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On differentially private frequent itemset mining

Chen Zeng, Jeffrey F. Naughton, Jin-Yi Cai
2012 Proceedings of the VLDB Endowment  
We begin by exploring the theoretical difficulty of simultaneously providing good utility and good privacy in this task.  ...  Related work has proposed differentially private algorithms for the top-k itemset mining problem ("find the k most frequent itemsets".)  ...  Theorem 4 shows that the sensitivity of computing q is equal to the maximal cardinality of transactions.  ... 
doi:10.14778/2428536.2428539 pmid:24039383 pmcid:PMC3771517 fatcat:aly5rcjiybglvcm52li5pfs3he

Cardinality Estimation Meets Good-Turing [article]

Reuven Cohen, Liran Katzir, Aviv Yehezkel
2015 arXiv   pre-print
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements.  ...  This paper presents and analyzes a generic algorithm for combining every cardinality estimation algorithm with a sampling process.  ...  The following theorem generalizes Theorem 2 for any cardinality estimation procedure.  ... 
arXiv:1508.06216v1 fatcat:ekyjtuwq3jeblly3rtdrlpdqge

Reconstructing Multivariate Trigonometric Polynomials from Samples Along Rank-1 Lattices [chapter]

Lutz Kämmerer
2014 Springer Proceedings in Mathematics & Statistics  
We use a componentby-component method in order to determine the generating vector and the lattice size.  ...  Given an arbitrary index set of frequencies, we construct rank-1 lattices that allow a stable and unique discrete Fourier transform.  ...  Theorem 2 . 2 Let d ∈ N, d ≥ 2, and I ⊂ Z d of finite cardinality |I| ≥ 2 be given.  ... 
doi:10.1007/978-3-319-06404-8_14 fatcat:s74amh7i4fg6bfcvzr5wim527e

Reconstructing Multivariate Trigonometric Polynomials by Sampling Along Generated Sets [chapter]

Lutz Kämmerer
2013 Monte Carlo and Quasi-Monte Carlo Methods 2012  
Given an index set of frequencies, we construct corresponding sampling sets that allow a stable and unique discrete Fourier transform.  ...  Applying the one-dimensional non-equispaced fast Fourier transform (NFFT) enables the fast evaluation and reconstruction of the multivariate trigonometric polynomials.  ...  Acknowledgements The author thanks Daniel Potts and Stefan Kunis for numerous valuable discussions. Moreover, he thanks the referees for their very useful suggestions for improvements  ... 
doi:10.1007/978-3-642-41095-6_21 fatcat:v36vg3sdnzdwdf4vvggecyavwe

MTS Sketch for Accurate Estimation of Set-Expression Cardinalities from Small Samples [article]

Reuven Cohen, Liran Katzir, Aviv Yehezkel
2016 arXiv   pre-print
In this paper we present a new framework that can accurately estimate the cardinality of any set expression between any number of streams using only a small sample of each stream.  ...  However, in many real-world applications it is impractical to collect and process the entire data stream, the common practice is thus to sample and process only a small part of it.  ...  Let f 1 be the smallest frequency of element in U X ; compute (precisely) the value of |U 1 |, namely, the number of elements that appear exactly f 1 times in U X .  ... 
arXiv:1611.01853v1 fatcat:tg7dxragxvczflk645acmvqavq

A gossip-based approach for Internet-scale cardinality estimation of XPath queries over distributed semistructured data

Vasil Slavov, Praveen Rao
2013 The VLDB journal  
The cardinality estimate of XPath expressions is useful in XQuery optimization, designing IR-style relevance ranking schemes, and statistical hypothesis testing.  ...  XGossip employs a novel divide-and-conquer strategy for load balancing and reducing the bandwidth consumption.  ...  We compute the sum of the frequency of the value predicate on all the signatures in R to obtain the desired cardinality estimate.  ... 
doi:10.1007/s00778-013-0314-1 fatcat:lfm34al6pfh3tltwelncxvu5ai

Computational Methods for the Fourier Analysis of Sparse High-Dimensional Functions [chapter]

Lutz Kämmerer, Stefan Kunis, Ines Melzer, Daniel Potts, Toni Volkmer
2014 Lecture Notes in Computational Science and Engineering  
: We present stable and effective algorithms for the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on an index set I ⊂ Z d .  ...  Efficient algorithms like the fast Fourier transform (FFT) have to be customised to these thinner discretisations and we focus on two major topics regarding the Fourier analysis of high-dimensional functions  ...  Acknowledgements We gratefully acknowledge support by the German Research Foundation (DFG) within the Priority Program 1324, project PO 711/10-2 and KU 2557/1-2.  ... 
doi:10.1007/978-3-319-08159-5_17 fatcat:nwbbldtm7vdl7hj3bmfw2rsm64

Skew in parallel query processing

Paul Beame, Paraschos Koutris, Dan Suciu
2014 Proceedings of the 33rd ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '14  
Second, in the case when the relations are skewed and the heavy hitters and their frequencies are known, we provide upper and lower bounds expressed in terms of packings of residual queries obtained by  ...  First, in the case when the only statistics on the database are the cardinalities of the input relations, and the data is skew-free, we provide matching upper and lower bounds (up to a polylogarithmic  ...  This work was partially supported by NSF grants IIS-1247469 and CCF-1217099.  ... 
doi:10.1145/2594538.2594558 dblp:conf/pods/BeameKS14 fatcat:szemzwmkajgofb7dh6yjih4dma

