Online Bayesian Inference in Some Time-Frequency Representations of Non-Stationary Processes

Everitt, Richard G.; Andrieu, Christophe; Davy, Manuel

doi:10.1109/tsp.2013.2280128

Cited by 7 publications

(4 citation statements)

References 36 publications

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“…For such situations, when particle MCMC is infeasible, alternative approximate inference techniques are required. Such methods might build on the work in this paper through the use of a local Whittle approximation (such as that in Everitt et al (2013)).…”

Section: Discussionmentioning

confidence: 99%

Fast approximate Bayesian inference for stable differential equation models

Maybank,

Bojak,

Everitt

2017

Preprint

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Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations. The dynamics in these models are approximately linear around a stable fixed point of the system. We exploit this property to develop fast approximate methods for posterior inference. We illustrate our approach using simulated data on a mechanistic neuroscience model with EEG data. More generally, stable differential equation models and the corresponding inference methods are useful for analysis of stationary time-series data. Compared to the existing state-of-the art, our methods are several orders of magnitude faster, and are particularly suited to analysis of long time-series (>10,000 time-points) and models of moderate dimension (10-50 state variables and 10-50 parameters.

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Section: Discussionmentioning

confidence: 99%

Fast approximate Bayesian inference for stable differential equation models

Maybank,

Bojak,

Everitt

2017

Preprint

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“…However, rather than using 10 spline basis functions we use 15, as this provides slightly better results along with superior computational stability. We note that the approach of Everitt et al (2013) is not considered here due to the fact that the parameterization of the spectral density through the Wittle likelihood requires subjective knowledge.…”

Section: Simulation Studiesmentioning

confidence: 99%

“…The most common nonparametric approach is the short-time Fourier transform (i.e., windowed Fourier transform) which produces a time-frequency representation characterizing local signal properties (Gröchenig, 2001;Oppenheim and Schafer, 2009). Another path to time-frequency proceeds using smoothing splines (Rosen et al, 2009(Rosen et al, , 2012 or by parameterizing the spectral density to estimate the local spectrum via the Whittle likelihood (Everitt et al, 2013). Similarly, time-frequency can be achieved by applying smooth localized complex exponential (SLEX) functions to the observed signal (Ombao et al, 2001).…”

Section: Introductionmentioning

confidence: 99%

Bayesian Lattice Filters for Time-Varying Autoregression and Time–Frequency Analysis

2016

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Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true timevarying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).

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“…It is a member of the generalized Gaussian scale mixture model family which has been used for image [45] and video [46] modeling. The approach does not treat the time-frequency representation as data [47], but rather as latent variables that are inferred from the signal.…”

Section: E Relationship To Existing Modelsmentioning

confidence: 99%

Time-Frequency Analysis as Probabilistic Inference

Turner

Sahani

2014

IEEE Trans. Signal Process.

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This paper proposes a new view of time-frequency analysis framed in terms of probabilistic inference. Natural signals are assumed to be formed by the superposition of distinct time-frequency components, with the analytic goal being to infer these components by application of Bayes' rule. The framework serves to unify various existing models for natural time-series; it relates to both the Wiener and Kalman filters, and with suitable assumptions yields inferential interpretations of the short-time Fourier transform, spectrogram, filter bank, and wavelet representations. Value is gained by placing time-frequency analysis on the same probabilistic basis as is often employed in applications such as denoising, source separation, or recognition. Uncertainty in the time-frequency representation can be propagated correctly to application-specific stages, improving the handing of noise and missing data. Probabilistic learning allows modules to be co-adapted; thus, the time-frequency representation can be adapted to both the demands of the application and the time-varying statistics of the signal at hand. Similarly, the application module can be adapted to fine properties of the signal propagated by the initial time-frequency processing. We demonstrate these benefits by combining probabilistic time-frequency representations with non-negative matrix factorization, finding benefits in audio denoising and inpainting tasks, albeit with higher computational cost than incurred by the standard approach.

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Online Bayesian Inference in Some Time-Frequency Representations of Non-Stationary Processes

Abstract: Manuscript received xxx xx, xxxx; revised xxx xx, xxxx.

Cited by 7 publications

References 36 publications

Fast approximate Bayesian inference for stable differential equation models

Fast approximate Bayesian inference for stable differential equation models

Bayesian Lattice Filters for Time-Varying Autoregression and Time–Frequency Analysis

Time-Frequency Analysis as Probabilistic Inference

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