| 1. |
- Bayisa, Fekadu, et al.
(author)
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Adaptive algorithm for sparse signal recovery
- 2019
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In: Digital signal processing (Print). - : Elsevier. - 1051-2004 .- 1095-4333. ; 87, s. 10-18
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Journal article (peer-reviewed)abstract
- The development of compressive sensing in recent years has given much attention to sparse signal recovery. In sparse signal recovery, spike and slab priors are playing a key role in inducing sparsity. The use of such priors, however, results in non-convex and mixed integer programming problems. Most of the existing algorithms to solve non-convex and mixed integer programming problems involve either simplifying assumptions, relaxations or high computational expenses. In this paper, we propose a new adaptive alternating direction method of multipliers (AADMM) algorithm to directly solve the suggested non-convex and mixed integer programming problem. The algorithm is based on the one-to-one mapping property of the support and non-zero element of the signal. At each step of the algorithm, we update the support by either adding an index to it or removing an index from it and use the alternating direction method of multipliers to recover the signal corresponding to the updated support. Moreover, as opposed to the competing “adaptive sparsity matching pursuit” and “alternating direction method of multipliers” methods our algorithm can solve non-convex problems directly. Experiments on synthetic data and real-world images demonstrated that the proposed AADMM algorithm provides superior performance and is computationally cheaper than the recently developed iterative convex refinement (ICR) and adaptive matching pursuit (AMP) algorithms.
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| 2. |
- Bayisa, Fekadu Lemessa, 1984-
(author)
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Statistical methods in medical image estimation and sparse signal recovery
- 2018
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Doctoral thesis (other academic/artistic)abstract
- This thesis presents work on methods for the estimation of computed tomography (CT) images from magnetic resonance (MR) images for a number of diagnostic and therapeutic workflows. The study also demonstrates sparse signal recovery method, which is an intermediate method for magnetic resonance image reconstruction. The thesis consists of four articles. The first three articles are concerned with developing statistical methods for the estimation of CT images from MR images. We formulated spatial and non-spatial models for CT image estimation from MR images, where the spatial models include hidden Markov model (HMM) and hidden Markov random field model (HMRF) while the non-spatial models incorporate Gaussian mixture model (GMM) and skewed-Gaussian mixture model (SGMM). The statistical models are estimated via a maximum likelihood approach using the EM-algorithm in GMM and SGMM, the EM gradient algorithm in HMRF and the Baum–Welch algorithm in HMM. We have also examined CT image estimation using GMM and supervised statistical learning methods. The performance of the models is evaluated using cross-validation on real data. Comparing CT image estimation performance of the models, we have observed that GMM combined with supervised statistical learning method has the best performance, especially on bone tissues. The fourth article deals with a sparse modeling in signal recovery. Using spike and slab priors on the signal, we formulated a sparse signal recovery problem and developed an adaptive algorithm for sparse signal recovery. The developed algorithm has better performance than the recent iterative convex refinement (ICR) algorithm. The methods introduced in this work are contributions to the lattice process and signal processing literature. The results are an input for the research on replacing CT images by synthetic or pseudo-CT images, and for an efficient way of recovering sparse signal.
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| 3. |
- Bayisa, Fekadu, et al.
(author)
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Large-scale modelling and forecasting of ambulance calls in northern Sweden using spatio-temporal log-Gaussian Cox processes
- 2020
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In: Spatial Statistics. - : Elsevier BV. - 2211-6753. ; 39
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Journal article (peer-reviewed)abstract
- Although ambulance call data typically come in the form of spatio-temporal point patterns, point process-based modelling approaches presented in the literature are scarce. In this paper, we study a unique set of Swedish spatio-temporal ambulance call data, which consist of the spatial (GPS) locations of the calls (within the four northernmost regions of Sweden) and the associated days of occurrence of the calls (January 1, 2014-December 31, 2018). Motivated by the nature of the data, we here employ log-Gaussian Cox processes (LGCPs) for the spatiotemporal modelling and forecasting of the calls. To this end, we propose a K-means clustering based bandwidth selection method for the kernel estimation of the spatial component of the separable spatio-temporal intensity function. The temporal component of the intensity function is modelled by means of Poisson regression, using different calendar covariates, and the spatiotemporal random field component of the random intensity of the LGCP is fitted using the Metropolis-adjusted Langevin algorithm. Spatial hot-spots have been found in the south-eastern part of the study region, where most people in the region live and our fitted model/forecasts manage to capture this behaviour quite well. Also, there is a significant association between the expected number of calls and the day-of-the-week, and the season-ofthe-year. A non-parametric second-order analysis indicates that LGCPs seem to be reasonable models for the data. Finally, we find that the fitted forecasts generate simulated future spatial event patterns which quite well resemble the actual future data. (C) 2020 The Author(s). Published by Elsevier B.V.
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| 4. |
- Bayisa, Fekadu, et al.
(author)
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Regularised Semi-parametric Composite Likelihood Intensity Modelling of a Swedish Spatial Ambulance Call Point Pattern
- 2023
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In: Journal of Agricultural Biological and Environmental Statistics. - : Springer. - 1085-7117 .- 1537-2693. ; 28, s. 664-83
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Journal article (peer-reviewed)abstract
- Motivated by the development of optimal dispatching strategies for prehospital resources, we model the spatial distribution of ambulance call events in the Swedish municipality Skelleftea during 2014-2018 in order to identify important spatial covariates and discern hotspot regions. Our large-scale multivariate data point pattern of call events consists of spatial locations and marks containing the associated priority levels and sex labels. The covariates used are related to road network coverage, population density, and socio-economic status. For each marginal point pattern, we model the associated intensity function by means of a log-linear function of the covariates and their interaction terms, in combination with lasso-like elastic-net regularized composite/Poisson process likelihood estimation. This enables variable selection and collinearity adjustment as well as reduction of variance inflation from overfitting and bias from underfitting. To incorporate mobility adjustment, reflecting people's movement patterns, we also include a nonparametric (kernel) intensity estimate as an additional covariate. The kernel intensity estimation performed here exploits a new heuristic bandwidth selection algorithm. We discover that hotspot regions occur along dense parts of the road network. A mean absolute error evaluation of the fitted model indicates that it is suitable for designing prehospital resource dispatching strategies. Supplementary materials accompanying this paper appear online.
