End-to-End Probabilistic Inference for Nonstationary Audio Analysis

TL;DR

This paper introduces a joint probabilistic model for nonstationary audio analysis that combines time-frequency analysis and NMF within a Gaussian process framework, enabling scalable inference on large datasets.

Contribution

It formulates a spectral mixture Gaussian process model with nonstationary priors and develops an efficient inference method using expectation propagation for audio processing.

Findings

Outperforms standard extended Kalman filtering techniques.

Scales linearly with data size, handling hundreds of thousands of points.

Demonstrates improved accuracy on various empirical audio tasks.

Abstract

A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and nonnegative matrix factorisation can be jointly formulated as a spectral mixture Gaussian process model with nonstationary priors over the amplitude variance parameters. Further, we formulate this nonlinear model's state space representation, making it amenable to infinite-horizon Gaussian process regression with approximate inference via expectation propagation, which scales linearly in the number of time steps and quadratically in the state dimensionality. By doing so, we are able to process audio signals with hundreds of thousands of data points. We demonstrate, on various tasks with empirical data, how this inference scheme outperforms more standard techniques that rely on extended Kalman filtering.