Related papers: Optimality of Frequency Moment Estimation

Suppose $\{\widehat\theta_n\colon n\ge1\}$ is a strongly consistent sequence of estimators for a parameter $\theta$, where $\widehat\theta_n$ is based on the first $n$ observations. Consider $Q_\varepsilon$, the number of times…

We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…

Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…

The use of realistic input models has gained popularity in the theory community. Assuming a realistic input model often precludes complicated hypothetical inputs, and the analysis yields bounds that better reflect the behaviour of…

The principal limits for the accuracy of the resonance frequency measurements set by the asymmetry of the natural resonance line shape are studied and applied to the recent accurate frequency measurements in the two-photon 1s-2s resonance…

The key point to prove the optimal $C^{1,\frac12}$ regularity of the thin obstacle problem is that the frequency at a point of the free boundary $x_0\in\Gamma(u)$, say $N^{x_0}(0^+,u)$, satisfies the lower bound $N^{x_0}(0^+,u)\ge\frac32$.…

A new converse bound is presented for the two-user multiple-access channel under the average probability of error constraint. This bound shows that for most channels of interest, the second-order coding rate -- that is, the difference…

Algorithms for numerical tasks in finite precision simultaneously seek to minimize the number of floating point operations performed, and also the number of bits of precision required by each floating point operation. This paper presents an…

We show that any quantum algorithm deciding whether an input function $f$ from $[n]$ to $[n]$ is 2-to-1 or almost 2-to-1 requires $\Theta(n)$ queries to $f$. The same lower bound holds for determining whether or not a function $f$ from…

We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…

The metric sketching problem is defined as follows. Given a metric on $n$ points, and $\epsilon>0$, we wish to produce a small size data structure (sketch) that, given any pair of point indices, recovers the distance between the points up…

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

Change point detection plays a fundamental role in many real-world applications, where the goal is to analyze and monitor the behaviour of a data stream. In this paper, we study change detection in binary streams. To this end, we use a…

Stochastic convex optimization is one of the most well-studied models for learning in modern machine learning. Nevertheless, a central fundamental question in this setup remained unresolved: "How many data points must be observed so that…

We propose a new algorithm that finds an $\varepsilon$-approximate fixed point of a smooth function from the $n$-dimensional $\ell_2$ unit ball to itself. We use the general framework of finding approximate solutions to a variational…

We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…

This work provides tight upper- and lower-bounds for the problem of mean estimation under $\epsilon$-differential privacy in the local model, when the input is composed of $n$ i.i.d. drawn samples from a normal distribution with variance…

According to a well known theorem of Haussler and Welzl (1987), any range space of bounded VC-dimension admits an $\eps$-net of size $O\left(\frac{1}{\eps}\log\frac1{\eps}\right)$. Using probabilistic techniques, Pach and Woeginger (1990)…

We show an Omega(sqrt{n}/T) lower bound for the space required by any unidirectional constant-error randomized T-pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well-parenthesized. This proves…

We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a…