TY - JOUR
T1 - Bayesian inference for spatio-temporal spike-and-slab priors
AU - Andersen, Michael Riis
AU - Vehtari, Aki
AU - Winther, Ole
AU - Kai Hansen, Lars
PY - 2017/12/1
Y1 - 2017/12/1
N2 - In this work, we address the problem of solving a series of underdetermined linear inverse problemblems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.
AB - In this work, we address the problem of solving a series of underdetermined linear inverse problemblems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the spike-and-slab probabilities. An expectation propagation (EP) algorithm for posterior inference under the proposed model is derived. For large scale problems, the standard EP algorithm can be prohibitively slow. We therefore introduce three different approximation schemes to reduce the computational complexity. Finally, we demonstrate the proposed model using numerical experiments based on both synthetic and real data sets.
KW - Bayesian inference
KW - Expectation propagation
KW - Linear inverse problems
KW - Sparsity-promoting priors
KW - Spike-and-slab priors
UR - http://www.scopus.com/inward/record.url?scp=85040715749&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85040715749
VL - 18
SP - 1
EP - 58
JO - Journal of Machine Learning Research
JF - Journal of Machine Learning Research
SN - 1532-4435
ER -