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Improving stochastic estimates with inference methods: Calculating matrix diagonals

Marco Selig, Niels Oppermann, Torsten A. Enßlin
2012 Physical Review E  
In such applications without spectral knowledge, the generalized Wiener filter can be extended to a generic filter derived in [6] .  ...  Forward model Instead of doing a simple averaging of the probes, we now want to develop a Bayesian estimate which exploits additional knowledge of the problem to infer the matrix diagonal from a smaller  ... 
doi:10.1103/physreve.85.021134 pmid:22463179 fatcat:letpwv4lzjagbecwgpaq5htipq

Calcium imaging and dynamic causal modelling reveal brain-wide changes in effective connectivity and synaptic dynamics during epileptic seizures

Richard E. Rosch, Paul R. Hunter, Torsten Baldeweg, Karl J. Friston, Martin P. Meyer, Saad Jbabdi
2018 PLoS Computational Biology  
Spectral changes of spontaneous neuronal activity during the seizure are then modelled using neural mass models, allowing Bayesian inference on changes in effective network connectivity and their underlying  ...  Author summary We show that Bayesian inversion techniques used in electrophysiological data are applicable to calcium imaging data derived from light sheet microscopy in the zebrafish brain.  ...  The variations in the single neural mass model parameter introduces spectral changes in both the surrogate LFP and fluorescence time traces (Fig 1B) .  ... 
doi:10.1371/journal.pcbi.1006375 pmid:30138336 fatcat:6dd7oelwjfayfjw5j5phawfcnu

Bayesian linear unmixing of hyperspectral images corrupted by colored Gaussian noise with unknown covariance matrix

N. Dobigeon, J.-Y. Tourneret, A. O. Hero
2008 Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing  
Index Terms-Bayesian inference, Monte Carlo methods, spectral unmixing, hyperspectral images.  ...  HIERARCHICAL BAYESIAN MODEL The likelihood and the priors inherent to the proposed hierarchical Bayesian model are defined for the spectral unmixing of hyperspectral images.  ...  This paper studies a new Bayesian linear unmixing algorithm for additive colored Gaussian noise. This algorithm allows one to analyze the impact of noise correlation on spectral unmixing.  ... 
doi:10.1109/icassp.2008.4518389 dblp:conf/icassp/DobigeonTH08 fatcat:ngsfuc3cjrhl5hl2by4rwms75i

Bayesian Approach for X-Ray and Neutron Scattering Spectroscopy [chapter]

Alessio De Francesco, Alessandro Cunsolo, Luisa Scaccia
2020 Inelastic X-Ray Scattering and X-Ray Powder Diffraction Applications [Working Title]  
Being aware of the severity of the problem, we illustrate here the new hopes brought in this area by Bayesian inference methods.  ...  The rapidly improving performance of inelastic scattering instruments has prompted tremendous advances in our knowledge of the high-frequency dynamics of disordered systems, yet also imposing new demands  ...  Bayesian inference, in fact, recognizes the importance of including prior knowledge in the analysis.  ... 
doi:10.5772/intechopen.92159 fatcat:rsrcwxvpkfayxg7witty56y22q

NV center based nano-NMR enhanced by deep learning [article]

Nati Aharon, Amit Rotem, Liam P. McGuinness, Fedor Jelezko, Alex Retzker, Zohar Ringel
2018 arXiv   pre-print
Over a wide range of scenarios we show that this approach outperforms Bayesian methods even when the latter have full pre-knowledge of the noise model and the former has none.  ...  Moreover, the DL methods outperform Bayesian learning methods when no knowledge of the signal or the noise model is assumed.  ...  This means that a DL algorithm can analyze a test signal with the same efficiency as numerically demanding Bayesian methods that rely on precise knowledge of the model.  ... 
arXiv:1809.02583v1 fatcat:rkpmuzp2azhwhoc3x5lzw4ikgq

Matrix and Tensor Factorization Methods for Natural Language Processing

Guillaume Bouchard, Jason Naradowsky, Sebastian Riedel, Tim Rocktäschel, Andreas Vlachos
2015 Tutorials  
Furthermore, we introduce Bayesian Personalized Ranking (BPR) for matrix and tensor factorization which deals with implicit feedback in ranking tasks (Rendle et al., 2009) .  ...  Tutorial Overview Matrix/Tensor Factorization Basics In this part, we first remind essential results on bilinear forms, spectral representations of matrices and low-rank approximation theorems, which are  ...  background knowledge.  ... 
doi:10.3115/v1/p15-5005 dblp:conf/acl/BouchardNRRV15 fatcat:q2zksc5hqfe5ffgbpv477trdu4

MEMe: An Accurate Maximum Entropy Method for Efficient Approximations in Large-Scale Machine Learning

Diego Granziol, Binxin Ru, Stefan Zohren, Xiaowen Dong, Michael Osborne, Stephen Roberts
2019 Entropy  
log determinant estimation and information-theoretic Bayesian optimisation.  ...  We showcase the usefulness of the proposed method, its equivalence to constrained Bayesian variational inference and demonstrate its superiority over existing approaches in two applications, namely, fast  ...  Polynomial Approximations to the Log Determinant Recent work [4] [5] [6] has considered incorporating knowledge of the non-central moments (Also using stochastic trace estimation.) of a normalised eigenspectrum  ... 
doi:10.3390/e21060551 pmid:33267265 fatcat:4lximq4lhveqtguxpeb7xplpvy

Rapid computations of spectrotemporal prediction error support perception of degraded speech [article]

