Carol Cuesta-Lazaro (IAIFI Fellow)
in collaboration with Siddarth Mishra-Sharma
Generative models for the Large Scale Structure
ML for Large Scale Structure:
Carol's wish list
Generative models
Learn p(x)
Evaluate the likelihood of a 3D map, as a function of the parameters of interest
1
Combine different galaxy properties (such as velocities and positions)
2
Sample 3D maps from the posterior distribution
3
p(
)
|
\mathrm{Cosmology}
Explicit Density
Implicit Density
Tractable Density
Approximate Density
Normalising flows
Variational Autoencoders
Diffusion models
Generative Adversarial Networks
The zoo of generative models
z_T
z_{0}
z_{1}
z_{2}
p(z_{t-1}|z_t)
p(z_t|z_{t-1})
Reverse diffusion: Denoise previous step
Forward diffusion: Add Gaussian noise (fixed)
Diffusion models
A person half Yoda half Gandalf
z_T
z_{0}
z_{1}
Diffusion on point clouds
z_{2}
q_\theta(z_{t-1}|z_t)
p(z_t|z_{t-1})
Reverse diffusion: Denoise previous step
Forward diffusion: Add Gaussian noise (fixed)
Cosmology
p(x,y,z, v_x, v_y, v_z, M_h|\Omega_m, \sigma_8)
Halo Mass Function
Velocity
Mean pairwise velocity
\log p(\boldsymbol{x}) =
\geq \mathbb{E}_{q_{\boldsymbol{\phi}}(\boldsymbol{z}\mid\boldsymbol{x})}\left[\log\frac{p(\boldsymbol{x}, \boldsymbol{z})}{q_{\boldsymbol{\phi}}(\boldsymbol{z}\mid\boldsymbol{x})}\right]
\mathbb{E}_{q_{\boldsymbol{\phi}}(\boldsymbol{z}\mid\boldsymbol{x})}\left[\log\frac{p(\boldsymbol{x}, \boldsymbol{z})}{q_{\boldsymbol{\phi}}(\boldsymbol{z}\mid\boldsymbol{x})}\right] + \mathcal{D}_{\text{KL}}(q_{\boldsymbol{\phi}}(\boldsymbol{z}\mid\boldsymbol{x}) \mid\mid p(\boldsymbol{z}\mid\boldsymbol{x}))
Evidence Lower Bound
Distance to true posterior
q_\theta(z|x) \approx p(z|x)
Find
1. ELBO is a lower bound of the evidence
2. Maximising ELBO = Minimising KL
Maximise ELBO to maximise ev/likelihood
Maximise ELBO to approximate true posterior
+ Galaxy formation
+ Observational systematics (Cut-sky, Fiber collisions)
+ Lightcone, Redshift Space Distortions....
Forward Model
N-body simulations
Observations
Copy of Copy of Copy of deck
By carol cuesta
