What does it look like to have a label-constrained latent-variable model that generates data and labels, for use in regression and inference? That's been the subject of discussion between me and Soledad Villar (NYU) and various students for many months now. We finally got serious and (in a collaborative notebook) Villar implemented her vision of this today. It works! And it works well; it appears to defeat similarly flexible discriminative models (where we are just trying to find a function of the data that predicts labels). If this holds up, it confirms my conjectures and my prejudice, so I am pretty enthusiastic about this.
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