Since it is same as the regularized training problem, a parameter norm penalty can be considered as imposing a constraint on weights. Based on ω, the region that the weights are constrained can be obtained. However, we cannot determine the value of k based on the value of α*. Instead,...
Tuning parameter selection for the concave 1-norm and 2-norm group penaltiesDingfeng Jiang
Hence, the key issue is to encourage the difference vector to be as sparse as possible; this work regularizes the vector by a differentiable approximation to the L0-norm penalty to achieve the goal of sparsity. Practically, because new parameters to be optimized are introduced in the learning...
We should say that the solver won’t always succeed in finding such solutions, and that this setting introduces a modest performance penalty, but the setting will significantly reduce the frequency and magnitude of such violations. For examples of how to query or modify parameter values from our...
The diff vector is adaptively pruned during training with a differentiable approximation to the L0-norm penalty to encourage sparsity. Diff pruning becomes parameter-efficient as the number of tasks increases, as it requires storing only the nonzero positions and weights of the diff vector for ...
these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior. The technique is based on penalized least squares with ageometrically intuitive penalty function that shrinks some coefficients to exactly zero. Additionally, this penalty yieldsexa...
We define the mesh dependent norm · h on V h as follows v 2 h = T∈T h |v| 2 H 2 (T) + e∈E h σ e |e| ∂v/∂n 2 L 2 (e) . (3.5) The penalty needs to be large enough to guarantee the ellipticity of a h (v, v) = T∈T h T D 2 v : D 2...
which remains fixed and is shared across different tasks. The diff vector is adaptively pruned during training with a differentiable approximation to the L0-norm penalty to encourage sparsity. Diff pruning becomes parameter-efficient as the number of tasks increases, as it requires storing only the...
Using a sparsity promoting penalty term in the Tikhonov regularization scheme has been shown to be efficient in reconstructing solutions which own a sparse structure. These penalty terms usually take the form of ℓ(quasi-)norm with p ∈ (0, 2). At the same time, some examples have been ...
A new method of choosing the regularization parameter, originally developed for a general class of discrete ill-posed problems, is investigated for electromagnetic inverse scattering problems that are formulated using a penalty method. This so-called Normalized Cumulative Periodogram (NCP) parameter-choice...