ner_tags: O O O B-Model O O O O O O O B-Model I-Model O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Model O O B-Model I-Model I-Model O O O O O B-Survey O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-Model I-Model O O O O O O O B-Model I-Model I-Model O O O O O O O O O B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O B-Model I-Model O O O O B-Model I-Model O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-CelestialObject I-CelestialObject O O O O O O O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: the results to QSANNdRA . Fig. 8 displays the ratio of QSANNdRA ’s relative prediction errors to our calculated relative prediction errors for the original model (Davies et al. 2018a ) and the extended PCA model described above. On average across all target wavelengths, we achieve a 14.2 per cent improvement in (left) and a 11.5 per cent improvement in σ ε (right) on the full test set as compared to Davies et al. ( 2018a ) (shown in grey). When compared to the extended PCA model, we achieve a 6.1 per cent improvement in (left) and a 4.9 per cent improvement in σ ε (right) on the full test set (shown in magenta) with the least improvement being at the Lyα peak. More interestingly, we can compare the performances of QSANNdRA to the extended PCA method on the QSOs in the SDSS data set that are most similar to the z > 7 QSOs that we will use to constrain the high-redshift neutral gas fraction. To do this, we selected the 100 quasars most similar to ULAS J1120+0641 and another 100 most similar to ULAS J1342+0928 based on the red side of the spectra. On these subsets, QSANNdRA ’s performance further improves with respect to the extended PCA method. In particular, on the 100 quasars most similar to ULAS J1120+0641 (at z = 7.085, shown in orange), we achieve a 22.1 per cent improvement in (left) and a 26.2 per cent improvement in σ ε (right). On the 100 nearest neighbours of ULAS J1342+0928 (at z = 7.5413, shown in purple), we achieve a 16.8 per cent improvement in (left) and a 17.5 per cent improvement in σ ε (right). This experiment indicates that overall, the QSANNdRA is more predictive than the model presented in Davies et al. ( 2018a ) as well as its extension and that this is especially true for the two z > 7 QSOs under consideration. Figure 8. Wavelength-dependent distribution of the ratio of QSANNdRA ’s performance to the original PCA model’s performance reported by Davies et al. ( 2018a ) as well as the extended PCA model’s performance in terms of (left) and σ ε (right). The full test set performance improvement as compared to the published model (Davies et al. 2018a ) is shown in grey. When compared to the extended PCA model, the full test set performance ratio (magenta) is compared to the performance ratios on the 100 nearest low-redshift quasar neighbours of ULAS J1120+0641 (orange) and ULAS J1342+0928 (purple) from the test set. 3 APPLICATION TO HIGH-<italic><italic>z</italic></italic> QUASARS Given that we are now confident that our model generalizes to high-redshift objects and performs better than other models in the literature, in this section, we apply QSANNdRA to two high-redshift quasars, namely ULAS J1120+0641 at z = 7.0851 (Mortlock et al. 2011 ; Venemans et al. 2017a ), and ULAS J1342+0928 at z = 7.5413 (Bañados et al. 2018 ) to reconstruct their blue-side spectra and constrain the neutral gas fraction at their corresponding redshifts. 3.1 Reconstructing high-redshift quasar spectra In order to apply our algorithm to the