| 971. |
- Babu, Prabhu, et al.
(författare)
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Multiple-hypothesis testing rules for high-dimensional model selection and sparse-parameter estimation
- 2023
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Ingår i: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 213
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of model selection for high-dimensional sparse linear regression models. We pose the model selection problem as a multiple-hypothesis testing problem and employ the methods of false discovery rate (FDR) and familywise error rate (FER) to solve it. We also present the reformulation of the FDR/FER-based approaches as criterion-based model selection rules and establish their relation to the extended Bayesian Information Criterion (EBIC), which is a state-of-the-art high-dimensional model selection rule. We use numerical simulations to show that the proposed FDR/FER method is well suited for high-dimensional model selection and performs better than EBIC.
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| 972. |
- Balabanov, Oleksandr, et al.
(författare)
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Bayesian Posterior Approximation With Stochastic Ensembles
- 2023
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Ingår i: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. - 1063-6919. - 9798350301298 ; 2023-June, s. 13701-13711
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Konferensbidrag (refereegranskat)abstract
- We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochas-tic ensembles are formulated as families of distributions and trained to approximate the Bayesian posterior with variational inference. We implement stochastic ensembles based on Monte Carlo dropout, DropConnect and a novel non-parametric version of dropout and evaluate them on a toy problem and CIFAR image classification. For both tasks, we test the quality of the posteriors directly against Hamil-tonian Monte Carlo simulations. Our results show that stochastic ensembles provide more accurate posterior esti-mates than other popular baselines for Bayesian inference.
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| 973. |
- Barth, A., et al.
(författare)
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Lp and almost sure convergence of a Milstein scheme for stochastic partial differential equations
- 2013
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Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 123:5, s. 1563-1587
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, Lp convergence and almost sure convergence of the Milstein approximation of a partial differential equation of advection-diffusion type driven by a multiplicative continuous martingale is proven. The (semidiscrete) approximation in space is a projection onto a finite dimensional function space. The considered space approximation has to have an order of convergence fitting to the order of convergence of the Milstein approximation and the regularity of the solution. The approximation of the driving noise process is realized by the truncation of the Karhunen-Loève expansion of the driving noise according to the overall order of convergence. Convergence results in Lp and almost sure convergence bounds for the semidiscrete approximation as well as for the fully discrete approximation are provided. © 2013 Elsevier B.V. All rights reserved.
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| 974. |
- Barth, A., et al.
(författare)
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Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises
- 2012
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Ingår i: Applied Mathematics and Optimization. - : Springer Science and Business Media LLC. - 1432-0606 .- 0095-4616. ; 66:3, s. 387-413
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, càdlàg, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L2 and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.© Springer Science+Business Media, LLC 2012.
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| 975. |
- Barth, A., et al.
(författare)
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Multilevel Monte Carlo method for parabolic stochastic partial differential equations
- 2013
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Ingår i: BIT (Copenhagen). - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 53:1, s. 3-27
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler-Maruyama discretization in time yields mean square convergence of order one in space and of order 1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mesh. © 2012 Springer Science + Business Media B.V.
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| 976. |
- Barth, A., et al.
(författare)
-
Multilevel Monte Carlo method with applications to stochastic partial differential equations
- 2012
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Ingår i: International Journal of Computer Mathematics. - : Informa UK Limited. - 1029-0265 .- 0020-7160. ; 89:18, s. 2479-2498
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Tidskriftsartikel (refereegranskat)abstract
- In this work, the approximation of Hilbert-space-valued random variables is combined with the approximation of the expectation by a multilevel Monte Carlo (MLMC) method. The number of samples on the different levels of the multilevel approximation are chosen such that the errors are balanced. The overall work then decreases in the optimal case to O(h2) if h is the error of the approximation. The MLMC method is applied to functions of solutions of parabolic and hyperbolic stochastic partial differential equations as needed, for example, for option pricing. Simulations complete the paper. © 2012 Copyright Taylor and Francis Group, LLC.
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| 977. |
- Barth, A., et al.
