\right)$ \texttt{Degree} and…

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…

A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a…

We study the reconstruction problem of permutation sequences from their $k$-minors, which are subsequences of length $k$ with entries renumbered by $1,2,\ldots,k$ preserving order. We prove that the minimum number $k$ such that any…

We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…

We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges…

We provide new lower bounds on the regret that must be suffered by adversarial bandit algorithms. The new results show that recent upper bounds that either (a) hold with high-probability or (b) depend on the total lossof the best arm or (c)…

We investigate the recovery of structures from large-area, low dose exposures that distribute the dose over many identical copies of an object. The reconstruction is done via a maximum likelihood approach that does neither require to…

We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…

The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability…

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…

The recovery of types from stripped binaries is a key to exact decompilation, yet its practical realization suffers. For composite structures in particular, both layout and semantic fidelity are required to enable end-to-end reconstruction.…

We investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. In the Tucker decomposition framework, we show that the Riemannian optimization algorithm with initial value…

We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general.…

A k-wise independent distribution on n bits is a joint distribution of the bits such that each k of them are independent. In this paper we consider k-wise independent distributions with identical marginals, each bit has probability p to be…

Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. The authors of [2] showed that the expected number of distinct consecutive patterns of all lengths $k\in\{1,2,\ldots,n\}$ in $\pi_n$ was $\frac{n^2}{2}(1-o(1))$ as $n\to\infty$,…

We show that uncloneable encryption exists with no computational assumptions, with security $\widetilde{O}\left(\tfrac{1}{\lambda}\right)$ in the security parameter $\lambda$.

In this paper we present two algorithms for the following problem: given a string and a rational $e > 1$, detect in the online fashion the earliest occurrence of a repetition of exponent $\ge e$ in the string. 1. The first algorithm…