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Polynomial regression under arbitrary product distributions

2010
*
Machine Learning
*

They showed that the L 1

doi:10.1007/s10994-010-5179-6
fatcat:3y7pokynffdv7ftr4gkvcovjly
*polynomial**regression*algorithm yields agnostic (tolerant to*arbitrary*noise) learning algorithms with respect to the class of threshold functions-*under*certain restricted instance ... We also extend these results to learning*under*mixtures of*product**distributions*. ... As a consequence,*polynomial**regression*agnostically learns with respect to C*under**arbitrary**product**distributions*in time n (O(log(s/ ))) c−1 / 2 . ...##
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Polynomial regression under arbitrary product distributions

2018

They showed that the L1

doi:10.1184/r1/6608468
fatcat:ivbexowrhbcb3dd4y7b6gj4mje
*polynomial**regression*algorithm yields agnostic (tolerant to*arbitrary*noise) learning algorithms with respect to the class of threshold functions —*under*certain restricted instance ... We also extend these results to learning*under*mixtures of*product**distributions*. ... This leads to an agnostic learning result for C*under**arbitrary**product**distributions*which is the same as the one would get for C*under*the uniform*distribution*on {0, 1} n , except for an extra factor ...##
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Weighted Polynomial Approximations: Limits for Learning and Pseudorandomness
[article]

2014
*
arXiv
*
pre-print

Firstly, the

arXiv:1412.2457v1
fatcat:xtydl6gpobhbjprfa3lglv25bq
*polynomial**regression*algorithm of Kalai et al. (SIAM J. ... The power of this algorithm relies on the fact that*under*log-concave*distributions*, halfspaces can be approximated arbitrarily well by low-degree*polynomials*. ... [DFT + 14] shows that, at least for*product**distributions*on the hypercube,*polynomials*yield the best basis for L 1*regression*. ...##
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Agnostically Learning Halfspaces

2008
*
SIAM journal on computing (Print)
*

The new algorithm, essentially L 1

doi:10.1137/060649057
fatcat:ipl2otjwwfasvcmisxhafi65ny
*polynomial**regression*, is a noise-tolerant*arbitrary*-*distribution*generalization of the "low-degree" Fourier algorithm of Linial, Mansour, & Nisan. ... −1, 1} n or the unit sphere in R n , as well as*under*any log-concave*distribution*over R n . ... et al. can be viewed as an algorithm for performing L 2*polynomial**regression**under*the uniform*distribution*on {−1, 1} n . ...##
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Page 1169 of Genetics Vol. 176, Issue 2
[page]

2007
*
Genetics
*

normal

*distribution*. ... The curves are definitely not logistic, which explains why animal breeders do not use logistic*regression*to fit milk*production*curves. ...##
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Special functions and characterizations of probability distributions by zero regression properties

1983
*
Journal of Multivariate Analysis
*

Kallianpur Characterizations of the binomial, negative binomial, gamma, Poisson, and normal

doi:10.1016/0047-259x(83)90022-2
fatcat:vzjfwf3ffjesfcanozey5n5c4q
*distributions*are obtained by the property of zero*regression*of certain*polynomial*statistics of*arbitrary*degree ... In each case, the equations which express zero*regression*are derived from the recurrence relations of a set of special functions. ... Therefore, by starting with those recurrence relations, we can find*polynomial*statistics of*arbitrary*degree which have zero*regression*on L when the underlying probability*distribution*is binomial. ...##
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Page 8096 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

, PA) Asymptotics for

*polynomial*spline*regression**under*weak conditions. ... By restricting attention to spaces built by*polynomial*splines and their tensor*products*the author can now verify the condition (iv)*under*weaker conditions on the growing rate of the dimension. ...##
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Partialed products are interactions; partialed powers are curve components

1978
*
Psychological bulletin
*

score

doi:10.1037//0033-2909.85.4.858
fatcat:uldkda5pcbbtlbpxl43eh4xhma
*regression*coefficients are simply rescaled. ... and anxiety about their use as independent variables in the representation of interactions and curve components in general multiple*regression*/correlation analysis. ... What are not invariant*under*linear transformation when the three IVs are simultaneously*regressed*on F are the semipartial and partial correlations and*regression*coefficients of X and Z, and their / ...##
###
Partialed products are interactions; partialed powers are curve components

