Gaussian processes (GP) method.

A model-independent method of Gaussian processes [@Seikel12a], can be employed to reconstruct the angular-diameter distance ratio from the strong lensing data straightforwardly, without any parametric assumption regarding cosmological model. Such approach has been used in various studies in the literature [@Qi19a; @Cao19]. The distribution over functions provided by GP is suitable to describe the observed data. Not that for each lens-source pairing, $D_{ls}/D_s$, two angular diameter distances are involved. Therefore, a reconstruction of $D_{ls}/D_s$ in two dimensions is required, which is very difficult to handle with GP. Following the methodology proposed by @Yennapureddy, one interesting solution of this problem is to consider small redshift ranges (with fixed source/lens redshift), which may effectively reduce the problem to a one-dimensional reconstruction. In this work, we choose to carry out the reconstruction within thin redshift-shells of lenses, which makes it possible to turn $D_{ls}/D_s$ into a one-dimensional function of source redshift ($z_s$) and thus achieve reasonable constraints on cosmological parameters at much higher redshifts ($z\sim4$). Note that for the purpose of GP reconstruction in one dimension, we assume that all the lenses in redshift bin $(z_l,z_l+\Delta z)$ have the same average redshift $z_l+\Delta z_l/2$. In order to minimize the 