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Tuning OPCG

Harris Quach

2021-11-16

Source: vignettes/Tuning OPCG.Rmd
Tuning OPCG.Rmd

Tuning OPCG

We can tune the bandwidth in the Outer Product of Canonical Gradients (OPCG) using the “supervised k-means”-like approach.

  1. For a given \(h\), we estimate \(\hat \beta\) using some training set;
  2. Construct the sufficient predictors for the given \(h\) on some tuning/validation set, denote \(\hat \beta^{\top} X^{(v)}\);
  3. Pick \(h\) that minimizes a k-means-like criterion;

Below is an interactive figure illustrating the methods on some synthetic data. We generate the data from five clusters that are labeled into 3 groups. By moving the slider, you will notice that the minimum of the criterion functions corresponds with very good separation of the labels.