# Learning summary statistics with machine learning

Carolina Cuesta-Lazaro

16th December 2021 - Oxford

Collaborators: Cheng-Zong Ruan, Yosuke Kobayashi, Alexander Eggemeier, Pauline Zarrouk, Sownak Bose, Takahiro Nishimichi, Baojiu Li, Carlton Baugh

1+\xi^S(s_\perp, s_\parallel) = \int dr_\parallel \left(1 + \blue{\xi^R(r)}\right) \red{\mathcal{P}(v_\parallel=s_\parallel-r_\parallel|r_\perp, r_\parallel)}
\blue{\xi^R(r)}

Two representative MG models:

- The background expansion is the same as LCDM

- One parameter to describe deviations from LCDM

(same large scale real space clustering)

Cosmology =

\{\vec{c}\}
\vec{c}_i

Neural Network Emulator

\vec{c}, \mathrm{redshift}, M_h
\xi^R_{hh}(r|M_h)
v_{hh}(r|M_h)
\xi^R_{hh}(r|c_i, M_h)
v_{hh}(r|c_i, M_h)

Galaxy =

\{\vec{g}\}
\xi_{gg} \propto \int d M_h W(\vec{g}_j, M_h) \xi_{hh}(M_h)
\xi_{gg} \propto \int d M_h W(\vec{g}_j, M_h) \xi_{hh}(M_h)

Voids

Clusters

r [h^{-1} \mathrm{Mpc}]
\Omega_M
\Omega_\Lambda
\sigma_8

Inputs

x

Neural network

f

Representation

(Summary statistic)

r = f(x)

Output

o = g(r)

By carol cuesta

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