The research paper is devoted to the measurement of poverty (and its depth) of the population of Russian regions on the basis of a hybrid approach. This approach involves both an objective assessment of the phenomenon under study (according to Rosstat data) and taking into account the subjective perception of poverty by the population. In the first case, the index method is used in combination with the method of self-organising maps by T. Kohonen and an ensemble of multilayer perseptrons of various configurations. Artificial intelligence allows not only to deepen the results of retrospective assessment of multidimensional poverty through cluster analysis, but also to realise the predictive function. In the second case, a sociological survey is conducted on the example of a certain region of Russia (the Republic of Bashkortostan). According to the results of the cluster analysis, taking into account the earlier retrospective assessment, we can conclude that there is a high degree of polarisation of Russian regions based on the actual level of ‘multidimensional poverty’. ‘Oases’ (St. Petersburg, Moscow and the Republic of Tatarstan) contrast with “centres” (the Republic of Ingushetia, the Republic of Tyva, the Karachay-Cherkess Republic and the Republic of Altai) of multidimensional poverty. At the same time, the Republic of Bashkortostan (one of the old-industrial regions with a rich mineral and raw material base) in the formed rating regularly occupied the median position among other constituent entities of the Russian Federation. The main (key) problems in the sphere of poverty for this region of Russia are specified based on the results of sociological research. Such a study also makes it possible to deepen the retrospective assessment of ‘multidimensional poverty’, since not all the necessary data for a comprehensive analysis of the phenomenon under study are generated by Rosstat on a regular basis. The results obtained in the framework of the study can be used in the actualisation of the most important direction of the state social policy of modern Russia – the fight against poverty. In the long term, the top management of the country needs to ensure a significant reduction in the poverty level of the population regardless of the territorial factor (constituent entity of the Russian Federation).