In this work, we investigate the application of Machine Learning (ML) algorithms to the identification and quantitative characterization of quantum entanglement in polarization-entangled photon pairs. The analysis is based on simulated symmetric, informationally complete, positive operator-valued measure (SIC-POVM) measurement data, where each two-qubit state is represented by a 16-dimensional measurement vector corresponding to experimentally accessible coincidence counts. The generated SIC-POVM measurement data include Poissonian shot noise. Several supervised ML algorithms, including Logistic Regression, k-Nearest Neighbors, Decision Trees, Support Vector Machines, and Random Forests, are applied to the classification of separable and entangled states directly from raw measurement data, without explicit density matrix reconstruction or the use of conventional separability criteria. The study additionally explores clustering methods and nonlinear regression techniques for estimating continuous entanglement measures. The obtained results demonstrate that ML methods can achieve very high classification accuracy, even under extremely limited training conditions. These findings indicate that ML may provide an efficient alternative to conventional quantum-state analysis under simulated Poissonian noise conditions.