In this paper we investigate how supervised machine learning can be leveraged to improve online prediction of thermoacoustic combustion instabilities using dynamic pressure readings. We discuss the current state of the art tools for the online detection of combustion instabilities, namely the Hurst exponent and Auto-Regressive model, the precursors they detect and how they go about doing so. We show that the generality of these tools comes at the cost of predictive power, which can be recovered using supervised machine learning. To demonstrate this we apply two different supervised machine learning approaches (using Hidden Markov Models and Automatic Machine Learning) to the classification of the state of a combustor given the dynamic pressure readings. We then observe the changes in predictive power when different information is added or removed from the signal. We find that the HMM based approach reduces to the AR model when the signal is normalised. We also find that the performance of a model trained on a signal transformed using the Detrended Fluctuation Analysis (DFA) can be met by a model trained on the Hurst exponent and the DFA transformation at a single (short) scale.