Foundations of data science (Springfield, Mo.)最新文献_第8页

Particle filters for inference of high-dimensional multivariate stochastic volatility models with cross-leverage effects 具有交叉杠杆效应的高维多元随机波动模型的粒子滤波

Foundations of data science (Springfield, Mo.) Pub Date : 2019-02-25 DOI: 10.3934/fods.2019003

Yaxian Xu, A. Jasra

{"title":"Particle filters for inference of high-dimensional multivariate stochastic volatility models with cross-leverage effects","authors":"Yaxian Xu, A. Jasra","doi":"10.3934/fods.2019003","DOIUrl":"https://doi.org/10.3934/fods.2019003","url":null,"abstract":"Multivariate stochastic volatility models are a popular and well-known class of models in the analysis of financial time series because of their abilities to capture the important stylized facts of financial returns data. We consider the problems of filtering distribution estimation and also marginal likelihood calculation for multivariate stochastic volatility models with cross-leverage effects in the high dimensional case, that is when the number of financial time series that we analyze simultaneously (denoted by begin{document}$ d $end{document} ) is large. The standard particle filter has been widely used in the literature to solve these intractable inference problems. It has excellent performance in low to moderate dimensions, but collapses in the high dimensional case. In this article, two new and advanced particle filters proposed in [ 4 ], named the space-time particle filter and the marginal space-time particle filter, are explored for these estimation problems. The better performance in both the accuracy and stability for the two advanced particle filters are shown using simulation and empirical studies in comparison with the standard particle filter. In addition, Bayesian static model parameter estimation problem is considered with the advances in particle Markov chain Monte Carlo methods. The particle marginal Metropolis-Hastings algorithm is applied together with the likelihood estimates from the space-time particle filter to infer the static model parameter successfully when that using the likelihood estimates from the standard particle filter fails.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43334711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Spectral methods to study the robustness of residual neural networks with infinite layers 用谱方法研究无穷层残差神经网络的鲁棒性

Foundations of data science (Springfield, Mo.) Pub Date : 2019-01-01 DOI: 10.3934/fods.2020012

T. Trimborn, Stephan Gerster, G. Visconti

引用次数: 4

Issues using logistic regression with class imbalance, with a case study from credit risk modelling 使用逻辑回归与阶级不平衡的问题，并以信用风险模型为例进行研究

Foundations of data science (Springfield, Mo.) Pub Date : 2019-01-01 DOI: 10.3934/fods.2019016

Yazhe Li, T. Bellotti, N. Adams

引用次数: 9

Background material 背景材料

Foundations of data science (Springfield, Mo.) Pub Date : 2018-12-11 DOI: 10.1090/surv/236/02

引用次数: 0

Markov chain simulation for multilevel Monte Carlo 多级蒙特卡罗的马尔可夫链仿真

Foundations of data science (Springfield, Mo.) Pub Date : 2018-06-26 DOI: 10.3934/FODS.2021004

A. Jasra, K. Law, Yaxian Xu

{"title":"Markov chain simulation for multilevel Monte Carlo","authors":"A. Jasra, K. Law, Yaxian Xu","doi":"10.3934/FODS.2021004","DOIUrl":"https://doi.org/10.3934/FODS.2021004","url":null,"abstract":"This paper considers a new approach to using Markov chain Monte Carlo (MCMC) in contexts where one may adopt multilevel (ML) Monte Carlo. The underlying problem is to approximate expectations w.r.t. an underlying probability measure that is associated to a continuum problem, such as a continuous-time stochastic process. It is then assumed that the associated probability measure can only be used (e.g. sampled) under a discretized approximation. In such scenarios, it is known that to achieve a target error, the computational effort can be reduced when using MLMC relative to exact sampling from the most accurate discretized probability. The ideas rely upon introducing hierarchies of the discretizations where less accurate approximations cost less to compute, and using an appropriate collapsing sum expression for the target expectation. If a suitable coupling of the probability measures in the hierarchy is achieved, then a reduction in cost is possible. This article focused on the case where exact sampling from such coupling is not possible. We show that one can construct suitably coupled MCMC kernels when given only access to MCMC kernels which are invariant with respect to each discretized probability measure. We prove, under assumptions, that this coupled MCMC approach in a ML context can reduce the cost to achieve a given error, relative to exact sampling. Our approach is illustrated on a numerical example.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47508531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

