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Distribution-Free Property-Testing
2007
SIAM journal on computing (Print)
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Chapter 8 Testing Monotonicity over Graph Products In this chapter we consider the problem of monotonicity testing over graph products. ...
Monotonicity testing over graph products. We study the use of graph products in monotonicity testing from several aspects. ...
It is left to prove that it is indeed a monotonicity tester. If f is monotone then clearly, by the definition of the tester, it is accepted by the tester with probability 1. ...
doi:10.1137/050645804
fatcat:sfoxbcmosvf2tjqyizghpdfyhq
L_p-Testers for Bounded Derivative Properties on Product Distributions
[article]
2014
arXiv
pre-print
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Previous results for L_p testing on [n]^d for this class were known for monotonicity and c-Lipschitz properties over uniformly distributed domains. ...
We consider the problem of L_p-testing of class of bounded derivative properties over hypergrid domain with points distributed according to some product distribution. ...
We unify the two settings and get better results for the L p -property testing over product distributions. Definition 1.1 formally defines the notion of L p -distance over general distributions. ...
arXiv:1404.5545v4
fatcat:du2dhomv3na27oks5lw4yc37l4
Subtractive Mixture Models via Squaring: Representation and Learning
[article]
2024
arXiv
pre-print
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2024 pre-print arXiv:2310.00724v2 fatcat:uasgbpymcfcnbouxf7jpvh33teOther Versions
A circuit c is a parameterized computational graph over variables X encoding a function c(X) and comprising three kinds of computational units: input, product, and sum. ...
U test between the log-likelihoods achieved by NPC 2 s and monotonic PCs on the test data (see also Fig. 5 ), using a total of 36 runs for layer dimensionalities K ≤ 256 and 18 runs for K > 256. ...
Best average test log-likelihoods and two standard errors achieved by monotonic PCs (MPC) and NPC 2 s built either from randomized linear tree RGs (LT) or from randomized binary tree RGs (BT) (see App. ...
arXiv:2310.00724v3
fatcat:b4bh3jaqtvchxebgdhfvqzv52a
Arithmetic Circuits and the Hadamard Product of Polynomials
2009
Foundations of Software Technology and Theoretical Computer Science
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. • We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class C = L, and over fields of characteristic p the problem ...
In contrast the Permanent can be expressed as the Hadamard product of two monotone multilinear formulas of quadratic size. ...
Next we show that identity testing noncommutative ABPs over any field is hard for NL by a reduction from directed graph reachability. Let (G, s, t) be a reachability instance. ...
doi:10.4230/lipics.fsttcs.2009.2304
dblp:conf/fsttcs/ArvindJS09
fatcat:7z73rdfejjcdfpwmunnnofprzq
Boolean Function Complexity Advances and Frontiers
2014
Bulletin of the European Association for Theoretical Computer Science
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Then L( f ) is at least the product of the average degrees of the left and right parts of the graph G f . ...
of two 0/1 √ n × √ n matrices over GF(2). ...
dblp:journals/eatcs/Jukna14
fatcat:x3y2bootivdd7mx4xswv7myrhy
The Complexity of Searching Several Classes of AND/OR Graphs
1985
International Joint Conference on Artificial Intelligence
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The correspondence bet ween AND/OR graphs and context free grammars i s that connectors (the AND arcs) correspond to productions, and OR arcs correspond to a choi ce of productions. ...
If the range of cost functions is over real numbers, there may be no minimum cost parse tree. ...
dblp:conf/ijcai/MottelerK85
fatcat:5jefpwfpqzcbbhh3wogihuze5q
On the Fourier spectrum of monotone functions
1995
Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
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-Any monotone Boolean function can be approximated within error ⑀ under product distributions by a non-monotone Boolean circuit of size 2 Õ(1/⑀͌n) and depth Õ(1/⑀ ͌ n). ...
The main result is that any monotone Boolean function has most of its power spectrum on its Fourier coefficients of "degree" at most O( ͌ n) under any product distribution. ...
for suggesting the notion of influence norm, Yishay Mansour, for suggesting the average sensitivity viewpoint, and Uriel Feige, for pointing out to us some references on Hamiltonian cycles in random graphs ...
doi:10.1145/225058.225125
dblp:conf/stoc/BshoutyT95
fatcat:xmpa3c6azzd4bf6zeyr6zcruki
On the Fourier spectrum of monotone functions
1996
Journal of the ACM
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-Any monotone Boolean function can be approximated within error ⑀ under product distributions by a non-monotone Boolean circuit of size 2 Õ(1/⑀͌n) and depth Õ(1/⑀ ͌ n). ...
