Depression in older adults is a significant public health issue with broad impacts on both individuals and society. The multifaceted nature of depression underscores the complexity of identifying and predicting risk factors, necessitating a sophisticated and accurate approach based on new emerging technologies. Compared to traditional statistical methods, machine learning provides a more detailed and individualized understanding of risk variables by analyzing large datasets, identifying patterns, and building predictive models. This study presented a novel feature selection method based on the relief and lasso algorithms. The proposed feature selection method selected the ten most significant features from the dataset. A neural network (NN) with hyperparameters optimized by a grid search technique was used to categorize depression. The feature selection and classification modules work together as a single unit, namely as (Relief_Lasso_NN). Data from the Swedish National Study on Aging and Care (SNAC) was used for this study. The collected dataset consists of 726 samples with 75 features per sample. Four experiments were conducted to validate the performance of the proposed (Relief_Lasso_NN) framework. The proposed model achieved an accuracy of 90.34% in predicting depression using only ten features from the dataset. The top 10 features identified by the proposed feature selection method significantly impact depression in older adults. Furthermore, the performance of seven other state-of-the-art machine learning models was also compared with the proposed framework.