Time-Frequency Analysis as Probabilistic Inference

This is the final published version. It was originally published by IEEE at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6918491.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.Funding was provided by EPSRC (grant numbers EP/G050821/1 and EP/L000776/1) and Google (R.E.T.) and by the Gatsby Charitable Foundation (M.S.)

Probabilistic Modeling Paradigms for Audio Source Separation

This is the author's final version of the article, first published as E. Vincent, M. G. Jafari, S. A. Abdallah, M. D. Plumbley, M. E. Davies. Probabilistic Modeling Paradigms for Audio Source Separation. In W. Wang (Ed), Machine Audition: Principles, Algorithms and Systems. Chapter 7, pp. 162-185. IGI Global, 2011. ISBN 978-1-61520-919-4. DOI: 10.4018/978-1-61520-919-4.ch007file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04file: VincentJafariAbdallahPD11-probabilistic.pdf:v\VincentJafariAbdallahPD11-probabilistic.pdf:PDF owner: markp timestamp: 2011.02.04Most sound scenes result from the superposition of several sources, which can be separately perceived and analyzed by human listeners. Source separation aims to provide machine listeners with similar skills by extracting the sounds of individual sources from a given scene. Existing separation systems operate either by emulating the human auditory system or by inferring the parameters of probabilistic sound models. In this chapter, the authors focus on the latter approach and provide a joint overview of established and recent models, including independent component analysis, local time-frequency models and spectral template-based models. They show that most models are instances of one of the following two general paradigms: linear modeling or variance modeling. They compare the merits of either paradigm and report objective performance figures. They also,conclude by discussing promising combinations of probabilistic priors and inference algorithms that could form the basis of future state-of-the-art systems

Evidence: Admission of Mathematical Probability Statistics Held Erroneous for Want of Demonstration of Validity

In State v. Sneed the New Mexico Supreme Court limited its disapproval of evidence of probability statistics to the particular facts presented but failed to articulate specific safeguards for subsequent use of such evidence. This note explores the nature of probability statistics, their potential utility in a legal context, and criteria by which their admissibility might be determined

Sparsity and persistence in time-frequency sound representations

13 pagesInternational audienceIt is a well known fact that the time-frequency domain is very well adapted for representing audio signals. The main two features of time-frequency representations of many classes of audio signals are sparsity (signals are generally well approximated using a small number of coefficients) and persistence (significant coefficients are not isolated, and tend to form clusters). This contribution presents signal approximation algorithms that exploit these properties, in the framework of hierarchical probabilistic models. Given a time-frequency frame (i.e. a Gabor frame, or a union of several Gabor frames or time-frequency bases), coefficients are first gathered into groups. A group of coefficients is then modeled as a random vector, whose distribution is governed by a hidden state associated with the group. Algorithms for parameter inference and hidden state estimation from analysis coefficients are described. The role of the chosen dictionary, and more particularly its structure, is also investigated. The proposed approach bears some resemblance with variational approaches previously proposed by the authors (in particular the variational approach exploiting mixed norms based regularization terms). In the framework of audio signal applications, the time-frequency frame under consideration is a union of two MDCT bases or two Gabor frames, in order to generate estimates for tonal and transient layers. Groups corresponding to tonal (resp. transient) coefficients are constant frequency (resp. constant time) time-frequency coefficients of a frequency-selective (resp. time-selective) MDCT basis or Gabor frame

The Bayesian sampler : generic Bayesian inference causes incoherence in human probability

Human probability judgments are systematically biased, in apparent tension with Bayesian models of cognition. But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the probability theory plus noise model (Costello & Watts, 2014, 2016a, 2017; Costello & Watts, 2019; Costello, Watts, & Fisher, 2018), making equivalent average predictions for simple events, conjunctions, and disjunctions. The Bayesian sampler does, however, make distinct predictions for conditional probabilities and distributions of probability estimates. We show in 2 new experiments that this model better captures these mean judgments both qualitatively and quantitatively; which model best fits individual distributions of responses depends on the assumed size of the cognitive sample

Stochastic Spin-Orbit Torque Devices as Elements for Bayesian Inference

Probabilistic inference from real-time input data is becoming increasingly popular and may be one of the potential pathways at enabling cognitive intelligence. As a matter of fact, preliminary research has revealed that stochastic functionalities also underlie the spiking behavior of neurons in cortical microcircuits of the human brain. In tune with such observations, neuromorphic and other unconventional computing platforms have recently started adopting the usage of computational units that generate outputs probabilistically, depending on the magnitude of the input stimulus. In this work, we experimentally demonstrate a spintronic device that offers a direct mapping to the functionality of such a controllable stochastic switching element. We show that the probabilistic switching of Ta/CoFeB/MgO heterostructures in presence of spin-orbit torque and thermal noise can be harnessed to enable probabilistic inference in a plethora of unconventional computing scenarios. This work can potentially pave the way for hardware that directly mimics the computational units of Bayesian inference