Speech production interferes with the measurement of changes in cardiac vagal activity during acute stress by attenuating the expected drop in heart rate variability. Speech also induces cardiac sympathetic changes similar to those induced by psychological stress. In the laboratory, confounding of physiological stress reactivity by speech may be controlled experimentally. In ambulatory assessments, however, detection of speech episodes would be necessary to separate the physiological effects of psychosocial stress from those of speech. Using machine learning (https://osf.io/bk9nf), we trained and tested speech classification models on data from 56 participants (ages 18-39) under controlled laboratory conditions. They were equipped with privacy-secure wearables measuring thoracoabdominal respiratory inductance plethysmography (RIP from a single and a dual-band set-up), thoracic impedance pneumography, and an upper sternum positioned unit with triaxial accelerometers and gyroscopes. Following an 80/20 train-test split, nested cross-validations were run with the machine learning algorithms XGBoost, gradient boosting, random forest, and logistic regression on the training set to get generalized performance estimates. Speech classification by the best model per method was then validated in the test set. Speech versus no-speech classification performance (AUC) for both nested cross-validation and test set predictions was excellent for thorax-abdomen RIP (nested cross-validation: 96.6%, test set prediction: 98.5%), thorax-only RIP (97.5%, 99.1%), impedance (97.0%, 97.8%), and accelerometry (99.3%, 99.6%). The sternal accelerometer method outperformed others. These open-access models leveraging biosignals have the potential to also work in daily life settings. This could enhance the trustworthiness of ambulatory psychophysiology, by enabling detection of speech and controlling for its confounding effects on physiology.