Distinguishing standard and modified gravity cosmologies with machine learning

 

Authors: A. Peel, F. Lalande, J.-L. Starck, V. Pettorino, J. Merten,  C. Giocoli, M. Meneghetti,  M. Baldi
Journal: Submitted to PRL
Year: 2018
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Abstract

We present a convolutional neural network to identify distinct cosmological scenarios based on the weak-lensing maps they produce. Modified gravity models with massive neutrinos can mimic the standard concordance model in terms of Gaussian weak-lensing observables, limiting a deeper understanding of what causes cosmic acceleration. We demonstrate that a network trained on simulated clean convergence maps, condensed into a novel representation, can discriminate between such degenerate models with 83%-100% accuracy. Our method outperforms conventional statistics by up to 40% and is more robust to noise.

On the dissection of degenerate cosmologies with machine learning

 

Authors: J. Merten,  C. Giocoli, M. Baldi, M. Meneghetti, A. Peel, F. Lalande, J.-L. Starck, V. Pettorino
Journal: Submitted to MNRAS
Year: 2018
Download: ADS | arXiv


Abstract

Based on the DUSTGRAIN-pathfinder suite of simulations, we investigate observational degeneracies between nine models of modified gravity and massive neutrinos. Three types of machine learning techniques are tested for their ability to discriminate lensing convergence maps by extracting dimensional reduced representations of the data. Classical map descriptors such as the power spectrum, peak counts and Minkowski functionals are combined into a joint feature vector and compared to the descriptors and statistics that are common to the field of digital image processing. To learn new features directly from the data we use a Convolutional Neural Network (CNN). For the mapping between feature vectors and the predictions of their underlying model, we implement two different classifiers; one based on a nearest-neighbour search and one that is based on a fully connected neural network. We find that the neural network provides a much more robust classification than the nearest-neighbour approach and that the CNN provides the most discriminating representation of the data. It achieves the cleanest separation between the different models and the highest classification success rate of 59% for a single source redshift. Once we perform a tomographic CNN analysis, the total classification accuracy increases significantly to 76% with no observational degeneracies remaining. Visualising the filter responses of the CNN at different network depths provides us with the unique opportunity to learn from very complex models and to understand better why they perform so well.

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

 

Authors: M.A. Schmitz, M. Heitz, N. Bonneel, F.-M. Ngolè, D. Coeurjolly, M. Cuturi, G. Peyré & J.-L. Starck
Journal: SIAM SIIMS
Year: 2018
Download: ADS | arXiv

 


Abstract

This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in the probability simplex. Our method simultaneously estimates such atoms, and, for each datapoint, the vector of weights that can optimally reconstruct it as an optimal transport barycenter of such atoms. Our method is computationally tractable thanks to the addition of an entropic regularization to the usual optimal transportation problem, leading to an approximation scheme that is efficient, parallel and simple to differentiate. Both atoms and weights are learned using a gradient-based descent method. Gradients are obtained by automatic differentiation of the generalized Sinkhorn iterations that yield barycenters with entropic smoothing. Because of its formulation relying on Wasserstein barycenters instead of the usual matrix product between dictionary and codes, our method allows for non-linear relationships between atoms and the reconstruction of input data. We illustrate its application in several different image processing settings.

Unsupervised feature learning for galaxy SEDs with denoising autoencoders

 

Authors: Frontera-Pons, J., Sureau, F., Bobin, J. and Le Floc'h E.
Journal: Astronomy & Astrophysics
Year: 2017
Download: ADS | arXiv


Abstract

With the increasing number of deep multi-wavelength galaxy surveys, the spectral energy distribution (SED) of galaxies has become an invaluable tool for studying the formation of their structures and their evolution. In this context, standard analysis relies on simple spectro-photometric selection criteria based on a few SED colors. If this fully supervised classification already yielded clear achievements, it is not optimal to extract relevant information from the data. In this article, we propose to employ very recent advances in machine learning, and more precisely in feature learning, to derive a data-driven diagram. We show that the proposed approach based on denoising autoencoders recovers the bi-modality in the galaxy population in an unsupervised manner, without using any prior knowledge on galaxy SED classification. This technique has been compared to principal component analysis (PCA) and to standard color/color representations. In addition, preliminary results illustrate that this enables the capturing of extra physically meaningful information, such as redshift dependence, galaxy mass evolution and variation over the specific star formation rate. PCA also results in an unsupervised representation with physical properties, such as mass and sSFR, although this representation separates out less other characteristics (bimodality, redshift evolution) than denoising autoencoders.