FIR system identification based on a nonparametric Bayesian model using the Indian buffet process

Tanji, Hiroki; Tanaka, Ryo; Murakami, Takahiro; Ishida, Yoshiteru

doi:10.1007/s11760-016-0865-x

Cited by 2 publications

(12 citation statements)

References 15 publications

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“…In this algorithm, dimension of z and b is approximated with a sufficiently big truncation level K tr . Conditional distribution P ( z k | z \ k ) required for sampling of z k is found as

P false(z_{k} = 1 false| z_{∖ k} false) = \hat{α} / false(\overset{α}{true} + L_{1} false)

. Here

\hat{α} = false(η_{α} + L_{1} - 1 false) / false(β_{α} + 1 false)

, and L 1 = 1 + ∑ l ≠ k z k .…”

Section: Fir System Identification Algorithm Based On Npb Modelmentioning

confidence: 99%

“…The simulation conditions are same as for the proposed method. In the conventional method, same as in the proposed method, parameters are integrated out to derive an efficient sampling algorithm. In Figure , the number of samplings required for samples from prior distribution of parameters to settle in a certain area is almost same for both methods.…”

Section: Simulationsmentioning

confidence: 99%

“…This subsection compares increase of computational time in the proposed method as compared to conventional methods under conditions of Section 5.1 at varied K tr . The conventional methods used for comparison are the one combining normally distributed likelihood function with AIC‐based order estimation and the one based on NPB model using normally distributed likelihood function . When determining optimal order by means of AIC, order candidates are considered in the range of 0 to K tr .…”

Section: Simulationsmentioning

confidence: 99%

“…This paper focuses on a nonparametric Bayesian model (NPB) proposed in Ref. . NPB model is a Bayesian model with infinite number of parameters developed in the field of machine learning.…”

Section: Introductionmentioning

confidence: 99%

“…This paper develops results of Ref. ; specifically, the paper proposes an NPB model using super‐Gaussian distribution for likelihood function, and an algorithm for efficient inference to search for posterior distribution. Noise is assumed to be normally distributed in Ref.…”

Section: Introductionmentioning

confidence: 99%

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A nonparametric Bayesian model for system identification based on a super‐Gaussian distribution

Tanji

Murakami

Kamata

2019

Elect Comm in Japan

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In the acoustic signal processing applications of finite impulse response (FIR) system identification, it is important to develop the identification method that is robust to super‐Gaussian noises. Moreover, the identification method that estimates the FIR coefficients and the order of the unknown system is required, because the order of the unknown system is unavailable in advance. Therefore, in this paper, we propose a nonparametric Bayesian (NPB) model for FIR system identification using a super‐Gaussian likelihood and the beta‐Bernoulli process. In the proposed NPB model, we employ the hyperbolic secant distribution for the likelihood function. Then, we derive the inference algorithm to simultaneously estimate the FIR coefficients and the order of the unknown system. Our inference algorithm based on a hybrid inference approach combining the majorization‐minimization (MM) algorithm and the Gibbs sampler. The simulation results suggest that the proposed method outperforms the conventional identification algorithms in a super‐Gaussian noise environment.

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“…In this algorithm, dimension of z and b is approximated with a sufficiently big truncation level K tr . Conditional distribution P ( z k | z \ k ) required for sampling of z k is found as

P false(z_{k} = 1 false| z_{∖ k} false) = \hat{α} / false(\overset{α}{true} + L_{1} false)

. Here

\hat{α} = false(η_{α} + L_{1} - 1 false) / false(β_{α} + 1 false)

, and L 1 = 1 + ∑ l ≠ k z k .…”

Section: Fir System Identification Algorithm Based On Npb Modelmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

“…This paper focuses on a nonparametric Bayesian model (NPB) proposed in Ref. . NPB model is a Bayesian model with infinite number of parameters developed in the field of machine learning.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations