  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.
