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Efficiently Approximating Weighted Sums with Exponentially Many Terms
[chapter]

2001
*
Lecture Notes in Computer Science
*

This is useful when there are

doi:10.1007/3-540-44581-1_6
fatcat:azrll3l4yrca3ownzuohcnwlvu
*exponentially**many*such inputs and no apparent means to*efficiently*compute their*weighted**sum*. ... These uses require*exponentially**many*inputs, so we define Markov chains over the inputs to*approximate*the*weighted**sums*. ... However, the*exponential*number of prunings motivates us to use an MCMC approach to*approximate*the*weighted**sum*of the experts' predictions. ...##
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Maintaining time-decaying stream aggregates

2006
*
Journal of Algorithms
*

We develop storage-

doi:10.1016/j.jalgor.2005.01.006
fatcat:244bqng2hrakjpzzdwdxzowc3a
*efficient*algorithms, and establish upper and lower bounds. ... of maintaining time-decaying aggregates and statistics of a data stream: the relative contribution of each data item to the aggregate is scaled down by a factor that depends on, and is non-increasing*with*... This result shows that polynomially decaying*sums*can be tracked nearly as*efficiently*as*Exponentially*decaying*sums*. ...##
###
Maintaining time-decaying stream aggregates

2003
*
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '03
*

We develop storage-

doi:10.1145/773153.773175
dblp:conf/pods/CohenS03
fatcat:zwgqbpxbafhehor34jqz5qoory
*efficient*algorithms, and establish upper and lower bounds. ... of maintaining time-decaying aggregates and statistics of a data stream: the relative contribution of each data item to the aggregate is scaled down by a factor that depends on, and is non-increasing*with*... This result shows that polynomially decaying*sums*can be tracked nearly as*efficiently*as*Exponentially*decaying*sums*. ...##
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Efficient estimation of neural weights by polynomial approximation

1999
*
IEEE Transactions on Information Theory
*

We design here algorithms for

doi:10.1109/18.771153
fatcat:tvp5brxe2fcepdbennkblomyfe
*efficient*uniform*approximation*by a certain class of neural networks*with*one hidden layer which we call nearly*exponential*. ... Index*Terms*-*Approximation*algorithms, complexity problem for neural networks, nearly*exponential*activation function, neural network*with*one hidden layer, order of uniform*approximation*. ... ACKNOWLEDGMENT The author thanks Herr Christoph Pesch for his help*with*the SNNS and a referee for pointing out [2] and [8] and a weakness of Algorithm 4.1 that led to the formulation of Algorithm ...##
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Numerical Error in Weighting Function-Based Unsteady Friction Models for Pipe Transients

2006
*
Journal of Hydraulic Engineering
*

*Approximation*of the

*weighting*function

*with*a

*sum*of

*exponential*

*terms*allows for a considerable increase in computation speed using recursive algorithms. ... In addition, the numerical algorithm used for unsteady friction should be highly

*efficient*, as inverse analysis requires the transient model to be run

*many*times. ... The recursive convolution method relies on the

*approximation*of the

*weighting*function by a

*sum*of

*exponential*

*terms*. ...

##
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Efficient Mean Shift Clustering Using Exponential Integral Kernels

2008
*
Zenodo
*

Novel corresponding

doi:10.5281/zenodo.1073240
fatcat:jtqslzxokbelpnmvwsshrqhcle
*exponential*integral kernels are introduced to allow the application of nonuniform kernels for clustering, which dramatically increases robustness without giving up the*efficiency*of ... For*efficiency*, all calculations are performed on integral images. ... In this paper,*exponential*integral kernels are introduced which allow mean shift to be calculated on integral images*with**weighted*non-uniform kernels. ...##
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A Novel Approach for the Efficient Computation of 1-D and 2-D Summations

2016
*
IEEE Transactions on Antennas and Propagation
*

The method is based on applying a subspace algorithm to the samples of partial

doi:10.1109/tap.2016.2521860
fatcat:iw7h5pmiwbfdhcbj7j4zsbmxje
*sums*and*approximating*them in*terms*of complex*exponentials*. ... For a convergent summation, the residue of the*exponential**term**with*zero complex pole of this*approximation*corresponds to the result of the summation. ... Once the S(m) values are computed, they can be*approximated*in*terms*of complex*exponentials*, and similarly, the residue of the*exponential**term**with*zero complex pole corresponds to the result of the ...##
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New summing algorithm using ensemble computing

