dealing with zero inflation

[dirknbr]

We have an observed outcome y that has a lot of 0s and some positive values.

Generally we find that any model will find theta where almost all prediction of y are 0. We could add a loss penalty for 0 predictions.

How would you estimate this in SBI and avoid the zero collapse?

[janfb]

Thanks for the question! A couple of clarifications first, since the right approach depends a lot on the setup.

In sbi, the neural network isn't trained to predict y, but the distribution over theta conditioned on y. theta are the parameters and we usually call the simulator output x. NPE fits a posterior p(theta | x), NLE fits a likelihood p(x | theta), and NRE fits a ratio. So there isn't a per-sample "prediction of y" with a loss you can add a zero-penalty to in the usual sense.

For your specific case, a couple of things to clarify:

1. Dimensionality of theta and of x (your y): is y a single scalar, or a vector / time series that's mostly zeros?
2. The nature of y: is it count data (zero-inflated Poisson / negative-binomial style) or a continuous quantity with a spike at exactly 0 (a "hurdle" distribution)?
3. Have you tried running sbi already, e.g., NPE? If so, did you use an an embedding network for y?

If you can post a minimal snippet of how you build the simulator, prior, and the NPE call (plus the shapes of theta and x), we can be much more concrete.

[dirknbr]

Imagine our true model is y = max(0, a + b * x + error), where x and y are continuous.

My simulator will be

def sim(theta, x):
return max(0, theta[0] + theta[1] * x + noise)

We want to estimate posterior theta given observed (x, y)