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Gamma Boltzmann Machine for Simultaneously Modeling Linear- and Log-amplitude Spectra

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Document pages: 6 pages

Abstract: In audio applications, one of the most important representations of audiosignals is the amplitude spectrogram. It is utilized in manymachine-learning-based information processing methods including the ones usingthe restricted Boltzmann machines (RBM). However, the ordinaryGaussian-Bernoulli RBM (the most popular RBM among its variations) cannotdirectly handle amplitude spectra because the Gaussian distribution is asymmetric model allowing negative values which never appear in the amplitude.In this paper, after proposing a general gamma Boltzmann machine, we propose apractical model called the gamma-Bernoulli RBM that simultaneously handles bothlinear- and log-amplitude spectrograms. Its conditional distribution of theobservable data is given by the gamma distribution, and thus the proposed RBMcan naturally handle the data represented by positive numbers as the amplitudespectra. It can also treat amplitude in the logarithmic scale which isimportant for audio signals from the perceptual point of view. The advantage ofthe proposed model compared to the ordinary Gaussian-Bernoulli RBM wasconfirmed by PESQ and MSE in the experiment of representing the amplitudespectrograms of speech signals.

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