Expectation Propagation for Rectified Linear Poisson Regression

Young-Jun Ko, Matthias W. Seeger
Asian Conference on Machine Learning, PMLR 45:253-268, 2016.

Abstract

The Poisson likelihood with rectified linear function as non-linearity is a physically plausible model to discribe the stochastic arrival process of photons or other particles at a detector. At low emission rates the discrete nature of this process leads to measurement noise that behaves very differently from additive white Gaussian noise. To address the intractable inference problem for such models, we present a novel efficient and robust Expectation Propagation algorithm entirely based on analytically tractable computations operating reliably in regimes where quadrature based implementations can fail. Full posterior inference therefore becomes an attractive alternative in areas generally dominated by methods of point estimation. Moreover, we discuss the rectified linear function in the context of other common non-linearities and identify situations where it can serve as a robust alternative.

Cite this Paper

BibTeX
@InProceedings{pmlr-v45-Ko15, title = {Expectation Propagation for Rectified Linear Poisson Regression}, author = {Ko, Young-Jun and Seeger, Matthias W.}, booktitle = {Asian Conference on Machine Learning}, pages = {253--268}, year = {2016}, editor = {Holmes, Geoffrey and Liu, Tie-Yan}, volume = {45}, series = {Proceedings of Machine Learning Research}, address = {Hong Kong}, month = {20--22 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v45/Ko15.pdf}, url = {https://proceedings.mlr.press/v45/Ko15.html}, abstract = {The Poisson likelihood with rectified linear function as non-linearity is a physically plausible model to discribe the stochastic arrival process of photons or other particles at a detector. At low emission rates the discrete nature of this process leads to measurement noise that behaves very differently from additive white Gaussian noise. To address the intractable inference problem for such models, we present a novel efficient and robust Expectation Propagation algorithm entirely based on analytically tractable computations operating reliably in regimes where quadrature based implementations can fail. Full posterior inference therefore becomes an attractive alternative in areas generally dominated by methods of point estimation. Moreover, we discuss the rectified linear function in the context of other common non-linearities and identify situations where it can serve as a robust alternative.} }
Endnote
%0 Conference Paper %T Expectation Propagation for Rectified Linear Poisson Regression %A Young-Jun Ko %A Matthias W. Seeger %B Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Geoffrey Holmes %E Tie-Yan Liu %F pmlr-v45-Ko15 %I PMLR %P 253--268 %U https://proceedings.mlr.press/v45/Ko15.html %V 45 %X The Poisson likelihood with rectified linear function as non-linearity is a physically plausible model to discribe the stochastic arrival process of photons or other particles at a detector. At low emission rates the discrete nature of this process leads to measurement noise that behaves very differently from additive white Gaussian noise. To address the intractable inference problem for such models, we present a novel efficient and robust Expectation Propagation algorithm entirely based on analytically tractable computations operating reliably in regimes where quadrature based implementations can fail. Full posterior inference therefore becomes an attractive alternative in areas generally dominated by methods of point estimation. Moreover, we discuss the rectified linear function in the context of other common non-linearities and identify situations where it can serve as a robust alternative.
RIS
TY - CPAPER TI - Expectation Propagation for Rectified Linear Poisson Regression AU - Young-Jun Ko AU - Matthias W. Seeger BT - Asian Conference on Machine Learning DA - 2016/02/25 ED - Geoffrey Holmes ED - Tie-Yan Liu ID - pmlr-v45-Ko15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 45 SP - 253 EP - 268 L1 - http://proceedings.mlr.press/v45/Ko15.pdf UR - https://proceedings.mlr.press/v45/Ko15.html AB - The Poisson likelihood with rectified linear function as non-linearity is a physically plausible model to discribe the stochastic arrival process of photons or other particles at a detector. At low emission rates the discrete nature of this process leads to measurement noise that behaves very differently from additive white Gaussian noise. To address the intractable inference problem for such models, we present a novel efficient and robust Expectation Propagation algorithm entirely based on analytically tractable computations operating reliably in regimes where quadrature based implementations can fail. Full posterior inference therefore becomes an attractive alternative in areas generally dominated by methods of point estimation. Moreover, we discuss the rectified linear function in the context of other common non-linearities and identify situations where it can serve as a robust alternative. ER -
APA
Ko, Y. & Seeger, M.W.. (2016). Expectation Propagation for Rectified Linear Poisson Regression. Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 45:253-268 Available from https://proceedings.mlr.press/v45/Ko15.html.

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