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Polynomial regression under arbitrary product distributions
2010
Machine Learning
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They showed that the L 1 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 . ...
doi:10.1007/s10994-010-5179-6
fatcat:3y7pokynffdv7ftr4gkvcovjly
Polynomial regression under arbitrary product distributions
2018
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They showed that the L1 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 ...
doi:10.1184/r1/6608468
fatcat:ivbexowrhbcb3dd4y7b6gj4mje
Weighted Polynomial Approximations: Limits for Learning and Pseudorandomness
[article]
2014
arXiv
pre-print
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Firstly, the 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. ...
arXiv:1412.2457v1
fatcat:xtydl6gpobhbjprfa3lglv25bq
Agnostically Learning Halfspaces
2008
SIAM journal on computing (Print)
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The new algorithm, essentially L 1 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 . ...
doi:10.1137/060649057
fatcat:ipl2otjwwfasvcmisxhafi65ny
Page 1169 of Genetics Vol. 176, Issue 2
[page]
2007
Genetics
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normal distribution. ...
The curves are definitely not logistic, which explains why animal breeders do not use logistic regression to fit milk production curves. ...
Special functions and characterizations of probability distributions by zero regression properties
1983
Journal of Multivariate Analysis
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Kallianpur Characterizations of the binomial, negative binomial, gamma, Poisson, and normal 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. ...
doi:10.1016/0047-259x(83)90022-2
fatcat:vzjfwf3ffjesfcanozey5n5c4q
Page 8096 of Mathematical Reviews Vol. , Issue 2004j
[page]
2004
Mathematical Reviews
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, 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. ...
Partialed products are interactions; partialed powers are curve components
1978
Psychological bulletin
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score 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 / ...
doi:10.1037//0033-2909.85.4.858
fatcat:uldkda5pcbbtlbpxl43eh4xhma
Partialed products are interactions; partialed powers are curve components
1978
Psychological bulletin
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score 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 / ...
doi:10.1037/0033-2909.85.4.858
fatcat:s2n426sjxvbjrk5mgkkz2eubku
Polynomial representations for response surface modeling
[chapter]
1998
Lecture Notes-Monograph Series
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We show that 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. ...
doi:10.1214/lnms/1215456198
fatcat:yizhds73yjctjpchka2o3il4ia
Regression for sets of polynomial equations
[article]
2013
arXiv
pre-print
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We propose a method called ideal 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. ...
arXiv:1110.4531v4
fatcat:hz5cboayqjeybileja23sald2e
The moments of products of quadratic forms in normal variables
1978
Statistica neerlandica (Print)
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The expectation of the 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. ...
doi:10.1111/j.1467-9574.1978.tb01399.x
fatcat:5i2egronjnhzpfjknyvcya6i5m
Model selection of polynomial kernel regression
[article]
2015
arXiv
pre-print
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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). ...
arXiv:1503.02143v1
fatcat:tuawhsgplvhkpexbrxiimf62hi
Submodular Functions Are Noise Stable
[article]
2011
arXiv
pre-print
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As a consequence, we obtain a 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. ...
arXiv:1106.0518v2
fatcat:yvphyxosvva3ff4lpauhgyw4pu
On the residuals of autoregressive processes and polynomial regression
1985
Stochastic Processes and their Applications
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The residual processes of a stationary AR(p) process and of 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 . ...
doi:10.1016/0304-4149(85)90380-1
fatcat:bvzbnpwutrb7df3kajp3shtoru
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