相关论文: Estimating small frequency moments of data stream:…

The traditional requirement for a randomized streaming algorithm is just {\em one-shot}, i.e., algorithm should be correct (within the stated $\eps$-error bound) at the end of the stream. In this paper, we study the {\em tracking} problem,…

A central problem in data streams is to characterize which functions of an underlying frequency vector can be approximated efficiently. Recently there has been considerable effort in extending this problem to that of estimating functions of…

Data observed at high sampling frequency are typically assumed to be an additive composite of a relatively slow-varying continuous-time component, a latent stochastic process or a smooth random function, and measurement error. Supposing…

Estimating the second frequency moment of a stream up to $(1\pm\varepsilon)$ multiplicative error requires at most $O(\log n / \varepsilon^2)$ bits of space, due to a seminal result of Alon, Matias, and Szegedy. It is also known that at…

In this paper, we resolve the one-pass space complexity of $L_p$ sampling for $p \in (0,2)$. Given a stream of updates (insertions and deletions) to the coordinates of an underlying vector $f \in \mathbb{R}^n$, a perfect $L_p$ sampler must…

The profile of a sample is the multiset of its symbol frequencies. We show that for samples of discrete distributions, profile entropy is a fundamental measure unifying the concepts of estimation, inference, and compression. Specifically,…

Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for marginal parameters of strictly stationary and ergodic processes,…

Interactive response time is important in analytical pipelines for users to explore a sufficient number of possibilities and make informed business decisions. We consider a forecasting pipeline with large volumes of high-dimensional time…

We introduce a new notion of information complexity for multi-pass streaming problems and use it to resolve several important questions in data streams. In the coin problem, one sees a stream of $n$ i.i.d. uniform bits and one would like to…

Given a finite set of points $P \subseteq \mathbb{R}^d$, we would like to find a small subset $S \subseteq P$ such that the convex hull of $S$ approximately contains $P$. More formally, every point in $P$ is within distance $\epsilon$ from…

Given a stream $p_1, \ldots, p_m$ of items from a universe $\mathcal{U}$, which, without loss of generality we identify with the set of integers $\{1, 2, \ldots, n\}$, we consider the problem of returning all $\ell_2$-heavy hitters, i.e.,…

The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…

We resolve several fundamental questions in the area of distributed functional monitoring, initiated by Cormode, Muthukrishnan, and Yi (SODA, 2008). In this model there are $k$ sites each tracking their input and communicating with a…

Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…

The quickest change detection problem is considered in the context of monitoring large-scale independent normal distributed data streams with possible changes in some of the means. It is assumed that for each individual local data stream,…

We consider the problem of sketching the $p$-th frequency moment of a vector, $p>2$, with multiplicative error at most $1\pm \epsilon$ and \emph{with high confidence} $1-\delta$. Despite the long sequence of work on this problem, tight…

We study the problem of change point localisation and inference for sequentially collected fragmented functional data, where each curve is observed only over discrete grids randomly sampled over a short fragment. The sequence of underlying…

For sequential data, a change point is a moment of abrupt regime switch in data streams. Such changes appear in different scenarios, including simpler data from sensors and more challenging video surveillance data. We need to detect…

We give the first optimal bounds for returning the $\ell_1$-heavy hitters in a data stream of insertions, together with their approximate frequencies, closing a long line of work on this problem. For a stream of $m$ items in $\{1, 2, \dots,…

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…