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Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical…

Statistical Mechanics · Physics 2017-09-13 S. E. Marzen , J. P. Crutchfield

A data stream is viewed as a sequence of $M$ updates of the form $(\text{index},i,v)$ to an $n$-dimensional integer frequency vector $f$, where the update changes $f_i$ to $f_i + v$, and $v$ is an integer and assumed to be in $\{-m, ...,…

Data Structures and Algorithms · Computer Science 2010-06-01 Sumit Ganguly , Purushottam Kar

Measurement samples are often taken in various monitoring applications. To reduce the sensing cost, it is desirable to achieve better sensing quality while using fewer samples. Compressive Sensing (CS) technique finds its role when the…

Information Theory · Computer Science 2016-11-18 Ying Li , Kun Xie , Xin Wang

This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system…

Information Theory · Computer Science 2016-12-21 Zhong Liu , Shengyao Chen , Feng Xi

Sorted data is usually easier to compress than unsorted permutations of the same data. This motivates a simple compression scheme: specify the sorted permutation of the data along with a representation of the sorted data compressed…

Data Structures and Algorithms · Computer Science 2014-11-24 Oscar Stiffelman

We consider the problem of estimating the frequency components of a mixture of s complex sinusoids from a random subset of n regularly spaced samples. Unlike previous work in compressed sensing, the frequencies are not assumed to lie on a…

Information Theory · Computer Science 2013-07-12 Gongguo Tang , Badri Narayan Bhaskar , Parikshit Shah , Benjamin Recht

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

Information Theory · Computer Science 2015-05-18 Dmitry Malioutov , Sujay Sanghavi , Alan Willsky

We analyze the statistical complexity vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period {\tau}. It is shown that if the Bandt and Pompe procedure is used to assign a probability distribution…

Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…

Computation · Statistics 2021-07-20 Luca Martino , Víctor Elvira

We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…

Machine Learning · Statistics 2013-12-18 Nikolaos M. Freris , Orhan Öçal , Martin Vetterli

The count-min sketch (CMS) is a randomized data structure that provides estimates of tokens' frequencies in a large data stream using a compressed representation of the data by random hashing. In this paper, we rely on a recent Bayesian…

Machine Learning · Statistics 2021-02-12 Emanuele Dolera , Stefano Favaro , Stefano Peluchetti

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-27 Seth Gilbert , Calvin Newport , Nitin Vaidya , Alex Weaver

This paper proposes a novel entropy encoding technique for lossless data compression. Representing a message string by its lexicographic index in the permutations of its symbols results in a compressed version matching Shannon entropy of…

Information Theory · Computer Science 2017-03-24 Abu Bakar Siddique

We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…

Data Structures and Algorithms · Computer Science 2008-12-18 Nicholas J. A. Harvey , Jelani Nelson , Krzysztof Onak

We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…

Machine Learning · Statistics 2021-06-23 Rémi Gribonval , Gilles Blanchard , Nicolas Keriven , Yann Traonmilin

We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…

Statistics Theory · Mathematics 2020-05-25 Masoud M Nasari , Mohamedou Ould-Haye

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can…

Statistics Theory · Mathematics 2013-04-29 Quentin Berthet , Philippe Rigollet

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

Information Theory · Computer Science 2016-11-17 Jin Tan , Danielle Carmon , Dror Baron

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K << N elements from an N-dimensional basis. Instead of taking periodic…

Information Theory · Computer Science 2016-11-17 Richard G. Baraniuk , Volkan Cevher , Marco F. Duarte , Chinmay Hegde

When individuals in a population can be classified in classes or categories, the coverage of a sample, $C$, is defined as the probability that a randomly selected individual from the population belongs to a class represented in the sample.…

Computation · Statistics 2025-04-08 Carlos Hernandez-Suarez