Block-Simultaneous Direction Method of Multipliers: A proximal primal-dual splitting algorithm for nonconvex problems with multiple constraints

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may be nonconvex as long as it is convex in every argument, while the constraints $g_\circ$ need to be convex but not smooth. If $f$ is smooth, the proposed Block-Simultaneous Direction Method of Multipliers (bSDMM) can be interpreted as a proximal analog to inexact coordinate descent methods under constraints. Unlike alternative approaches for joint solvers of multiple-constraint problems, we do not require linear operators $L$ of a constraint function $g(L\ \cdot)$ to be invertible or linked between each other. bSDMM is well-suited for a range of optimization problems, in particular for data analysis, where $f$ is the likelihood function of a model and $L$ could be a transformation matrix describing e.g. finite differences or basis transforms. We apply bSDMM to the Non-negative Matrix Factorization task of a hyperspectral unmixing problem and demonstrate convergence and effectiveness of multiple constraints on both matrix factors. The algorithms are implemented in python and released as an open-source package.Comment: 13 pages, 4 figure

Joint Cosmic Density Reconstruction from Photometric and Spectroscopic Samples

We reconstruct the dark matter density field from spatially overlapping spectroscopic and photometric redshift catalogs through a forward modelling approach. Instead of directly inferring the underlying density field, we find the best fitting initial Gaussian fluctuations that will evolve into the observed cosmic volume. To account for the substantial uncertainty of photometric redshifts we employ a differentiable continuous Poisson process. In the context of the upcoming Prime Focus Spectrograph (PFS), we find improvements in cosmic structure classification equivalent to 50-100\% more spectroscopic targets by combining relatively sparse spectroscopic with dense photometric samples.Comment: 7 pages, 6 figure

Multiscale Feature Attribution for Outliers

Machine learning techniques can automatically identify outliers in massive datasets, much faster and more reproducible than human inspection ever could. But finding such outliers immediately leads to the question: which features render this input anomalous? We propose a new feature attribution method, Inverse Multiscale Occlusion, that is specifically designed for outliers, for which we have little knowledge of the type of features we want to identify and expect that the model performance is questionable because anomalous test data likely exceed the limits of the training data. We demonstrate our method on outliers detected in galaxy spectra from the Dark Energy Survey Instrument and find its results to be much more interpretable than alternative attribution approaches.Comment: 6 pages, 2 figures, accepted to NeurIPS 2023 Workshop on Machine Learning and the Physical Sciences. Code available at https://github.com/al-jshen/im

Plausible Adversarial Attacks on Direct Parameter Inference Models in Astrophysics

In this abstract we explore the possibility of introducing biases in physical parameter inference models from adversarial-type attacks. In particular, we inject small amplitude systematics into inputs to a mixture density networks tasked with inferring cosmological parameters from observed data. The systematics are constructed analogously to white-box adversarial attacks. We find that the analysis network can be tricked into spurious detection of new physics in cases where standard cosmological estimators would be insensitive. This calls into question the robustness of such networks and their utility for reliably detecting new physics.Comment: Accepted submission to Machine Learning and the Physical Sciences workshop, NeurIPS 202

Spotting Hallucinations in Inverse Problems with Data-Driven Priors

Hallucinations are an inescapable consequence of solving inverse problems with deep neural networks. The expressiveness of recent generative models is the reason why they can yield results far superior to conventional regularizers; it can also lead to realistic-looking but incorrect features, potentially undermining the trust in important aspects of the reconstruction. We present a practical and computationally efficient method to determine, which regions in the solutions of inverse problems with data-driven priors are prone to hallucinations. By computing the diagonal elements of the Fisher information matrix of the likelihood and the data-driven prior separately, we can flag regions where the information is prior-dominated. Our diagnostic can directly be compared to the reconstructed solutions and enables users to decide if measurements in such regions are robust for their application. Our method scales linearly with the number of parameters and is thus applicable in high-dimensional settings, allowing it to be rolled out broadly for the large-volume data products of future wide-field surveys.Comment: 7 pages 3 figures, Accepted at the ICML 2023 Workshop on Machine Learning for Astrophysic

First measurement of gravitational lensing by cosmic voids in SDSS

We report the first measurement of the diminutive lensing signal arising from matter underdensities associated with cosmic voids. While undetectable individually, by stacking the weak gravitational shear estimates around 901 voids detected in SDSS DR7 by Sutter et al. (2012a), we find substantial evidence for a depression of the lensing signal compared to the cosmic mean. This depression is most pronounced at the void radius, in agreement with analytical models of void matter profiles. Even with the largest void sample and imaging survey available today, we cannot put useful constraints on the radial dark-matter void profile. We invite independent investigations of our findings by releasing data and analysis code to the public at https://github.com/pmelchior/void-lensingComment: 6 pages, 5 figures, as accepted by MNRA

Lightweight starshade position sensing with convolutional neural networks and simulation-based inference

Starshades are a leading technology to enable the direct detection and spectroscopic characterization of Earth-like exoplanets. To keep the starshade and telescope aligned over large separations, reliable sensing of the peak of the diffracted light of the occluded star is required. Current techniques rely on image matching or model fitting, both of which put substantial computational burdens on resource-limited spacecraft computers. We present a lightweight image processing method based on a convolutional neural network paired with a simulation-based inference technique to estimate the position of the spot of Arago and its uncertainty. The method achieves an accuracy of a few centimeters across the entire pupil plane, while only requiring 1.6 MB in stored data structures and 5.3 MFLOPs (million floating point operations) per image at test time. By deploying our method at the Princeton Starshade Testbed, we demonstrate that the neural network can be trained on simulated images and used on real images, and that it can successfully be integrated in the control system for closed-loop formation flying.Comment: submitted to JATI

Parametrising arbitrary galaxy morphologies: potentials and pitfalls

We demonstrate that morphological observables (e.g. steepness of the radial light profile, ellipticity, asymmetry) are intertwined and cannot be measured independently of each other. We present strong arguments in favour of model-based parametrisation schemes, namely reliability assessment, disentanglement of morphological observables, and PSF modelling. Furthermore, we demonstrate that estimates of the concentration and Sersic index obtained from the Zurich Structure & Morphology catalogue are in excellent agreement with theoretical predictions. We also demonstrate that the incautious use of the concentration index for classification purposes can cause a severe loss of the discriminative information contained in a given data sample. Moreover, we show that, for poorly resolved galaxies, concentration index and M_20 suffer from strong discontinuities, i.e. similar morphologies are not necessarily mapped to neighbouring points in the parameter space. This limits the reliability of these parameters for classification purposes. Two-dimensional Sersic profiles accounting for centroid and ellipticity are identified as the currently most reliable parametrisation scheme in the regime of intermediate signal-to-noise ratios and resolutions, where asymmetries and substructures do not play an important role. We argue that basis functions provide good parametrisation schemes in the regimes of high signal-to-noise ratios and resolutions. Concerning Sersic profiles, we show that scale radii cannot be compared directly for profiles of different Sersic indices. Furthermore, we show that parameter spaces are typically highly nonlinear. This implies that significant caution is required when distance-based classificaton methods are used.Comment: 18 pages, 13 figure