## 2015 |

Martino, Luca; Elvira, Victor; Luengo, David; Corander, Jukka An Adaptive Population Importance Sampler: Learning From Uncertainty Journal Article IEEE Transactions on Signal Processing, 63 (16), pp. 4422–4437, 2015, ISSN: 1053-587X. Abstract | Links | BibTeX | Tags: Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks @article{Martino2015bbb, title = {An Adaptive Population Importance Sampler: Learning From Uncertainty}, author = {Luca Martino and Victor Elvira and David Luengo and Jukka Corander}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=7117437}, doi = {10.1109/TSP.2015.2440215}, issn = {1053-587X}, year = {2015}, date = {2015-08-01}, journal = {IEEE Transactions on Signal Processing}, volume = {63}, number = {16}, pages = {4422--4437}, publisher = {IEEE}, abstract = {Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network.}, keywords = {Adaptive importance sampling, adaptive multiple IS, adaptive population importance sampler, AMIS, APIS, Estimation, Importance sampling, IS estimators, iterative estimation, iterative methods, Journal, MC methods, Monte Carlo (MC) methods, Monte Carlo methods, population Monte Carlo, Proposals, Signal processing algorithms, simple temporal adaptation, Sociology, Standards, Wireless sensor network, Wireless Sensor Networks}, pubstate = {published}, tppubtype = {article} } Monte Carlo (MC) methods are well-known computational techniques, widely used in different fields such as signal processing, communications and machine learning. An important class of MC methods is composed of importance sampling (IS) and its adaptive extensions, such as population Monte Carlo (PMC) and adaptive multiple IS (AMIS). In this paper, we introduce a novel adaptive and iterated importance sampler using a population of proposal densities. The proposed algorithm, named adaptive population importance sampling (APIS), provides a global estimation of the variables of interest iteratively, making use of all the samples previously generated. APIS combines a sophisticated scheme to build the IS estimators (based on the deterministic mixture approach) with a simple temporal adaptation (based on epochs). In this way, APIS is able to keep all the advantages of both AMIS and PMC, while minimizing their drawbacks. Furthermore, APIS is easily parallelizable. The cloud of proposals is adapted in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. The result is a fast, simple, robust, and high-performance algorithm applicable to a wide range of problems. Numerical results show the advantages of the proposed sampling scheme in four synthetic examples and a localization problem in a wireless sensor network. |

## 2013 |

Koblents, Eugenia; Miguez, Joaquin A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces Inproceedings 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 6318–6322, IEEE, Vancouver, 2013, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: Approximation methods, computational inference, degeneracy of importance weights, high dimensional spaces, Importance sampling, importance weights, iterative importance sampling, iterative methods, mixture-PMC, mixture-PMC algorithm, Monte Carlo methods, MPMC, nonlinear transformations, population Monte Carlo, population Monte Carlo scheme, Probability density function, probability distributions, Proposals, Sociology, Standards @inproceedings{Koblents2013a, title = {A Population Monte Carlo Scheme for Computational Inference in High Dimensional Spaces}, author = {Eugenia Koblents and Joaquin Miguez}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6638881}, issn = {1520-6149}, year = {2013}, date = {2013-01-01}, booktitle = {2013 IEEE International Conference on Acoustics, Speech and Signal Processing}, pages = {6318--6322}, publisher = {IEEE}, address = {Vancouver}, abstract = {In this paper we address the Monte Carlo approximation of integrals with respect to probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling (IS) approach. Both IS and PMC suffer from the well known problem of degeneracy of the importance weights (IWs), which is closely related to the curse-of-dimensionality, and limits their applicability in large-scale practical problems. In this paper we investigate a novel PMC scheme that consists in performing nonlinear transformations of the IWs in order to smooth their variations and avoid degeneracy. We apply the modified IS scheme to the well-known mixture-PMC (MPMC) algorithm, which constructs the importance functions as mixtures of kernels. We present numerical results that show how the modified version of MPMC clearly outperforms the original scheme.}, keywords = {Approximation methods, computational inference, degeneracy of importance weights, high dimensional spaces, Importance sampling, importance weights, iterative importance sampling, iterative methods, mixture-PMC, mixture-PMC algorithm, Monte Carlo methods, MPMC, nonlinear transformations, population Monte Carlo, population Monte Carlo scheme, Probability density function, probability distributions, Proposals, Sociology, Standards}, pubstate = {published}, tppubtype = {inproceedings} } In this paper we address the Monte Carlo approximation of integrals with respect to probability distributions in high-dimensional spaces. In particular, we investigate the population Monte Carlo (PMC) scheme, which is based on an iterative importance sampling (IS) approach. Both IS and PMC suffer from the well known problem of degeneracy of the importance weights (IWs), which is closely related to the curse-of-dimensionality, and limits their applicability in large-scale practical problems. In this paper we investigate a novel PMC scheme that consists in performing nonlinear transformations of the IWs in order to smooth their variations and avoid degeneracy. We apply the modified IS scheme to the well-known mixture-PMC (MPMC) algorithm, which constructs the importance functions as mixtures of kernels. We present numerical results that show how the modified version of MPMC clearly outperforms the original scheme. |

