Non-linear terms in Bayesian Hierachical Models

Questions
1

I’ve been building a Bayesian Logistic regression at work. However it’s hit a limitation, and one of the limitations is that there isn’t a linear structure between the covariates and the target variable.

In a Machine Learning paradigm I’d either use a Neural Network or I’d apply some transformation to the feature space to make the model linear.

Is anyone aware of any literature on this - does anyone have any examples?

2

If the dataset is not too big, Gaussian Process usually performs quite well.

3

The sample I’m building a model on is 1000 rows but the total dataset is about 1M rows. Can Gaussian process take into account hierarchical structure? What’s the tradeoffs I get.

4

You will need minibatch with informative prior for inference, but should be doable. It is worth to try.

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