A QUICK GLANCE OF SPLINE WAVELETS AND ITS APPLICATIONS

B Kunwar .
2016 International Journal of Research in Engineering and Technology  
As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation.  ...  The orthogonality and finite support properties make the spline wavelets useful for numerical applications and also have the best approximation properties among all the known wavelets.  ...  Theorem 1: The m th order cardinal B-spline satisfies the following properties; i) Supp = 0, ii) > 0 0 < < iii) − = 1 ∀ ∞ =−∞ iv) The Cardinal B-spline and −1 are related by the identity = −1 −1 + − −1  ... 
doi:10.15623/ijret.2016.0510009 fatcat:3n5c4znpljgi7i5meh5iwlz7wm

Multiparty Reach and Frequency Histogram: Private, Secure, and Practical

Badih Ghazi, Ben Kreuter, Ravi Kumar, Pasin Manurangsi, Jiayu Peng, Evgeny Skvortsov, Yao Wang, Craig Wright
2021 Proceedings on Privacy Enhancing Technologies  
Consider the setting where multiple parties each hold a multiset of users and the task is to estimate the reach (i.e., the number of distinct users appearing across all parties) and the frequency histogram  ...  Our protocol exhibits both differential privacy and security guarantees in the honest-but-curious model and in the presence of large subsets of colluding workers; furthermore, its reach and frequency histogram  ...  Acknowledgements We thank Matthew Clegg, Raimundo Mirisola, and Jelani Nelson for helpful discussions and feedback.  ... 
doi:10.2478/popets-2022-0019 fatcat:nyokf2rl4fcnrns7mpnohqkgie

Enumeration formulas for latin and frequency squares

József Dénes, Gary L. Mullen
1993 Discrete Mathematics  
Denes, J. and G.L. Mullen, Enumeration formulas for latin and frequency squares, Discrete Mathematics 111 (1993) 1577163.  ...  Acknowledgement The authors thank S.J. Suchower for a number of helpful comments and for his calculations of the validity of (4) for n < 6. The first author thanks Dr. L.F.  ...  Frequency squares and latin square enumeration We now present a formula which relates the number of latin squares of order n to the cardinalities of the isotopy classes of reduced frequency squares.  ... 
doi:10.1016/0012-365x(93)90152-j fatcat:haaiyenf5fcsdj3a6dhowwk6eq

Constructing spatial discretizations for sparse multivariate trigonometric polynomials that allow for a fast discrete Fourier transform [article]

Lutz Kämmerer
2017 arXiv   pre-print
Furthermore, we analyze the computational complexities of the resulting FFT algorithms in detail and obtain upper bounds in O(M M), where the constants depend only linearly on the spatial dimension.  ...  The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonometric polynomial is known  ...  Acknowledgments The author thanks the referees for the valuable comments and suggestions and gratefully acknowledges the funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)  ... 
arXiv:1703.07230v2 fatcat:r4f5zeumsng2zksjj724dyx3za

A Deterministic Algorithm for Constructing Multiple Rank-1 Lattices of Near-Optimal Size [article]

Craig Gross, Mark A. Iwen, Lutz Kämmerer, Toni Volkmer
2020 arXiv   pre-print
Both algorithms are tested numerically and surpass the theoretical bounds.  ...  The algorithm works by converting a potentially large reconstructing single rank-1 lattice for some d-dimensional frequency set I ⊂ [N]^d into a collection of much smaller rank-1 lattices which allow for  ...  Let I ⊂ Z d be some frequency set with cardinality I = s and expansion N I ∶= max j=1,...,d (max k∈I k j − min h∈I h j ).  ... 
arXiv:2003.09753v1 fatcat:2veetkelofelhlqsbnie7l2mse

Cardinal spline filters: Stability and convergence to the ideal sinc interpolator

A. Aldroubi, M. Unser, M. Eden
1992 Signal Processing  
We prove that the frequency responses of the cardinal spline filters converge to the ideal lowpass filter in all Lfnorms with 1 ~<p < + ~ as the order of the spline tends to infinity.  ...  We provide estimates for the resolution errors and the interpolation errors of the various filters.  ...  They also found through numerical computation that the frequency response of the cardinal spline interpolator of order n approaches an ideal lowpass filter for increasing values of n.  ... 
doi:10.1016/0165-1684(92)90030-z fatcat:ivaey6rac5h7nohmpoznhc2xqa

Improved approximation algorithms for low-density instances of the Minimum Entropy Set Cover Problem [article]

Cosmin Bonchis, Gabriel Istrate
2012 arXiv   pre-print
The optimal parameter choice has a phase transition around average density e and leads to improved approximation guarantees when average element frequency is less than e.  ...  We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets.  ...  The corresponding author has been supported by CNCS IDEI Grant PN-II-ID-PCE-2011-3-0981 "Structure and computational difficulty in combinatorial optimization: an interdisciplinary approach".  ... 
arXiv:1207.7134v1 fatcat:7v2l4fbs5zcoxejsmlgdcl7ffq
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