## 2012 |

Zhong, Jingshan; Dauwels, Justin; Vazquez, Manuel A; Waller, Laura Efficient Gaussian Inference Algorithms for Phase Imaging Inproceedings 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 617–620, IEEE, Kyoto, 2012, ISSN: 1520-6149. Abstract | Links | BibTeX | Tags: biomedical optical imaging, complex optical field, computational complexity, defocus distances, Fourier domain, Gaussian inference algorithms, image sequences, inference mechanisms, intensity image sequence, iterative Kalman smoothing, iterative methods, Kalman filter, Kalman filters, Kalman recursions, linear model, Manganese, Mathematical model, medical image processing, Noise, noisy intensity image, nonlinear observation model, Optical imaging, Optical sensors, Phase imaging, phase inference algorithms, smoothing methods @inproceedings{Zhong2012a, title = {Efficient Gaussian Inference Algorithms for Phase Imaging}, author = {Jingshan Zhong and Justin Dauwels and Manuel A Vazquez and Laura Waller}, url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=6287959}, issn = {1520-6149}, year = {2012}, date = {2012-01-01}, booktitle = {2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pages = {617--620}, publisher = {IEEE}, address = {Kyoto}, abstract = {Novel efficient algorithms are developed to infer the phase of a complex optical field from a sequence of intensity images taken at different defocus distances. The non-linear observation model is approximated by a linear model. The complex optical field is inferred by iterative Kalman smoothing in the Fourier domain: forward and backward sweeps of Kalman recursions are alternated, and in each such sweep, the approximate linear model is refined. By limiting the number of iterations, one can trade off accuracy vs. complexity. The complexity of each iteration in the proposed algorithm is in the order of N logN, where N is the number of pixels per image. The storage required scales linearly with N. In contrast, the complexity of existing phase inference algorithms scales with N3 and the required storage with N2. The proposed algorithms may enable real-time estimation of optical fields from noisy intensity images.}, keywords = {biomedical optical imaging, complex optical field, computational complexity, defocus distances, Fourier domain, Gaussian inference algorithms, image sequences, inference mechanisms, intensity image sequence, iterative Kalman smoothing, iterative methods, Kalman filter, Kalman filters, Kalman recursions, linear model, Manganese, Mathematical model, medical image processing, Noise, noisy intensity image, nonlinear observation model, Optical imaging, Optical sensors, Phase imaging, phase inference algorithms, smoothing methods}, pubstate = {published}, tppubtype = {inproceedings} } Novel efficient algorithms are developed to infer the phase of a complex optical field from a sequence of intensity images taken at different defocus distances. The non-linear observation model is approximated by a linear model. The complex optical field is inferred by iterative Kalman smoothing in the Fourier domain: forward and backward sweeps of Kalman recursions are alternated, and in each such sweep, the approximate linear model is refined. By limiting the number of iterations, one can trade off accuracy vs. complexity. The complexity of each iteration in the proposed algorithm is in the order of N logN, where N is the number of pixels per image. The storage required scales linearly with N. In contrast, the complexity of existing phase inference algorithms scales with N3 and the required storage with N2. The proposed algorithms may enable real-time estimation of optical fields from noisy intensity images. |