Not yet reviewed by Pith; the record is open.

Correlating BASS DR3 catalogue with ALLWISE database, the data from optical and infrared information are obtained. The quasars from SDSS are taken as training and test samples while those from LAMOST are considered as external test sample. We propose two schemes to construct the redshift estimation models with XGBoost, CatBoost and Random forest. One scheme (namely one-step model) is to predict photometric redshifts directly based on the optimal models created by these three algorithms; the other scheme (namely two-step model) is to firstly classify the data into low- and high- redshift datasets, and then predict photometric redshifts of these two datasets separately. For one-step model, the performance of these three algorithms on photometric redshift estimation is compared with different training samples, and CatBoost is superior to XGBoost and Random forest. For two-step model, the performance of these three algorithms on the classification of low- and high-redshift subsamples are compared, and CatBoost still shows the best performance. Therefore CatBoost is regard as the core algorithm of classification and regression in two-step model. By contrast with one-step model, two-step model is optimal when predicting photometric redshift of quasars, especially for high redshift quasars. Finally the two models are applied to predict photometric redshifts of all quasar candidates of BASS DR3. The number of high redshift quasar candidates is 3938 (redshift $\ge 3.5$) and 121 (redshift $\ge 4.5$) by two-step model. The predicted result will be helpful for quasar research and follow up observation of high redshift quasars.