1978
*
Psychological bulletin
*

score

doi:10.1037/0033-2909.85.4.858
fatcat:s2n426sjxvbjrk5mgkkz2eubku
*regression*coefficients are simply rescaled. ... and anxiety about their use as independent variables in the representation of interactions and curve components in general multiple*regression*/correlation analysis. ... What are not invariant*under*linear transformation when the three IVs are simultaneously*regressed*on F are the semipartial and partial correlations and*regression*coefficients of X and Z, and their / ...##
###
Polynomial representations for response surface modeling
[chapter]

1998
*
Lecture Notes-Monograph Series
*

We show that

doi:10.1214/lnms/1215456198
fatcat:yizhds73yjctjpchka2o3il4ia
*under*this partial ordering there is a constructive path of design improvement. ... We overview some of the recent work on design optimality for response surface models and*polynomial**regression*. However, our emphasis is not on scalar optimality criteria. ... This greatly facilitates our calculations when we now apply Kronecker*products*to response surface models. 3.*Polynomial**regression*. ...##
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Regression for sets of polynomial equations
[article]

2013
*
arXiv
*
pre-print

We propose a method called ideal

arXiv:1110.4531v4
fatcat:hz5cboayqjeybileja23sald2e
*regression*for approximating an*arbitrary*system of*polynomial*equations by a system of a particular type. ... Ideal*regression*is useful whenever the solution to a learning problem can be described by a system of*polynomial*equations. ... D do 2: that is, sets of*polynomials*closed*under*addition in the set, and*under*multiplication with*arbitrary**polynomials*4 F. J. KIRÁLY, P. VON BÜNAU, J. S. MÜLLER, D. A. J. BLYTHE, F. C. ...##
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The moments of products of quadratic forms in normal variables

1978
*
Statistica neerlandica (Print)
*

The expectation of the

doi:10.1111/j.1467-9574.1978.tb01399.x
fatcat:5i2egronjnhzpfjknyvcya6i5m
*product*of an*arbitrary*number of quadratic forms in normally*distributed*variables is derived. ... Note that this formula can be used to compute all the moments of a*product*of an*arbitrary*number of quadratic forms. ... ., x, from an*arbitrary**distribution*. Then, is a quadratic form in x; The n-vector 1, consists of ones only. ...##
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Model selection of polynomial kernel regression
[article]

2015
*
arXiv
*
pre-print

*Polynomial*kernel

*regression*is one of the standard and state-of-the-art learning strategies. ... On one hand, based on the worst-case learning rate analysis, we show that the regularization term in

*polynomial*kernel

*regression*is not necessary. ...

*Under*this circumstance, the computational burden of

*polynomial*kernel

*regression*can be reduced and much less than that of Gaussian kernel

*regression*(See Table 4 in Section 5). ...

##
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Submodular Functions Are Noise Stable
[article]

2011
*
arXiv
*
pre-print

As a consequence, we obtain a

arXiv:1106.0518v2
fatcat:yvphyxosvva3ff4lpauhgyw4pu
*polynomial*-time learning algorithm for this class with respect to any*product**distribution*on {-1,1}^n (for any constant accuracy parameter ϵ). ... In Section 3.2 we will prove Theorem 3 in the general setting of*arbitrary**product**distributions*. ... n is a*product**distribution*. ...##
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On the residuals of autoregressive processes and polynomial regression

1985
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Stochastic Processes and their Applications
*

The residual processes of a stationary AR(p) process and of

doi:10.1016/0304-4149(85)90380-1
fatcat:bvzbnpwutrb7df3kajp3shtoru
*polynomial**regression*are considered. The residuals are obtained from ordinary least squares fitting. ... In the*polynomial*case, they converge to generalized Brownian bridges. Other uses of the residuals are considered. ...*Polynomial**regression*residual process Consider the*polynomial**regression*k=O or k+j+l' j=0,1,. B~")-~, ( B, -tB1) -3t( t-1) ( B, -2 Io' Bs ds ) -5t(t-1)(2t-1) Bl+6 B~ds-12 sB, ds . ...
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