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In this section, we propose a novel approach to perform PCE regression with known physical constraints. The approach, referred to as Physically Constrained Polynomial Chaos (PC2), expands the classes of regression models that can obey physical constraints to include PCE, which is widely used for ...
We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and ...
In particular, they have been popular as nonlinear basis functions in regression problems [12, 20], for example in kernel methods [22, 63], and in finite element methods [23]. Yet, few references [5, 15] apply splines within mathematical programming beyond the optimization of spline design ...
Note that approach (b) is an instance of the so-called debiasing methods, which is sometimes done in regular- ized regression, based on the a priori knowledge that the regularizer biases the estimate. As an example, debiasing is commonly done in LASSO estimation [39, 41], where the biased...
It turns out that the coercivity of the objective function provides nice properties to the dual problem, which can then be solved efficiently by a succession of projections onto the cone, as we explain later on in Section 2. Thus, in practice, we can solve (4) with this dual approach as...
If the observed data is unreliable, regression may be preferable because a regression model alleviates anomalies. But here we assume the observed data is reliable and valuable. This is particularly true when the data is obtained from numerical simulations. On the other hand, linear interpolation is...
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