Neural Inference of Gaussian Processes for Time Series Data of Quasars

TL;DR

This paper introduces a novel stochastic model called Convolved Damped Random Walk and a neural inference method to improve the modeling and interpolation of quasar light curves, outperforming traditional approaches.

Contribution

The paper proposes the Convolved Damped Random Walk model and Neural Inference technique, enhancing Gaussian process inference for quasar time series analysis.

Findings

Neural Inference significantly improves parameter estimation accuracy.

The CDRW model better captures quasar spectral smoothness.

Combined CDRW and Neural Inference outperform baseline models in interpolation.

Abstract

The study of quasar light curves poses two problems: inference of the power spectrum and interpolation of an irregularly sampled time series. A baseline approach to these tasks is to interpolate a time series with a Damped Random Walk (DRW) model, in which the spectrum is inferred using Maximum Likelihood Estimation (MLE). However, the DRW model does not describe the smoothness of the time series, and MLE faces many problems in terms of optimization and numerical precision. In this work, we introduce a new stochastic model that we call $\textit{Convolved Damped Random Walk}$ (CDRW). This model introduces a concept of smoothness to a DRW, which enables it to describe quasar spectra completely. We also introduce a new method of inference of Gaussian process parameters, which we call $\textit{Neural Inference}$. This method uses the powers of state-of-the-art neural networks to improve the conventional MLE inference technique. In our experiments, the Neural Inference method results in significant improvement over the baseline MLE (RMSE: $0.318 \rightarrow 0.205$, $0.464 \rightarrow 0.444$). Moreover, the combination of both the CDRW model and Neural Inference significantly outperforms the baseline DRW and MLE in interpolating a typical quasar light curve ($\chi^2$: $0.333 \rightarrow 0.998$, $2.695 \rightarrow 0.981$). The code is published on GitHub.