Simulation-Efficient Implicit Inference with Differentiable Simulators"

Simulation-Efficient Implicit Inference with Differentiable Simulators

Justine Zeghal, François Lanusse, Alexandre Boucaud, Denise Lanzieri

$ \underbrace{p(\theta|x_0)}_{\text{posterior}}$ $\propto$ $ \underbrace{p(x_0|\theta)}_{\text{likelihood}}$ $ \underbrace{p(\theta)}_{\text{prior}}$

$\to$ Full-Field Inference

Pros:

Information beyond Gaussian signal

Cons:

Need large number of simulations

Computationnally expensive (HMC)

Our goal: doing Implicit Inference with a minimum number of simulations.

We developped a Differentiable LogNormal Mass Maps simulator

with 5 tomographic bins

and 6 cosmological parameters to infer.

sbi_lens package developped with Denise Lanzieri

For our studies, we used LSST Year 10 configuration.

Information beyond Gaussian signal

Realistic enough for our purpose

Fast

With infinite number of simulations, our Implicit Inference contours are as good as the Full Field contours obtained through HMC

But now, how can we reduce this number of simulations?

$\to$ by using the gradients $\nabla_{\theta} \log p(\theta|x)$ (also known as the score) from our differentiable simulator

With a few simulations it's hard to approximate the distribution.

$\to$ we need more simulations

but if we have a few simulations

and the gradients

then it's possible to have an idea of the shape of the distribution.