Related papers: Sketching and Streaming Entropy via Approximation …
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…
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…
Maximum coverage and minimum set cover problems --collectively called coverage problems-- have been studied extensively in streaming models. However, previous research not only achieve sub-optimal approximation factors and space…
Low-rank approximation in data streams is a fundamental and significant task in computing science, machine learning and statistics. Multiple streaming algorithms have emerged over years and most of them are inspired by randomized…
In this thesis, we explore streaming algorithms for approximating constraint satisfaction problems (CSPs). The setup is roughly the following: A computer has limited memory space, sees a long "stream" of local constraints on a set of…
Entropy Estimation is an important problem with many applications in cryptography, statistic,machine learning. Although the estimators optimal with respect to the sample complexity have beenrecently developed, there are still some…
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…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
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…
We identify a connection between the approximability of CSPs in two models: (i) sublinear space streaming algorithms, and (ii) the basic LP relaxation. We show that whenever the basic LP admits an integrality gap, there is an…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
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…
We initiate a broad study of classical problems in the streaming model with insertions and deletions in the setting where we allow the approximation factor $\alpha$ to be much larger than $1$. Such algorithms can use significantly less…
Most known algorithms in the streaming model of computation aim to approximate a single function such as an $\ell_p$-norm. In 2009, Nelson [\url{https://sublinear.info}, Open Problem 30] asked if it possible to design \emph{universal…
Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that $(1-\epsilon)$-approximation for Max-Cut must use $n^{1-O(\epsilon)}$ space; moreover,…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
In this survey we describe progress over the last decade or so in understanding the complexity of solving constraint satisfaction problems (CSPs) approximately in the streaming and sketching models of computation. After surveying some of…
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
We give near-optimal algorithms for computing an ellipsoidal rounding of a convex polytope whose vertices are given in a stream. The approximation factor is linear in the dimension (as in John's theorem) and only loses an excess logarithmic…
This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…