  Current models of galaxy evolution are constrained by the analysis of
catalogs containing the flux and size of galaxies extracted from multiband deep
fields carrying inevitable observational and extraction-related biases which
can be highly correlated. In practice, taking all of these effects
simultaneously into account is difficult, and derived models are inevitably
biased. To address this issue, we use robust likelihood-free methods for the
inference of luminosity function parameters, made possible via massive
compression of multiband images using artificial neural networks. This
technique makes the use of catalogs unnecessary when comparing observed and
simulated multiband deep fields and constraining model parameters. A forward
modeling approach generates galaxies of multiple types depending on luminosity
function parameters and paints them on photometric multiband deep fields
including both the instrumental and observational characteristics. The
simulated and the observed images present the same selection effects and can
therefore be properly compared. We train a fully-convolutional neural network
to extract the most model-parameter-sensitive summary statistics out of these
realistic simulations, shrinking down the dimensionality of the summary space.
Finally, using the trained network to compress both observed and simulated deep
fields, the model parameter values are constrained through Population Monte
Carlo likelihood-free inference. Using synthetic photometric multiband deep
fields similar to the CFHTLS and D1/D2 deep fields and massively compressing
them through the convolutional neural network, we demonstrate the robustness,
accuracy and consistency of this new catalog-free inference method. We are able
to constrain the parameters of luminosity functions of different types of
galaxies and our results are fully compatible with the classic catalog
extraction approaches.