The main result is that any monotone Boolean function has most of its power spectrum on its Fourier coefficients of "degree" at most O( ͌ n) under any product distribution. ...
for suggesting the notion of influence norm, Yishay Mansour, for suggesting the average sensitivity viewpoint, and Uriel Feige, for pointing out to us some references on Hamiltonian cycles in random graphs ...
doi:10.1145/234533.234564
fatcat:36owbohnrvawtnk5wy5a4pmjma
Superpolynomial Lower Bounds for Monotone Span Programs
1999
Combinatorica
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We also show that the perfect matching function can be computed by polynomial size (non-monotone) span programs over arbitrary fields. * Part of this work has been presented at the 28th ACM STOC'96. ...
Our lower bounds are based on an analysis of Paley-type bipartite graphs via Weil's character sum estimates. ...
Based on Tutte's theorem and the Schwartz-Zippel lemma [Schw, Zi] about probabilistic testing of polynomial identities, Lovász [L] reduced the problem if a graph contains a perfect matching to testing ...
doi:10.1007/s004930050058
fatcat:2sem6zdsmnehjnonloifotmk4m
Stress-strain behaviour of bamboo beyond its elastic limit under uniaxial compressive load, using the principles of plasticity and damage mechanics
2020
Zenodo
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The stress-strain curves produced from the proposed mathematical model are compared with the test results and the comparison shows that the results from the model provide a good agreement with the test ...
Several samples of the bamboo species Oxytenantera abyssinica, from the Congo Basin Rain Forest were tested to collect the necessary data for this study. ...
Some of the graphs from the tests results are shown in figures 2a to 2h. The stress-strain graphs are made up of the unloading and reloading curves as well as the envelope curves. ...
doi:10.5281/zenodo.3737878
fatcat:qmpzkw7s3bernjplpua57xzt64
Sampling and Reconstruction of Signals on Product Graphs
[article]
2018
arXiv
pre-print
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The proposed scheme is particularly useful for processing signals on large-scale product graphs. ...
Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. ...
Furthermore, since the multiplication of two monotone nondecreasing functions results in a monotone non-decreasing function, and the addition of a constant preserves monotonicity, G is a monotone non-decreasing ...
arXiv:1807.00145v1
fatcat:faymgirmjfdg7awr6zbdzmv62m
Mixing under monotone censoring
[article]
2013
arXiv
pre-print
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Our results are based on new connections with the field of property testing. A number of open problems are presented. ...
We initiate the study of mixing times of Markov chain under monotone censoring. Suppose we have some Markov Chain M on a state space Ω with stationary distribution π and a monotone set A ⊂Ω. ...
In a different direction our results suggest testing non-product measures. ...
arXiv:1311.5945v2
fatcat:z564exapbjcmnpaqfowt5q73ei
SAMPLING AND RECONSTRUCTION OF SIGNALS ON PRODUCT GRAPHS
2018
2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
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The proposed scheme is particularly useful for processing signals on large-scale product graphs. ...
Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. ...
the product graph. ...
doi:10.1109/globalsip.2018.8646609
dblp:conf/globalsip/Ortiz-JimenezCC18
fatcat:fxeklgiey5fgfhp75wdj4dlini
Convergent message passing algorithms - a unifying view
[article]
2012
arXiv
pre-print
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In particular, we show that Wainwright's non-convergent sum-product algorithm for tree based variational bounds, is actually convergent with the right update order for the case where trees are monotonic ...
We present a simple derivation of an abstract algorithm, tree-consistency bound optimization (TCBO) that is provably convergent in both its sum and max product forms. ...
In each case we tested the new TCBO algorithms. ...
arXiv:1205.2625v1
fatcat:35cfl2uzsvff3bads2mxyxpljy
Page 7063 of Mathematical Reviews Vol. , Issue 2003i
[page]
2003
Mathematical Reviews
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The paper investigates the complexity of testing for solvability systems of equations over a finite group. ...
More precisely, they prove that if a nontrivial monotone Boolean function f(x),X%2,...,- X,), N= N,-A, is transitively invariant under the direct product G,, x G,, of permutation groups G,, and G,,, where ...
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