arXiv - STAT - Computation最新文献_第4页

Optimised Annealed Sequential Monte Carlo Samplers 优化的校正序列蒙特卡罗采样器

arXiv - STAT - Computation Pub Date : 2024-08-22 DOI: arxiv-2408.12057

Saifuddin Syed, Alexandre Bouchard-Côté, Kevin Chern, Arnaud Doucet

{"title":"Optimised Annealed Sequential Monte Carlo Samplers","authors":"Saifuddin Syed, Alexandre Bouchard-Côté, Kevin Chern, Arnaud Doucet","doi":"arxiv-2408.12057","DOIUrl":"https://doi.org/arxiv-2408.12057","url":null,"abstract":"Annealed Sequential Monte Carlo (SMC) samplers are special cases of SMC\u0000samplers where the sequence of distributions can be embedded in a smooth path\u0000of distributions. Using this underlying path of distributions and a performance\u0000model based on the variance of the normalisation constant estimator, we\u0000systematically study dense schedule and large particle limits. From our theory\u0000and adaptive methods emerges a notion of global barrier capturing the inherent\u0000complexity of normalisation constant approximation under our performance model.\u0000We then turn the resulting approximations into surrogate objective functions of\u0000algorithm performance, and use them for methodology development. We obtain\u0000novel adaptive methodologies, Sequential SMC (SSMC) and Sequential AIS (SAIS)\u0000samplers, which address practical difficulties inherent in previous adaptive\u0000SMC methods. First, our SSMC algorithms are predictable: they produce a\u0000sequence of increasingly precise estimates at deterministic and known times.\u0000Second, SAIS, a special case of SSMC, enables schedule adaptation at a memory\u0000cost constant in the number of particles and require much less communication.\u0000Finally, these characteristics make SAIS highly efficient on GPUs. We develop\u0000an open-source, high-performance GPU implementation based on our methodology\u0000and demonstrate up to a hundred-fold speed improvement compared to\u0000state-of-the-art adaptive AIS methods.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"230 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189504","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: 0

Adaptive Stereographic MCMC 自适应立体 MCMC

arXiv - STAT - Computation Pub Date : 2024-08-21 DOI: arxiv-2408.11780

Cameron Bell, Krzystof Łatuszyński, Gareth O. Roberts

{"title":"Adaptive Stereographic MCMC","authors":"Cameron Bell, Krzystof Łatuszyński, Gareth O. Roberts","doi":"arxiv-2408.11780","DOIUrl":"https://doi.org/arxiv-2408.11780","url":null,"abstract":"In order to tackle the problem of sampling from heavy tailed, high\u0000dimensional distributions via Markov Chain Monte Carlo (MCMC) methods, Yang,\u0000Latuszy'nski, and Roberts (2022) (arXiv:2205.12112) introduces the\u0000stereographic projection as a tool to compactify $mathbb{R}^d$ and transform\u0000the problem into sampling from a density on the unit sphere $mathbb{S}^d$.\u0000However, the improvement in algorithmic efficiency, as well as the\u0000computational cost of the implementation, are still significantly impacted by\u0000the parameters used in this transformation. To address this, we introduce adaptive versions of the Stereographic Random\u0000Walk (SRW), the Stereographic Slice Sampler (SSS), and the Stereographic Bouncy\u0000Particle Sampler (SBPS), which automatically update the parameters of the\u0000algorithms as the run progresses. The adaptive setup allows us to better\u0000exploit the power of the stereographic projection, even when the target\u0000distribution is neither centered nor homogeneous. We present a simulation study\u0000showing each algorithm's robustness to starting far from the mean in heavy\u0000tailed, high dimensional settings, as opposed to Hamiltonian Monte Carlo (HMC).\u0000We establish a novel framework for proving convergence of adaptive MCMC\u0000algorithms over collections of simultaneously uniformly ergodic Markov\u0000operators, including continuous time processes. This framework allows us to\u0000prove LLNs and a CLT for our adaptive Stereographic algorithms.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189500","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: 0