Quantum topological data analysis with continuous variables 连续变量的量子拓扑数据分析

Foundations of data science (Springfield, Mo.) Pub Date : 2018-04-05 DOI: 10.3934/fods.2019017

G. Siopsis

引用次数: 7

Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model 在双层准地转模型中利用随机输运噪声模拟不确定性

Foundations of data science (Springfield, Mo.) Pub Date : 2018-02-15 DOI: 10.3934/fods.2020010

C. Cotter, D. Crisan, Darryl D. Holm, Wei Pan, I. Shevchenko

{"title":"Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model","authors":"C. Cotter, D. Crisan, Darryl D. Holm, Wei Pan, I. Shevchenko","doi":"10.3934/fods.2020010","DOIUrl":"https://doi.org/10.3934/fods.2020010","url":null,"abstract":"The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic parameterisation in a two-layer quasi-geostrophic model for a begin{document}$ beta $end{document} -plane channel flow configuration. We present a new method for estimating the stochastic forcing (used in the parameterisation) to approximate unresolved components using data from the high resolution deterministic simulation, and describe a procedure for computing physically-consistent initial conditions for the stochastic model. We also quantify uncertainty of coarse grid simulations relative to the fine grid ones in homogeneous (teamed with small-scale vortices) and heterogeneous (featuring horizontally elongated large-scale jets) flows, and analyse how the spread of stochastic solutions depends on different parameters of the model. The parameterisation is tested by comparing it with the true eddy-resolving solution that has reached some statistical equilibrium and the deterministic solution modelled on a low-resolution grid. The results show that the proposed parameterisation significantly depends on the resolution of the stochastic model and gives good ensemble performance for both homogeneous and heterogeneous flows, and the parameterisation lays solid foundations for data assimilation.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43640188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 47

Randomized learning of the second-moment matrix of a smooth function 光滑函数二阶矩阵的随机学习

Foundations of data science (Springfield, Mo.) Pub Date : 2016-12-19 DOI: 10.3934/fods.2019015

Armin Eftekhari, M. Wakin, Ping Li, P. Constantine

引用次数: 4

Geometric adaptive Monte Carlo in random environment 随机环境下的几何自适应蒙特卡罗算法

Foundations of data science (Springfield, Mo.) Pub Date : 2016-08-29 DOI: 10.3934/FODS.2021014

T. Papamarkou, Alexey Lindo, E. Ford

{"title":"Geometric adaptive Monte Carlo in random environment","authors":"T. Papamarkou, Alexey Lindo, E. Ford","doi":"10.3934/FODS.2021014","DOIUrl":"https://doi.org/10.3934/FODS.2021014","url":null,"abstract":"Manifold Markov chain Monte Carlo algorithms have been introduced to sample more effectively from challenging target densities exhibiting multiple modes or strong correlations. Such algorithms exploit the local geometry of the parameter space, thus enabling chains to achieve a faster convergence rate when measured in number of steps. However, acquiring local geometric information can often increase computational complexity per step to the extent that sampling from high-dimensional targets becomes inefficient in terms of total computational time. This paper analyzes the computational complexity of manifold Langevin Monte Carlo and proposes a geometric adaptive Monte Carlo sampler aimed at balancing the benefits of exploiting local geometry with computational cost to achieve a high effective sample size for a given computational cost. The suggested sampler is a discrete-time stochastic process in random environment. The random environment allows to switch between local geometric and adaptive proposal kernels with the help of a schedule. An exponential schedule is put forward that enables more frequent use of geometric information in early transient phases of the chain, while saving computational time in late stationary phases. The average complexity can be manually set depending on the need for geometric exploitation posed by the underlying model.","PeriodicalId":73054,"journal":{"name":"Foundations of data science (Springfield, Mo.)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70248343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Consistent manifold representation for topological data analysis 拓扑数据分析的一致流形表示

Foundations of data science (Springfield, Mo.) Pub Date : 2016-06-07 DOI: 10.3934/FODS.2019001

Tyrus Berry, T. Sauer

引用次数: 53