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Sampling Sketches for Concave Sublinear Functions of Frequencies [article]

Edith Cohen, Ofir Geri
2019 arXiv   pre-print
Our main contribution is the design of composable sampling sketches that can be tailored to any concave sublinear function of the frequencies.  ...  The family of concave sublinear functions includes low frequency moments (p ≤ 1), capping, logarithms, and their compositions.  ...  Acknowledgments Ofir Geri was supported by NSF grant CCF-1617577, a Simons Investigator Award for Moses Charikar, and the Google Graduate Fellowship in Computer Science in the School of Engineering at  ... 
arXiv:1907.02218v3 fatcat:kg6l33hu4bedlnwpx6m532cbdu

Composable Sketches for Functions of Frequencies: Beyond the Worst Case [article]

Edith Cohen, Ofir Geri, Rasmus Pagh
2021 arXiv   pre-print
In this paper we study when it is possible to construct compact, composable sketches for weighted sampling and statistics estimation according to functions of data frequencies.  ...  Surprisingly, we show analytically and empirically that "in practice" small polylogarithmic-size sketches provide accuracy for "hard" functions.  ...  Acknowledgments We are grateful to the authors of [28] , especially Chen-Yu Hsu and Ali Vakilian, for sharing their data, code, and predictions with us.  ... 
arXiv:2004.04772v3 fatcat:nejlrz4evzdejgpziiwcbmea7a

HyperLogLog Hyper Extended: Sketches for Concave Sublinear Frequency Statistics [article]

Edith Cohen
2017 arXiv   pre-print
We design composable sketches of double-logarithmic size for all concave sublinear statistics. Our design combines theoretical optimality and practical simplicity.  ...  We consider here all statistics of the frequency distribution of keys, where a contribution of a key to the aggregate is concave and grows (sub)linearly with its frequency.  ...  Sketches for Concave Sublinear Frequency Statistics , , provided inTable 1.  ... 
arXiv:1607.06517v5 fatcat:rcnsfczacbbmxj23opbou4fwtu

Subspace exploration: Bounds on Projected Frequency Estimation [article]

Graham Cormode, Charlie Dickens, David P. Woodruff
2021 arXiv   pre-print
We study the space complexity of computing data analysis functions over such subspaces, including heavy hitters and norms, when the subspaces are revealed only after observing the data.  ...  That is, for c,c' ∈ (0,1) and a parameter N=2^d an N^c-approximation can be obtained in space min(N^c',n), showing that it is possible to improve on the naïve approach of keeping information for all 2^  ...  Muthukrishnan and Jacques Dark for helpful discussions about this problem. The work of GC and CD was supported by European Research Council grant ERC-2014-CoG 647557.  ... 
arXiv:2101.07546v1 fatcat:z7eyi6jm5jhoxenwuotooqy47i

Visualizing Van der Waals Epitaxial Growth of 2D Heterostructures

Kenan Zhang, Changchun Ding, Baojun Pan, Zhen Wu, Austin Marga, Lijie Zhang, Hao Zeng, Shaoming Huang
2021 Advanced Materials  
Understanding the growth mechanisms of 2D van der Waals (vdW) heterostructures is of great importance in exploring their functionalities and device applications.  ...  This allows the identification of a new growth mode with a distinctly different growth rate and morphology from those of the conventional linear growth mode.  ...  Acknowledgements We thank Shao-Yi Wu of University of Electronic Science and Technology of China for his help with the VASP calculations.  ... 
doi:10.1002/adma.202105079 pmid:34541723 fatcat:f6hoamih3jfppap3i7eijixohi

WOR and p's: Sketches for ℓ_p-Sampling Without Replacement [article]

Edith Cohen, Rasmus Pagh, David P. Woodruff
2020 arXiv   pre-print
We design novel composable sketches for WOR ℓ_p sampling, weighted sampling of keys according to a power p∈[0,2] of their frequency (or for signed data, sum of updates).  ...  and higher accuracy for the same number of samples.  ...  This approach yields WOR distinct ( 0 ) sampling [53] , 1 sampling [41, 22] , and sampling with respect to any concave sublinear functions of frequency (including p sampling for p ≤ 1) [20, 24] ).  ... 
arXiv:2007.06744v3 fatcat:sns6m6vyabbcfjqqwarvnjifzm

Streaming and sublinear approximation of entropy and information distances

Sudipto Guha, Andrew McGregor, Suresh Venkatasubramanian
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
In a data stream setting (sublinear space), we give the first algorithm for estimating the entropy of a distribution.  ...  In this paper we design streaming and sublinear time property testing algorithms for entropy and various information theoretic distances.  ...  There has been a long history of papers for computing the frequency moments of streams.  ... 
doi:10.1145/1109557.1109637 fatcat:rxplmcvhijg5fluzcbcthblcdy

Online Monotone Optimization [article]

Ian Gemp, Sridhar Mahadevan
2016 arXiv   pre-print
The framework hinges on a special choice of a system-wide loss function we have developed.  ...  Furthermore, to our knowledge, this is the first framework to provide a suitable notion of regret for variational inequalities.  ...  We refer the reader to [15] for a Figure 1 : The sketch on the left represents the gradient map of a convex function (e.g., x 2 + y 2 ) while the sketch on the right is of a circular vector field.  ... 
arXiv:1608.07888v1 fatcat:td4feopzgbgzvapvwwj5jelpmu

