Open quantum systems can undergo dissipative phase transitions, and their critical behavior can be used to enhance, e.g., the fidelity of superconducting qubit readout measurements, a central problem toward the creation of reliable quantum hardware. For example, a recently introduced measurement protocol, named ``critical parametric quantum sensing'', uses the parametric (two-photon driven) Kerr resonator's driven-dissipative phase transition to reach single-qubit detection fidelity of 99.9\%. These classification algorithms are applied to the time series data of weak quantum measurements (homodyne detection) of a circuit-QED implementation of the Kerr resonator coupled to a superconducting qubit. This demonstrates how machine learning methods enable a fast and reliable measurement protocol in critical open quantum systems.