A statistical method trained and optimized to retrieve relative humidity (RH) profiles is presented and evaluated with measurements from radiosoundings. The method makes use of the microwave payload of the Megha-Tropiques plateform, namely the SAPHIR sounder and the MADRAS imager. The approach, based on a Generalized Additive Model (GAM), embeds both the physical and statistical characteritics of the inverse problem in the training phase and no explicit thermodynamical constraint, such as a temperature profile or an integrated water vapor content, is provided to the model at the stage of retrieval. The model is built for cloud-free conditions in order to avoid the cases of scattering of the microwave radiation in the 18.7-183.31 GHz range covered by the payload. Two instrumental configurations are tested: a SAPHIR-MADRAS scheme and a SAPHIR-only scheme, to deal with the stop of data acquisition of MADRAS in January 2013 for technical reasons. A comparison to retrievals based on the Multi-Layer Perceptron (MLP) technique and on the Least Square-Support Vector Machines (LS-SVM) shows equivalent performance over a large realistic set, promising low errors (bias < 2.2%) and scatters (correlation > 0.8) throughout the troposphere (150-900 hPa). A comparison to radiosounding measurements performed during the international field experiment CINDY/DYNAMO/AMIE of winter 2011-2012 confirms these results for the mid-tropospheric layers (correlation between 0.6 and 0.92), with an expected degradation of the quality of the estimates at the surface and top layers. Finally a rapid insight of the large-scale RH field from Megha-Tropiques is discussed and compared to ERA-Interim.