Truly Perfect Samplers for Data Streams and Sliding Windows [article]

Rajesh Jayaram, David P. Woodruff, Samson Zhou
2021 arXiv   pre-print
In the G-sampling problem, the goal is to output an index i of a vector f ∈ℝ^n, such that for all coordinates j ∈ [n], Pr[i=j] = (1 ±ϵ) G(f_j)/∑_k∈[n] G(f_k) + γ, where G:ℝ→ℝ_≥ 0 is some non-negative function  ...  Abstract truncated due to arXiv limits; please see paper for full abstract.  ...  CCF-1815840, National Institute of Health (NIH) grant 5R01 HG 10798-2, and a Simons Investigator Award.  ... 
arXiv:2108.12017v1 fatcat:urlnlecdwfam5il6mdac6b7ywa

SetSketch: Filling the Gap between MinHash and HyperLogLog [article]

Otmar Ertl
2021 arXiv   pre-print
MinHash and HyperLogLog are sketching algorithms that have become indispensable for set summaries in big data applications.  ...  While HyperLogLog allows counting different elements with very little space, MinHash is suitable for the fast comparison of sets as it allows estimating the Jaccard similarity and other joint quantities  ...  In particular, log (1 − ( − )(1 − 1/ )) and log (1 − ( − )(1 − 1/ )) are both concave, because the logarithm of a linear function is concave. □ Lemma 15.  ... 
arXiv:2101.00314v2 fatcat:ccybanavojgp5mviczyvljk4iq

Device-independent randomness generation with sublinear shared quantum resources

Cédric Bamps, Serge Massar, Stefano Pironio
2018 Quantum  
We present a two-device protocol for DI random number generation (DIRNG) which produces approximately n bits of randomness starting from n pairs of arbitrarily weakly entangled qubits.  ...  Operationally, this leads to a DIRNG protocol between distant laboratories that requires only a sublinear amount of quantum communication to prepare the devices.  ...  In the following corollary to Theorem 3, we show that there exists a choice for the parameters θ, ξ, and γ, expressed as functions of n, such that the consumption of ebits m is sublinear in the number  ... 
doi:10.22331/q-2018-08-22-86 fatcat:v3l7gydypvcevcj56ggrxf4ncm

Meta-Learning Bandit Policies by Gradient Ascent [article]

Branislav Kveton, Martin Mladenov, Chih-Wei Hsu, Manzil Zaheer, Csaba Szepesvari, Craig Boutilier
2021 arXiv   pre-print
This setting is of a particular importance because it lays foundations for meta-learning of bandit policies and reflects more realistic assumptions in many practical domains.  ...  We derive reward gradients that reflect the structure of bandit problems and policies, for both non-contextual and contextual settings, and propose a number of interesting policies that are both differentiable  ...  By definition, the above function is continuous and concave in h. This concludes the proof.  ... 
arXiv:2006.05094v2 fatcat:5lkjkzjy55cwhmxkkjc7idjp2a

ANLS: Adaptive Non-Linear Sampling Method for Accurate Flow Size Measurement

Chengchen Hu, Bin Liu, Sheng Wang, Jia Tian, Yu Cheng, Yan Chen
2012 IEEE Transactions on Communications  
Instead of statically pre-configuring the sampling rate, ANLS dynamically adjusts the sampling rate for each flow according to the value of a corresponding counter.  ...  However, most of the existing methods suffer from large errors for the estimation of smallsize flows.  ...  Furthermore, we find a broad category of sampling functions that can be used for ANLS.  ... 
doi:10.1109/tcomm.2011.112311.100622 fatcat:25vcyouyvvf5zmdn27idf3apsy

Sketching Transformed Matrices with Applications to Natural Language Processing [article]

Yingyu Liang, Zhao Song, Mengdi Wang, Lin F. Yang, Xin Yang
2020 arXiv   pre-print
In this paper, we first propose a space-efficient sketching algorithm for computing the product of a given small matrix with the transformed matrix.  ...  However, we need to compute a matrix decomposition of the entry-wisely transformed matrix, f(A):=(f(a_i,j)) for some function f. Is it possible to do it in a space efficient way?  ...  Streaming space complexity of nearly all functions of one variable on frequency vectors.  ... 
arXiv:2002.09812v1 fatcat:gcwy7iysnbhafhu4mcxydmk3hm

Direct Multifield Volume Ray Casting of Fiber Surfaces

Kui Wu, Aaron Knoll, Benjamin J Isaac, Hamish Carr, Valerio Pascucci
2017 IEEE Transactions on Visualization and Computer Graphics  
Fiber surfaces, an analogy of isosurfaces to bivariate volume data, are a promising new mechanism for understanding multifield volumes.  ...  Our method requires little preprocess, and enables real-time exploration of data, dynamic modification and pixel-exact rendering of fiber surfaces, and support for higher-order interpolation in domain  ...  [19] note that the sampling rate required for volume rendering with sharp feature reconstruction is the product of the frequencies of all component fields convolved via the transfer function.  ... 
doi:10.1109/tvcg.2016.2599040 pmid:27875207 fatcat:bbq4lqlcvjbppelajcxrrernya
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