Predicting hospital length of stay (LOS) reliably is an essential need for efficient resource allocation at hospitals. Traditional predictive modeling tools frequently have difficulty acquiring sufficient and diverse data because healthcare institutions have privacy rules in place. In our study, we modeled this problem as an empirical graph where nodes are the hospitals. This modeling approach facilitates collaborative model training by modeling decentralized data sources from different hospitals without extracting sensitive data outside of hospitals. A local model is trained on a node (hospital) by aiming the generalized total variation minimization (GTVMin). Moreover, we implemented and compared two different federated learning optimization algorithms named federated stochastic gradient descent (FedSGD) and federated averaging (FedAVG). Our results show that federated learning enables accurate prediction of hospital LOS while addressing privacy concerns without extracting data outside healthcare institutions.