In each case, the medium and the best case regularization scenarios clearly outperformed the non-regularized estimation, leading to better generalizable calibrated models.
As a result of problem division, N neigh (i) regular scenarios are built and solved for each cell i. Figure 5 Scenario regularization.
In broad terms, regularization describes a scenario where estimation for somewhat ill-posed or overparameterized problems is improved through use of some form of additional information.
Such a list is used later for regularization of local scenarios, as will be explained later.
The regularized optimization is solved for a set of regularization parameters in each scenario and depending on the amount of data at hand the generalized cross validation method (GCV) – for larger dataset– or the robust generalized cross-validation method (RGCV) – for smaller dataset– is recommended to choose the optimal candidate.
As the algorithms described by (62) and (64) do not depend strongly on a regularization in the considered scenario, δ=0.03 was chosen.
Based on the above results, we recommend the following regularization procedures for the three scenarios defined previously (in Section " Scenarios based on prior information"): I Best case: a good guess of the parameter values (θ guess) is available.
In the presence of limited or noisy data (a common scenario in neurophysiological experiments), regularization introduces a prior that constrains the STRF estimate in a way that is independent of the underlying tuning properties of the neuron, but can introduce additional biases in the STRF.
To achieve a sparse pattern of interactions, such methods usually employ sparsity-inducing priors in a Bayesian setting or regularization penalties in an optimization-based scenario.
Each case study was solved in the traditional, non-regularized way and with regularization assuming different level of prior knowledge (worst, medium and best case scenarios).
