(V)iolet (C)rumble dimension

I guess it's great to know about it but, gosh, all the detail... Perhaps variable elimination is a good compromise.

I'll weigh in with Bayesian networks: excellent to understand conditional independence, probabilistic structure and information flow.

Let's say the more submissions the truer the statement 😅
About doubts of a proof and these things: yes, that's what I meant with "not substantially worse".

The trick adopted from #probabilistic #circuits: make PCs deep and structured, representing an exponential number of polynomials! DeepPCE nicely scales to thousands of inputs and is competitive with standard deep neural nets. Big bonus: tractable expectations, covariances and Sobol indices!

PCE, a classical physical surrogate model, is a linear combination of (tensorproducts of) orthogonal polynomials. But, it doesn't scale gracefully to high dimensions, as the number of polynomials grows exponentially in the number of input dimensions. Also sparseness only helps to a limited extent.

As I have PERSONALLY worked with him, I can say with certainty that it's the right guy.

Obscure but works?