Machine cosmology: investigating the dark sector through novel inference methods

Cosmology during the last few decades has experienced an influx of new theory and observations, pushed forward by ever-increasing capabilities of current and upcoming large-scale surveys, computational and methodological capabilities, and new theoretical work being fueled by these latter factors. Observational measurements often carry uncertainties from noise or random processes, with inference methods being concerned with inverse probability as the quest to explore underlying distributions of data. Over the same time frame, Bayesian statistics has thus quickly found itself in a central role in cosmological analysis, as the field is rife with inverse problems such as hypothesis testing, model selection, and parameter estimation. More recently, inference models from the field of machine learning have also experienced a surge in applications to cosmology. We delve into the utility of such inference methods for challenges in cosmology in different degrees of granularity and focusing on the dark sector of our Universe, traveling from the largest scale to more local problems in the process. Starting in the area of cosmological parameter estimation, we develop a novel parallel-iterative parameter estimation method rooted in Bayesian nonparametrics and recent developments in variational inference from the field of machine learning in Chapter 2. In doing so, we propose, implement, and test a new approach to fast high-dimensional parameter estimation in an embarrassingly parallel manner. For this work, we make use of large-scale supercomputing facilities to speed up the functional extraction of cosmological parameter posteriors based on data from the Dark Energy Survey. Next, we concentrate on the dark energy equation of state in Chapter 3, stress-testing its imprint on type Ia supernovae measurements through an introduced random curve generator for smooth function perturbation. We then investigate the robustness of standard model analyses based on such data with regard to deviations from a cosmological constant in the form of a redshift-dependent equation of state. With regard to large-scale structure, we show the advantages of density ridges as curvilinear principal curves from Dark Energy Survey weak lensing data for cosmic trough identification in Chapter 4. Denoising large-scale structure in this way allows for the more fine-grained identification of structural components in the cosmic web. We also compare the results of our extended version of the subspace-constrained mean shift algorithm to curvelet denoising as an alternative method, as well as trough structure from measurements of the foreground matter density field. Lastly, in the area of galaxy formation and evolution, we combine analytic formalisms and machine learning methods in a hybrid prediction framework in Chapter 5. We use a two-step process to populate dark matter haloes taken from the SIMBA cosmological simulation with baryonic galaxy properties of interest. For this purpose, we use the equilibrium model of galaxy evolution as a precursory module to enable an improved prediction of remaining baryonic properties as a way to quickly complete cosmological simulations

Lagged correlation-based deep learning for directional trend change prediction in financial time series

Trend change prediction in complex systems with a large number of noisy time series is a problem with many applications for real-world phenomena, with stock markets as a notoriously difficult to predict example of such systems. We approach predictions of directional trend changes via complex lagged correlations between them, excluding any information about the target series from the respective inputs to achieve predictions purely based on such correlations with other series. We propose the use of deep neural networks that employ step-wise linear regressions with exponential smoothing in the preparatory feature engineering for this task, with regression slopes as trend strength indicators for a given time interval. We apply this method to historical stock market data from 2011 to 2016 as a use case example of lagged correlations between large numbers of time series that are heavily influenced by externally arising new information as a random factor. The results demonstrate the viability of the proposed approach, with state-of-the-art accuracies and accounting for the statistical significance of the results for additional validation, as well as important implications for modern financial economics.Comment: 11 pages, 4 figure