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| 5. |
- Cronie, Ottmar, 1979, et al.
(author)
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A cross-validation-based statistical theory for point processes
- 2024
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In: Biometrika. - : Oxford University Press. - 0006-3444 .- 1464-3510. ; 111:2, s. 625-641
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Journal article (peer-reviewed)abstract
- Motivated by the general ability of cross-validation to reduce overfitting and mean square error, we develop a cross-validation-based statistical theory for general point processes. It is based on the combination of two novel concepts for general point processes: cross-validation and prediction errors. Our cross-validation approach uses thinning to split a point process/pattern into pairs of training and validation sets, while our prediction errors measure discrepancy between two point processes. The new statistical approach, which may be used to model different distributional characteristics, exploits the prediction errors to measure how well a given model predicts validation sets using associated training sets. Having indicated that our new framework generalizes many existing statistical approaches, we then establish different theoretical properties for it, including large sample properties. We further recognize that nonparametric intensity estimation is an instance of Papangelou conditional intensity estimation, which we exploit to apply our new statistical theory to kernel intensity estimation. Using independent thinning-based cross-validation, we numerically show that the new approach substantially outperforms the state-of-the-art in bandwidth selection. Finally, we carry out intensity estimation for a dataset in forestry and a dataset in neurology.
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| 6. |
- Cronie, Ottmar, et al.
(author)
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A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions
- 2018
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In: Biometrika. - : Oxford University Press. - 0006-3444 .- 1464-3510. ; 105:2, s. 455-462
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Journal article (peer-reviewed)abstract
- We propose a new bandwidth selection method for kernel estimators of spatial point process intensity functions. The method is based on an optimality criterion motivated by the Campbell formula applied to the reciprocal intensity function. The new method is fully nonparametric, does not require knowledge of higher-order moments, and is not restricted to a specific class of point process. Our approach is computationally straightforward and does not require numerical approximation of integrals.
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| 7. |
- Cronie, Ottmar, 1979-, et al.
(author)
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A J-function for Inhomogeneous Spatio-temporal Point Processes
- 2015
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In: Scandinavian Journal of Statistics. - : John Wiley & Sons. - 0303-6898 .- 1467-9469. ; 42:2, s. 562-579
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Journal article (peer-reviewed)abstract
- We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.
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| 8. |
- Cronie, Ottmar, 1979
(author)
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Different Aspects of Inference for Spatio-Temporal Point Processes
- 2010
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Licentiate thesis (other academic/artistic)abstract
- This thesis deals with inference problems related to the Renshaw-Särkkä growth interaction model (RS-model). It is a continuous time spatio-temporal point process with time dependent interacting marks, in which the immigrationdeath process (a continuous time Markov chain) controls the arrivals of new marked points as well as their potential life-times. The data considered are marked point patterns sampled at fixed time points. First we propose three edge correction methods for discretely sampled (marked) spatio-temporal point processes. These are all based on the idea of placing an approximated expected behaviour of our process at hand (based on simulated realisations) outside the study region, which in turn interacts with the data during the estimation. We study the methods and evaluate them numerically in the context of the RS-model. The parameters related to the development of the marks are estimated using the least-squares approach. Secondly, we propose (approximate) maximum likelihood (ML) estimators for the two parameters of the immigration-death process; the arrival intensity and the death rate. The arrival intensity is assumed to be constant and the death rate is assumed to be proportional to a function of the current mark size of a point. The arrival intensity estimator is constructed to compensate for the (unobserved) individuals arriving and dying between two sampled time points. When assumed that the death rate is constant we can derive the transition probabilities of the immigration-death process. These in turn give us the exact likelihood of its parameter pair. We are able to reduce the likelihood maximisation problem from two dimensions to one dimension. Furthermore, under the condition that the parameter pair lies in some compact subset of the positive part of the real plane, we manage to show the consistency and the asymptotic normality of its ML-estimator under an equidistant sampling scheme. These results are also evaluated numerically.
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| 9. |
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| 10. |
- Cronie, Ottmar, et al.
(author)
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Functional marked point processes : Unifying spatio-temporal frameworks and analysing spatially dependent functional data
- 2019
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In: Statistical Analysis for Space-Time Data. - : Eurpean Courses in Advanced Statistics (ECAS). ; , s. 7-7
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Conference paper (peer-reviewed)abstract
- This paper treats functional marked point processes (FMPPs), which are defined as marked point processes where the marks are random elements in some (Polish) function space. Such marks may represent e.g. spatial paths or functions of time. To be able to consider e.g. multivariate FMPPs, we also attach an additionally, Euclidean, mark to each point. We indicate how the FMPP framework quite naturally connects the point process framework with both the functional data analysis framework and the geostatistical framework; in particular we define spatio-temporal geostatistical marking for point processes. We further show that various existing stochastic models fit well into the FMPP framework, in particular marked point processes with real valued marks. To be able to carry out non-parametric statistical analyses for functional marked point patterns, we study characteristics such as product densities and Palm distributions, which are the building blocks for summary statistics such as marked inhomogeneous J-functions and our so-called K-functionals. We finally apply these statistical tools to analyse a few different functional marked point patterns.
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