Context. Based on the finding that molecular hydrogen is unobservable in cold molecular clouds, the column density measurements of molecular gas currently rely either on dust emission observation in the far-infrared, which requires space telescopes, or on star counting, which is limited in angular resolution by the stellar density. The (sub)millimeter observations of numerous trace molecules can be effective using ground-based telescopes, but the relationship between the emission of one molecular line and the H_(2)column density is non-linear and sensitive to excitation conditions, optical depths, and abundance variations due to the underlying physico- chemistry. Aims. We aim to use multi-molecule line emission to infer the H_(2)molecular column density from radio observations. Methods. We propose a data-driven approach to determine the H_(2)gas column densities from radio molecular line observations. We use supervised machine-learning methods (random forest) on wide-field hyperspectral IRAM-30m observations of the Orion B molecular cloud to train a predictor of the H_(2)column density, using a limited set of molecular lines between 72 and 116 GHz as input, and the Herschel -based dust-derived column densities as “ground truth” output. Results. For conditions similar to those of the Orion B molecular cloud, we obtained predictions of the H_(2)column density within a typical factor of 1.2 from the Herschel -based column density estimates. A global analysis of the contributions of the different lines to the predictions show that the most important lines are~(13)CO(1–0),~(12)CO(1–0), C~(18)O(1–0), and HCO~(+)(1–0). A detailed analysis distinguishing between diffuse, translucent, filamentary, and dense core conditions show that the importance of these four lines depends on the regime, and that it is recommended that the N_(2)H~(+)(1–0) and CH_(3)OH(2_(0)–1_(0)) lines be added for the prediction of the H_(2)column density in dense core conditions. Conclusions. This article opens a promising avenue for advancing direct inferencing of important physical parameters from the molecular line emission in the millimeter domain. The next step will be to attempt to infer several parameters simultaneously (e.g., the column density and far-UV illumination field) to further test the method.
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