This paper presents a dynamic data-driven method for early detection of thermoacoustic instabilities in combustors based on short-length time series of sensor data, where the objective is near-real-time monitoring and active control of pressure oscillations. The main idea is to use the available data at different regimes of the combustion process to train respective hidden-variable models using the concept of Hidden Markov Modeling (HMM) as a statistical learning tool; here, (short-length) time-series data of pressure oscillations are used to infer a Markov chain with unobserved (hidden) states. The proposed HMM-based method has been validated on experimental data collected from an electrically heated Rijke tube apparatus for predicting onset of thermoacoustic instabilities. The results have been compared with those of the current state-of-the-art measurement techniques for instability growth rate and associated computational complexity. The applicability of the proposed method has been demonstrated with respect to anomaly detection and regime identification with limited data requirements, making it a potential candidate for monitoring and active control of thermoacoustic instabilities in commercial-scale combustors.