Learning dictionaries of stable autoregressive models for audio scene analysis

Abstract

In this paper, we explore an application of basis pursuit to audio scene analysis. The goal of our work is to detect when certain sounds are present in a mixed audio signal. We focus on the regime where out of a large number of possible sources, a small but unknown number combine and overlap to yield the observed signal. To infer which sounds are present, we decompose the observed signal as a linear combination of a small number of active sources. We cast the inference as a regularized form of linear regression whose sparse solutions yield decompositions with few active sources. We characterize the acoustic variability of individual sources by autoregressive models of their time domain waveforms. When we do not have prior knowledge of the individual sources, the coefficients of these autoregressive models must be learned from audio examples. We analyze the dynamical stability of these models and show how to estimate stable models by substituting a simple convex optimization for a difficult eigenvalue problem. We demonstrate our approach by learning dictionaries of musical notes and using these dictionaries to analyze polyphonic recordings of piano, cello, and violin.

On the Linearity of Bayesian Interpolators for Non-Gaussian Continuous-Time AR(1) Processes

“…When is not bandlimited, however, the conditional expectation in (8) does not necessarily result in a linear estimator. The Gaussian processes are well-studied examples for which the optimal estimator is often linear.…”

“…Early investigations of the non-Gaussian case can be found in [6]; the research work in this field is still ongoing [7], [8].…”

Deep Kernel for Genomic and Near Infrared Predictions in Multi-environment Breeding Trials

“…There have been alternatives for increasing the prediction ability of genetic values of these kernel methods; for example, Jiang et al (2018) model the local epistatic effects with different kernels constructed by means of haplotypes. A kernel of different characteristics was proposed by Cho and Saul (2009) that emulates the artificial neural networks. To achieve this, the structure of the covariance matrix is constructed with a similarity matrix between genotypes that takes the Arc-cosine angle between the vector of genotypes.…”

“…This makes it possible to generate a non-linear Arc-cosine kernel (named AK) that emulates the artificial neural network with one layer (Neal 1996). Cho and Saul (2009) used the theoretical framework of the kernels as the interior product of characteristic functions to emulate the hidden layers of an artificial neural network such that the kernel at one level is a function of the kernel at a previous level. Thus, the result mimics a multiple hidden layer structure (or levels) that can be used with the Bayesian paradigm from a Gaussian process with the machine learning infrastructure.…”

“…In general, kernel methods have been perceived as being much less flexible than neural network methods (Cho and Saul 2009). That is why Cho and Saul (2009) investigated the use of kernel methods in deep learning by proposing a family of kernel functions that mimic the computation of large neural networks and used those kernel functions that exploit the advantages of deep learning.…”