Related papers: Two maximum entropy based algorithms for running q…
We address the problem of estimating the running quantile of a data stream when the memory for storing observations is limited. We (i) highlight the limitations of approaches previously described in the literature which make them unsuitable…
The need to estimate a particular quantile of a distribution is an important problem which frequently arises in many computer vision and signal processing applications. For example, our work was motivated by the requirements of many…
In this paper we consider the problem of estimating quantiles when data are received sequentially (data stream). For real life data streams, the distribution of the data typically varies with time making estimation of quantiles challenging.…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…
Estimating the quantiles of a large dataset is a fundamental problem in both the streaming algorithms literature and the differential privacy literature. However, all existing private mechanisms for distribution-independent quantile…
Approximating quantiles and distributions over streaming data has been studied for roughly two decades now. Recently, Karnin, Lang, and Liberty proposed the first asymptotically optimal algorithm for doing so. This manuscript complements…
Modern applications require processing streams of data for estimating statistical quantities such as quantiles with small amount of memory. In many such applications, in fact, one needs to compute such statistical quantities for each of a…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…
The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
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…
Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of…
Many well-known, real-world problems involve dynamic data which describe the relationship among the entities. Hypergraphs are powerful combinatorial structures that are frequently used to model such data. For many of today's data-centric…
Computing the approximate quantiles or ranks of a stream is a fundamental task in data monitoring. Given a stream of elements $x_1, x_2, \dots, x_n$ and a query $x$, a relative-error quantile estimation algorithm can estimate the rank of…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
In this paper, we consider the parameter estimation problem over sensor networks in the presence of quantized data and directed communication links. We propose a two-stage algorithm aiming at achieving the centralized sample mean estimate…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…