Related papers: Improving Compressed Counting
Compressed Counting (CC)} was recently proposed for approximating the $\alpha$th frequency moments of data streams, for $0<\alpha \leq 2$. Under the relaxed strict-Turnstile model, CC dramatically improves the standard algorithm based on…
The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that…
Compressed Counting (CC), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating Shannon entropy of data…
Compressed Counting (CC) was recently proposed for very efficiently computing the (approximate) $\alpha$th frequency moments of data streams, where $0<\alpha <= 2$. Several estimators were reported including the geometric mean estimator,…
Counting is among the most fundamental operations in computing. For example, counting the pth frequency moment has been a very active area of research, in theoretical computer science, databases, and data mining. When p=1, the task (i.e.,…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using…
This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…
Modern statistical estimation is often performed in a distributed setting where each sample belongs to a single user who shares their data with a central server. Users are typically concerned with preserving the privacy of their samples,…
In this paper, we consider contention resolution algorithms that are augmented with predictions about the network. We begin by studying the natural setup in which the algorithm is provided a distribution defined over the possible network…
We consider the problem of approximating the empirical Shannon entropy of a high-frequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
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…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
Estimating frequency moments of data streams is a very well studied problem and tight bounds are known on the amount of space that is necessary and sufficient when the stream is adversarially ordered. Recently, motivated by various…
We present a near-optimal quantum algorithm, up to logarithmic factors, for estimating the Shannon entropy in the quantum probability oracle model. Our approach combines the singular value separation algorithm with quantum amplitude…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…