Adaptive control and self-tuning of mode-locked fiber laser systems is an interesting topic in applied optics. Rapid and accurate detection of the cavity birefringence value is critical for the adaptive control and self-tuning of fiber laser systems. The birefringence varies randomly and significantly affects the mode-locking performance of fiber laser. In addition, the birefringence value in the laser cavity cannot be measured directly. In this study, from a new perspective, the birefringence value is determined (estimated) by hierarchical implementation of supervised machine learning algorithms. Unlike previous studies, instead of using the laser pulse energy directly, the energy evolution is recorded and a separate time series is obtained for each case of birefringence. The four statistical moments (mean, variance, skewness and kurtosis) of these time series are used as input variables (features) in the machine learning algorithm. When the findings of this study are compared with the results of previous studies, it is seen that the birefringence value can be estimated with higher accuracy in a short time with the hierarchical approach. More accurate classification of birefringence increases efficiency of algorithms that enable adaptive control and self-tuning of mode-locked fiber laser systems. Consequently, the study contributes to the advancement of mode-locked fiber laser technology by enhancing performance in various industrial and scientific applications, enabling broader and more efficient use of laser systems.