2002
*
Journal of Physics A: Mathematical and General
*

From a practical point of view, the proposed algorithm may result in an

doi:10.1088/0305-4470/35/42/102
fatcat:wtvwv5igwbafjjichzogcorsyq
*exponential*speedup, compared to known quantum and classical*summing*algorithms. ... The query complexity of the algorithm depends only on the scaling of the measurement sensitivity*with*the number of distinct spin sub-ensembles. ... Unfortunately, these results simply state that in the limit of infinite number of*terms*, the*approximating**sums*coincide*with*the desired integrals. ...##
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Forward Decay: A Practical Time Decay Model for Streaming Systems

2009
*
Proceedings / International Conference on Data Engineering
*

We provide

doi:10.1109/icde.2009.65
dblp:conf/icde/CormodeSSX09
fatcat:qc4xkd4nt5hahli7eksp3hgdgm
*efficient*algorithms to compute a variety of aggregates and draw samples under forward decay, and show that these are easy to implement scalably. ... We argue that this is because the usual definitions of time decay are "backwards": the decayed*weight*of a tuple is based on its age, measured backward from the current time. ... Here,*efficient**approximate*solutions are known. ...##
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Truncated Exponential Series based partial Euler Product calculations at quiescent regions of oscillatory divergence to produce approximations of the Riemann Siegel Z function

2021
*
figshare.com
*

Truncated

doi:10.6084/m9.figshare.14842803.v1
fatcat:ibswcvflczaxflhi3tunle7bgy
*exponential*series based partial Euler Product calculations about the two quiescent regions at N ≈ ( t/π ) & sqrt(t/2/π) match finite Riemann Zeta Dirichlet series*sum**approximations*of the Riemann ... Since the calculation is computationally expensive some*approximations*of the Euler product calculations are also explored. ... To reduce the residual high frequency*terms*, a 31*term*sinc function is applied as a low pass averaging filter to equation (11)*with*the*terms*spaced by 1/log(t). ...##
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Optimal approximations of power laws with exponentials: application to volatility models with long memory

2007
*
Quantitative finance (Print)
*

a power-law

doi:10.1080/14697680701278291
fatcat:4eydzh3evba5vpue4bbnbzxmom
*with*a finite*sum*of*weighted**exponentials*. ... CONCLUSIONS We have provided a simple method to use*efficiently*a*sum*of*weighted**exponentials*as a parsimonious*approximation*of a power-law*with*any exponent. ...##
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The monomial method: Extensions, variations, and performance issues

1994
*
International Journal for Numerical Methods in Engineering
*

The monomial method solves systems of non-linear algebraic equations by constructing a sequence of

doi:10.1002/nme.1620371206
fatcat:sia33ar5w5acdgblhkcuar52ui
*approximating*monomial (single-*term*polynomial) systems, much as Newton's method generates a sequence ... Two new versions ofthe algorithm are presented, both of which are simplified and computationally more*efficient*to implement in comparison to the original algorithm. ... Instead, a*sum*of products is*exponentiated*once for each*term*. ...##
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Solving Factored MDPs with Continuous and Discrete Variables
[article]

2012
*
arXiv
*
pre-print

We present a new linear program

arXiv:1207.4150v1
fatcat:mtpzbz74yzebhcuke6ccc33e2q
*approximation*method that exploits the structure of the hybrid MDP and lets us compute*approximate*value functions more*efficiently*. ... Although*many*real-world stochastic planning problems are more naturally formulated by hybrid models*with*both discrete and continuous variables, current state-of-the-art methods cannot adequately address ...*exponentially*-large*sums*and complex integrals. ...##
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Tensor Monte Carlo: particle methods for the GPU era
[article]

2019
*
arXiv
*
pre-print

While the

arXiv:1806.08593v3
fatcat:rtlm6ux6yfgxvhnjow4gulai3q
*sum*over*exponentially**many**terms*might seem to be intractable, in*many*cases it can be computed*efficiently*as a series of tensor inner-products. ... However, IWAEs scale poorly: as the latent dimensionality grows, they require*exponentially**many*samples to retain the benefits of importance*weighting*. ... While the*sum*over*exponentially**many**terms*might seem to be intractable, in*many*cases it can be computed*efficiently*as a series of tensor inner-products. ...##
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On approximation of functions by exponential sums

2005
*
Applied and Computational Harmonic Analysis
*

We introduce a new approach, and associated algorithms, for the

doi:10.1016/j.acha.2005.01.003
fatcat:6clifgejqrdqff4zpcxciz7fqa
*efficient**approximation*of functions and sequences by short linear combinations of*exponential*functions*with*complex-valued exponents and ... These*approximations*are obtained for a finite but arbitrary accuracy and typically have significantly fewer*terms*than Fourier representations. ... Brad Alpert (NIST) for pointing out connections*with*the steepest descent method and Dr. Martin Mohlenkamp (Ohio University) for*many*useful suggestions. ...
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