The above-computation scheme is called regularized kernel CCA [13].
We eclectically list a few references regarding constituent quark models [6 10], effective field theories [11 13], lattice-regularized QCD [14 19], QCD sum rules [20 25], and the renormalization-group approach to QCD [26,27] (always see also references therein).
Due to the linearity of the Stokes equations, the velocity at any point in the fluid can be computed by summing the contributions of regularized Stokeslets, and the time evolution of positions can be computed using standard methods for ordinary differential equations.
L1-regularized methods aim to minimize the sum of squared errors with a bound on the sum of the absolute values of the coefficients [ 65].
We will call the sum of this series a regularized trace of the operator L0.
The resulting binned regularized data was extracted and for each protein was summed across wells by scaled Gaussian summation at the peak position and width of the log-scale time base.
This expresses the index as the sum of an interior contribution, given in terms of regularized zeta functions, and a boundary contribution generalizing the eta invariant of Atiyah-Patodi-Singer.
In such distributed scenario, the training problem can be formulated as the (regularized) optimization of a non-convex social cost function, given by the sum of local (non-convex) costs, where each agent contributes with a single error term defined with respect to its local dataset.
The MSE plots of both standard least squares and regularized estimation are given in Fig. 3. Fig. 2. Weighted residual sum of the squares as a function of regularization constant (a) net #1 (b) net #2 (c) net #3.
The factor matrices (P) and (Q) are learned by minimizing the regularized squared error on the set of observed affinities (kappa): mathop {min}limits_{Q,P} mathop sum limits_{{(d_{i},t_{j} ) in kappa }}^ (m_{i,j} - q_{i}^{T} p_{j} )^{2} + lambda (||p||^{2} + ||q||^{2} ).
In Jalali et al.'s work [34], the sum of two matrices are used to represent the parameters and these are regularized differently to learn both shared features and individual outliers for different tasks separately.