(författare)
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Simulation of stochastic partial differential equations using finite element methods
- 2012
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Ingår i: Stochastics. - : Informa UK Limited. - 1744-2508 .- 1744-2516. ; 84:2-3, s. 217-231
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Tidskriftsartikel (refereegranskat)abstract
- These notes describe numerical issues that may arise when implementing a simulation method for a stochastic partial differential equation (SPDE). It is shown that an additional approximation of the noise does not necessarily affect the order of convergence of a discretization method for a SPDE driven by Lévy noise. Furthermore, finite element methods are explicitly given and simulations are done. In statistical tests, it is shown that the simulations obey the theoretical orders of convergence. © 2012 Copyright Taylor and Francis Group, LLC.
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| 978. |
- Bello, Luca, et al.
(författare)
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Compressed computations using wavelets for hidden Markov models with continuous observations
- 2023
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Ingår i: Plos One. - 1932-6203. ; 18:6
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Tidskriftsartikel (refereegranskat)abstract
- Compression as an accelerant of computation is increasingly recognized as an important component in engineering fast real-world machine learning methods for big data; c.f., its impact on genome-scale approximate string matching. Previous work showed that compression can accelerate algorithms for Hidden Markov Models (HMM) with discrete observations, both for the classical frequentist HMM algorithms-Forward Filtering, Backward Smoothing and Viterbi-and Gibbs sampling for Bayesian HMM. For Bayesian HMM with continuous-valued observations, compression was shown to greatly accelerate computations for specific types of data. For instance, data from large-scale experiments interrogating structural genetic variation can be assumed to be piece-wise constant with noise, or, equivalently, data generated by HMM with dominant self-transition probabilities. Here we extend the compressive computation approach to the classical frequentist HMM algorithms on continuous-valued observations, providing the first compressive approach for this problem. In a large-scale simulation study, we demonstrate empirically that in many settings compressed HMM algorithms very clearly outperform the classical algorithms with no, or only an insignificant effect, on the computed probabilities and infered state paths of maximal likelihood. This provides an efficient approach to big data computations with HMM. An open-source implementation of the method is available from .
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| 979. |
- Bengtsson, Anders, et al.
(författare)
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Uncertainty in fatigue life prediction of structures subject to Gaussian loads
- 2009
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Ingår i: Probabilistic Engineering Mechanics. - : Elsevier BV. - 0266-8920 .- 1878-4275. ; 24:2, s. 224-235
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we shall concentrate on Gaussian (or close to Gaussian) loads acting on a structure. The goal is to compute a measure of risk for fatigue of a component during a specific time period and the so called "safety index" will be used to combine different types of uncertainties. The presented methodology can be applied in a more general situation of environmental loads which properties may vary with time of the year. The load is assumed to be "locally" stationary such that the mean load is constant (and taken to be zero) but the variance of the load can change slowly with time. Non-stationary hierarchical processes, separable into a stationary Gaussian process and a process describing the load amplitude and period, e.g. processes with Pierson-Moskowitz or JONSWAP spectrum, are treated in detail. The variability of a load, relevant for the fatigue accumulation process, will be described by means of rainflow cycles counted in the load. Moreover, common damage intensity approximations are reviewed and evaluated in a simulation study. © 2008 Elsevier Ltd. All rights reserved.
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| 980. |
- Bengtsson, Anders, et al.
(författare)
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Uncertainty of estimated rainflow damage for random loads
- 2009
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Ingår i: Marine Structures. - : Elsevier BV. - 0951-8339 .- 1873-4170. ; 22:2, s. 261-274
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Tidskriftsartikel (refereegranskat)abstract
- One way to assess the uncertainty in fatigue damage analysis is to use a so-called safety index. In the computation of such an index the coefficient of variation for the accumulated damage is needed. Employing the rainflow cycle count method for fatigue damage leads to, in most cases, complicated calculations. Here we present a new and simplified method to estimate the coefficient of variation for the accumulated damage when only one sample path of the load is available. Non-stationary, slowly changing, Gaussian loads are given special attention. The approach is illustrated by means of stationary Gaussian loads with nine different spectra, a measured non-Gaussian load, a skewed load and the wave load accumulated during one year in a "seasonally changing environment"
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