Our new approach is much faster and yields better performance in terms of mean squared error (MSE). We derive simple formulas for low-dimensional slices and averages facilitating the visualization of an estimated tensor product smooth of dimension three or higher. We demonstrate the applicability ...
We train the model with the Adam optimizer to minimize a mean-squared-error loss function with a mini-batch size B of 32. Note, Ci denotes the irreducible representation of the model predicted elasticity tensor with 21 components (see eqn (2)), but not the Cartesian tensor with 81 ...
This artifact has been made patent through some experimental set-ups, but it is not clear how the distortion translates in the reconstructed DT, and how important it is when compared to the other source of error contributing to the Mean Squared Error (MSE) in the estimate, i.e. the ...
For example, the squared-error loss function which is minimized in vector sparse cod- ing methods comes from the squared Euclidean distance, which is the Bregman divergence corresponding to the multivariate Gaussian distribution. Thus, the minimization of a squared error objective function corresponds ...
The corresponding loss function (12) as a mean squared error MSE reads as (21)L(Θ)=1M∑I=1M(yI−zI(Θ,xI))2. For optimization and testing, the total data set {(xI,yI)}I=1M is decomposed into three sets, (i) the training set T={(xI,yI)}I=1MT with MT=card(T), (ii)...
In analogy to the R´enyi entropies, we can generalize the logarithmic negativity to a one-parameter family of negativities. The kth R´enyi negativity is given by Nk(ρAB) = tr (ρTABB)k . If we let Nm(even)(ρAB) = N2m(ρAB), then the logarithmic negativity is ob- tained...
The crucial point is that the remaining term in the error bound becomes o(1) when m=Ω~((r∗)2n3/2) which for polylogarithmic r∗ improves over the näive algorithm for tensor completion by a polynomial factor in terms of the number of observations. Moreover our algorithm works ...
The logarithmic factor provides a slight oversampling beyond the rank k, which helps to ensure that enough information is captured to accurately represent the k-dimensional subspace of the data. This oversampling accounts for potential noise or minor variations in the data that might not be ...
The logarithmic factor provides a slight oversampling beyond the rank k, which helps to ensure that enough information is captured to accurately represent the k-dimensional subspace of the data. This oversampling accounts for potential noise or minor variations in the data that might not be ...
The logarithmic factor provides a slight oversampling beyond the rank k, which helps to ensure that enough information is captured to accurately represent the k-dimensional subspace of the data. This oversampling accounts for potential noise or minor variations in the data that might not be ...