Ediz Sohoglu, Matthew H. Davis
2020 biorxiv/medrxiv   pre-print
Human speech perception can be described as Bayesian perceptual inference but how are these Bayesian computations instantiated neurally?  ...  We use magnetoencephalographic recordings of brain responses to degraded spoken words as a function of signal quality and prior knowledge to demonstrate that spectrotemporal modulations in speech are more  ...  Abstract 23 Human speech perception can be described as Bayesian perceptual inference but 24 how are these Bayesian computations instantiated neurally?  ... 
doi:10.1101/2020.04.22.054726 fatcat:pbve3zpferf2replyxv4wnmec4

Bayesian graph convolutional neural networks via tempered MCMC

Rohitash Chandra, Ayush Bhagat, Manavendra Maharana, Pavel N. Krivitsky
2021 IEEE Access  
In our proposed Bayesian graph CNN (Bayes-GCNN), we use the fast approximate spectral graph convolution technique of Kipf et al. [30] instead.  ...  (See FIGURE 4 . 4 Posterior and trace plot for selected weights for Cora FIGURE 5 . 2016 FIGURE 6 . 520166 Posterior and trace plot for selected weights for CiteSeer VOLUME 4, Posterior and trace plot  ... 
doi:10.1109/access.2021.3111898 fatcat:kwwwa7vdcrgv3hm5ainkkmpiba

Bayesian Unsupervised Unmixing Of Hyperspectral Images Using A Post-Nonlinear Model

Yoann Altmann, Nicolas Dobigeon, J.-Y. Tourneret
2013 Zenodo  
Hyperparameter priors The performance of the proposed Bayesian model for spectral unmixing depends on the values of the hyperparameters σ 2 b and w.  ...  CONCLUSIONS AND FUTURE WORK We proposed a new hierarchical Bayesian algorithm for unsupervised nonlinear spectral unmixing of hyperspectral im-ages.  ... 
doi:10.5281/zenodo.43574 fatcat:vmg4zvqi2zdabdct756tnyyh6a

A Bayesian Analysis of Spectral ARMA Model

Manoel I. Silvestre Bezerra, Fernando Antonio Moala, Yuzo Iano
2012 Mathematical Problems in Engineering  
Bezerra et al. (2008) proposed a new method, based on Yule-Walker equations, to estimate the ARMA spectral model.  ...  In this paper, a Bayesian approach is developed for this model by using the noninformative prior proposed by Jeffreys (1967).  ...  Introduction The spectral estimation of autoregressive moving average ARMA is considered a topic of interest in several applied areas of knowledge, for example, engineering, econometrics, and so forth  ... 
doi:10.1155/2012/565894 fatcat:6rlbcpnuijfwfcikorduwj77je

Agent Identification Using a Sparse Bayesian Model

Huiping Duan, Hongbin Li, Jing Xie, N. S. Panikov, Hong-Liang Cui
2011 IEEE Sensors Journal  
In this paper, we propose a new agent identification method by using a sparse Bayesian model.  ...  In general, the size of the spectral signature library is usually much larger than the number of agents really present.  ...  prior knowledge.  ... 
doi:10.1109/jsen.2011.2130521 fatcat:iupeesc73ngzphaooawmvxehu4

NV center based nano-NMR enhanced by deep learning

Nati Aharon, Amit Rotem, Liam P. McGuinness, Fedor Jelezko, Alex Retzker, Zohar Ringel
2019 Scientific Reports  
In the case of frequency resolution we show that this approach outperforms Bayesian methods even when the latter have full pre-knowledge of the noise model and the former has none.  ...  We show that in the case of frequency discrimination DL algorithms reach the optimal discrimination without having any pre-knowledge of the physical model.  ...  methods even though Bayesian methods have full knowledge of the noise model, and the DL methods have no prior knowledge at all.  ... 
doi:10.1038/s41598-019-54119-9 pmid:31780783 pmcid:PMC6882844 fatcat:utcdt26xfrccpkl7bgg34glxf4

Bayesian graph convolutional neural networks via tempered MCMC [article]

Rohitash Chandra, Ayush Bhagat, Manavendra Maharana, Pavel N. Krivitsky
2021 arXiv   pre-print
Bayesian inference provides a principled and robust approach to uncertainty quantification of model parameters for deep learning models.  ...  In this paper, we present Bayesian graph deep learning techniques that employ state-of-art methods such as tempered MCMC sampling and advanced proposal schemes.  ...  In our proposed Bayesian graph CNN (Bayes-GCNN), we use the fast approximate spectral graph convolution technique of Kipf et al. [30] instead.  ... 
arXiv:2104.08438v1 fatcat:ot3wt2mobzggxn3zusrpkxaj6u

Effects of Artifact Rejection and Bayesian Weighting on the Auditory Brainstem Response During Quiet and Active Behavioral Conditions

Jason Tait Sanchez, Donald Gans
2006 American Journal of Audiology  
Wave V amplitudes and residual noise root-meansquare values were measured following the offline application of artifact rejection and Bayesian weighting.  ...  Consequently, strict artifact rejection levels resulted in an inherent underestimation of wave V amplitudes when compared with the Bayesian approach.  ...  Overall, artifact rejection yielded significantly smaller wave V amplitudes in 90% of the traces (108 of 120 traces) compared with Bayesian weighting.  ... 
doi:10.1044/1059-0889(2006/019) pmid:17182880 fatcat:cwbazjs3v5d53k3tjl5dclj2qa
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