| 961. |
- Andersson, Adam, 1979, et al.
(författare)
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Weak error analysis for semilinear stochastic Volterra equations with additive noise
- 2014
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our weak convergence result concerns not only the solution at a fixed time but also integrals of the entire path with respect to any finite Borel measure. The proof does not rely on a Kolmogorov equation. Instead it is based on a duality argument from Malliavin calculus.
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| 962. |
- Andersson, Adam, 1979, et al.
(författare)
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Weak error analysis for semilinear stochastic Volterra equations with additive noise
- 2016
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 437:2, s. 1283-1304
-
Tidskriftsartikel (refereegranskat)abstract
- We prove a weak error estimate for the approximation in space and time of a semilinear stochastic Volterra integro-differential equation driven by additive space-time Gaussian noise. We treat this equation in an abstract framework, in which parabolic stochastic partial differential equations are also included as a special case. The approximation in space is performed by a standard finite element method and in time by an implicit Euler method combined with a convolution quadrature. The weak rate of convergence is proved to be twice the strong rate, as expected. Our convergence result concerns not only functionals of the solution at a fixed time but also more complicated functionals of the entire path and includes convergence of covariances and higher order statistics. The proof does not rely on a Kolmogorov equation. Instead it is based on a duality argument from Malliavin calculus.
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| 963. |
- Anguzu, Collins, et al.
(författare)
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A Comparison of Graph Centrality Measures Based on Lazy Random Walks
- 2021
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Ingår i: Applied Modeling Techniquesand Data Analysis 1. - : John Wiley & Sons, Inc. Hoboken, NJ, USA. - 9781786306739 ; , s. 91-111
-
Bokkapitel (refereegranskat)abstract
- When working with a network, it is often of interest to locate the “most important”nodes in the network. A common way to do this is by using some graph centralitymeasures. Since what constitutes as an important node varies from one network toanother, or even in applications on the same network, there is a large number ofdifferent centrality measures proposed in the literature. Due to the large amount ofdifferent centrality measures proposed in different fields, there is also a large amountof very similar or equivalent centrality measures (in the sense that they give the sameranks). In this chapter, we focus on the centrality measures based on powers of theadjacency matrix and those based on random walk. In this case, we show how someof these centrality measures are related, as well as their lazy variants.We will performsome experiments to demonstrate the similarities between the centrality measures.
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| 964. |
- Anguzu, Collins, et al.
(författare)
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Algorithms for recalculating alpha and eigenvector centrality measures using graph partitioning techniques
- 2022
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Ingår i: <em>Springer Proceedings in Mathematics and Statistics</em>. - Cham : Springer Nature. - 9783031178191 ; , s. 541-562
-
Konferensbidrag (refereegranskat)abstract
- In graph theory, centrality measures are very crucial in ranking vertices of the graph in order of their importance. Alpha and eigenvector centralities are some of the highly placed centrality measures applied especially in social network analysis, disease diffusion networks and mechanical infrastructural developments. In this study we focus on recalculating alpha and eigenvector centralities using graph partitioning techniques. We write an algorithm for partitioning, sorting and efficiently computing these centralities for a graph. We then numerically demonstrate the technique on some sample small-sized networks to recalculate the two centrality measures
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| 965. |
- Arya, Gaurav, et al.
(författare)
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Differentiating Metropolis-Hastings to Optimize Intractable Densities
- 2023
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We develop an algorithm for automatic differentiation of Metropolis-Hastings samplers, allowing us to differentiate through probabilistic inference, even if the model has discrete components within it. Our approach fuses recent advances in stochastic automatic differentiation with traditional Markov chain coupling schemes, providing an unbiased and low-variance gradient estimator. This allows us to apply gradient-based optimization to objectives expressed as expectations over intractable target densities. We demonstrate our approach by finding an ambiguous observation in a Gaussian mixture model and by maximizing the specific heat in an Ising model.
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| 966. |
- Athanasopoulos, George, et al.
(författare)
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Forecast reconciliation : A review
- 2024
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Ingår i: International Journal of Forecasting. - : Elsevier. - 0169-2070 .- 1872-8200. ; 40:2, s. 430-456
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Forskningsöversikt (refereegranskat)abstract
- Collections of time series formed via aggregation are prevalent in many fields. These are commonly referred to as hierarchical time series and may be constructed cross-sectionally across different variables, temporally by aggregating a single series at different frequencies, or even generalised beyond aggregation as time series that respect linear constraints. When forecasting such time series, a desirable condition is for forecasts to be coherent: to respect the constraints. The past decades have seen substantial growth in this field with the development of reconciliation methods that ensure coherent forecasts and improve forecast accuracy. This paper serves as a comprehensive review of forecast reconciliation and an entry point for researchers and practitioners dealing with hierarchical time series. The scope of the article includes perspectives on forecast reconciliation from machine learning, Bayesian statistics and probabilistic forecasting, as well as applications in economics, energy, tourism, retail demand and demography.
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| 967. |
- Auriol, Jean, et al.
(författare)
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Mean-square exponential stabilization of coupled hyperbolic systems with random parameters
- 2023
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Ingår i: IFAC-PapersOnLine. - 2405-8963. ; 56:2, s. 8153-8158
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Konferensbidrag (refereegranskat)abstract
- In this paper, we consider a system of two coupled scalar-valued hyperbolic partial differential equations (PDEs) with random parameters. We formulate a stability condition under which the classical backstepping controller (designed for a nominal system whose parameters are constant) stabilizes the system. More precisely, we guarantee closed-loop mean-square exponential stability under random system parameter perturbations, provided the nominal parameters are sufficiently close to the stochastic ones on average. The proof is based on a Lyapunov analysis, the Lyapunov functional candidate describing the contraction of L2-norm of the system states. An illustrative traffic flow regulation example shows the viability and importance of the proposed result
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| 968. |
- Baaz, Marcus, 1993
(författare)
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Nonlinear Mixed Effects Modeling of Combination Therapies in Oncology
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- It has been shown that simultaneous administration of two or more anticancer agents can have a beneficial effect on cancer patients. This type of treatment is called combination therapy and is nowadays commonly used in the fight against cancer. New anticancer drugs are constantly being developed and what drugs to proceed with to the next development phase can be challenging. This thesis introduces the reader to how mathematical modeling can be used to inform such decisions by modeling the relationship between, e.g., drug concentration and in vivo efficacy. Specifically, compartment models based on ordinary differential equations and the nonlinear mixed-effects (NLME) framework are examined. The thesis contains three papers in manuscript form. The first paper, "Model- Based Assessment of Combination Therapies – Ranking of Radiosensitizing Agents in Oncology" explores preclinical radiation treatment data, inter-study variability, and ranking of test compounds. The second paper is entitled "A Model-Based Approach for Translation in On- cology - From Xenografts to RECIST". Here the focus is on the translational potential of semi-mechanistic NLME models. Preclinical data is used to cali- brate three models, which are then translated using commonly used techniques, and used to predict the result of clinical studies. The third paper, "Probabilistic Analysis of Tumor Models to Support Early Clinical Trial Design", details how one can derive probabilistic expressions for the predicted proportion of patients in each RECIST category in a clinical study. These are used to develop a method for predicting the required sample size to show a certain significance level and test power, for newly developed drugs.
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| 969. |
- 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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| 970. |
- 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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