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While automated condition monitoring of rotating machines often use vibration signals for defect detection, diagnosis, and residual life predictions, in this paper, the acoustic noise signal (<; 25 kHz), acquired via non-contact microphone sensors, is used to predict the remaining useful life (RUL). Modulation spectral (MS) analysis of acoustic signals has the potential to provide additional long-term information over more conventional short-term signal spectral components. However, the high dimensionality of MS features has been cited as a limitation to their applicability in this area in the literature. Therefore, in this study, a novel approach is proposed which employs an information theoretic approach to feature subset selection of modulation spectra features. This approach does not require information regarding the spectral location of defect frequencies to be known or pre-estimated and leverages information regarding the chronological order of data samples for dimensionality reduction. The results of this study show significant improvements for this proposed approach over the other commonly used spectral-based approaches for the task of predicting RUL by up to 19% relative over the standard envelope analysis approach used in the literature. A further 16% improvement was achieved by applying a more rigorous approach to labeling of acoustic samples acquired over the lifetime of the machines over a fixed length class labeling approach. A detailed misclassification analysis is provided to interpret the relative cost of system errors for the task of residual life predictions of rotating machines used in industrial applications.