This study integrates geospatial analysis with machine learning to understand the interplay and spatial dependencies among various indicators of food insecurity. Specifically, we use the VASyR data on Syrian refugees in Lebanon and merge it with novel geospatial data to uncover why certain indicators of food security are successful in specific contexts, while others fall short in providing accurate insights. Our findings indicate that geolocational indicators significantly influence food insecurity, overshadowing traditional factors like household sociodemographics and living conditions. They suggest a shift in focus from labor-intensive socioeconomic surveys to readily accessible geospatial data. The study underscores the variability of food insecurity across different locations and subpopulations, challenging the effectiveness of individual measures like FCS, HDDS, and rCSI in capturing localized needs. From a policy perspective, our insights call for a refined approach to addressing food insecurity among refugees. By disaggregating the various dimensions of food insecurity and understanding their distribution, policymakers and humanitarian organizations can better tailor their strategies, directing resources to areas where refugees face the most severe challenges, thereby enhancing the effectiveness of food security measures.