A Multiple Random Scan Strategy for Latent Space Models 潜空间模型的多重随机扫描策略

arXiv - STAT - Computation Pub Date : 2024-08-21 DOI: arxiv-2408.11725

Antonio Peruzzi, Roberto Casarin

{"title":"A Multiple Random Scan Strategy for Latent Space Models","authors":"Antonio Peruzzi, Roberto Casarin","doi":"arxiv-2408.11725","DOIUrl":"https://doi.org/arxiv-2408.11725","url":null,"abstract":"Latent Space (LS) network models project the nodes of a network on a\u0000$d$-dimensional latent space to achieve dimensionality reduction of the network\u0000while preserving its relevant features. Inference is often carried out within a\u0000Markov Chain Monte Carlo (MCMC) framework. Nonetheless, it is well-known that\u0000the computational time for this set of models increases quadratically with the\u0000number of nodes. In this work, we build on the Random-Scan (RS) approach to\u0000propose an MCMC strategy that alleviates the computational burden for LS models\u0000while maintaining the benefits of a general-purpose technique. We call this\u0000novel strategy Multiple RS (MRS). This strategy is effective in reducing the\u0000computational cost by a factor without severe consequences on the MCMC draws.\u0000Moreover, we introduce a novel adaptation strategy that consists of a\u0000probabilistic update of the set of latent coordinates of each node. Our\u0000Adaptive MRS adapts the acceptance rate of the Metropolis step to adjust the\u0000probability of updating the latent coordinates. We show via simulation that the\u0000Adaptive MRS approach performs better than MRS in terms of mixing. Finally, we\u0000apply our algorithm to a multi-layer temporal LS model and show how our\u0000adaptive strategy may be beneficial to empirical applications.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189502","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: 0

Optical ISAC: Fundamental Performance Limits and Transceiver Design 光学 ISAC：基本性能限制和收发器设计

arXiv - STAT - Computation Pub Date : 2024-08-21 DOI: arxiv-2408.11792

Alireza Ghazavi Khorasgani, Mahtab Mirmohseni, Ahmed Elzanaty

{"title":"Optical ISAC: Fundamental Performance Limits and Transceiver Design","authors":"Alireza Ghazavi Khorasgani, Mahtab Mirmohseni, Ahmed Elzanaty","doi":"arxiv-2408.11792","DOIUrl":"https://doi.org/arxiv-2408.11792","url":null,"abstract":"This paper characterizes the optimal capacity-distortion (C-D) tradeoff in an\u0000optical point-to-point (P2P) system with single-input single-output for\u0000communication and single-input multiple-output for sensing (SISO-SIMO-C/S)\u0000within an integrated sensing and communication (ISAC) framework. We introduce\u0000practical, asymptotically optimal maximum a posteriori (MAP) and maximum\u0000likelihood estimators (MLE) for target distance, addressing nonlinear\u0000measurement-to-state relationships and non-conjugate priors. Our results show\u0000these estimators converge to the Bayesian Cramer-Rao bound (BCRB) as sensing\u0000antennas increase. We also demonstrate that the achievable rate-CRB (AR-CRB)\u0000serves as an outer bound (OB) for the optimal C-D region. To optimize input\u0000distribution across the Pareto boundary of the C-D region, we propose two\u0000algorithms: an iterative Blahut-Arimoto algorithm (BAA)-type method and a\u0000memory-efficient closed-form (CF) approach, including a CF optimal distribution\u0000for high optical signal-to-noise ratio (O-SNR) conditions. Additionally, we\u0000extend and modify the Deterministic-Random Tradeoff (DRT) to this optical ISAC\u0000context.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189503","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: 0

armadillo: An R Package to Use the Armadillo C++ Library 犰狳：使用犰狳 C++ 库的 R 软件包

arXiv - STAT - Computation Pub Date : 2024-08-19 DOI: arxiv-2408.11074

Mauricio Vargas Sepúlveda, Jonathan Schneider Malamud

引用次数: 0

Issues of parameterization and computation for posterior inference in partially identified models 部分确定模型的参数化和后验推断计算问题

arXiv - STAT - Computation Pub Date : 2024-08-19 DOI: arxiv-2408.10416

Seren Lee, Paul Gustafson

{"title":"Issues of parameterization and computation for posterior inference in partially identified models","authors":"Seren Lee, Paul Gustafson","doi":"arxiv-2408.10416","DOIUrl":"https://doi.org/arxiv-2408.10416","url":null,"abstract":"A partially identified model, where the parameters can not be uniquely\u0000identified, often arises during statistical analysis. While researchers\u0000frequently use Bayesian inference to analyze the models, when Bayesian\u0000inference with an off-the-shelf MCMC sampling algorithm is applied to a\u0000partially identified model, the computational performance can be poor. It is\u0000found that using importance sampling with transparent reparameterization (TP)\u0000is one remedy. This method is preferable since the model is known to be\u0000rendered as identified with respect to the new parameterization, and at the\u0000same time, it may allow faster, i.i.d. Monte Carlo sampling by using conjugate\u0000convenience priors. In this paper, we explain the importance sampling method\u0000with the TP and a pseudo-TP. We introduce the pseudo-TP, an alternative to TP,\u0000since finding a TP is sometimes difficult. Then, we test the methods'\u0000performance in some scenarios and compare it to the performance of the\u0000off-the-shelf MCMC method - Gibbs sampling - applied in the original\u0000parameterization. While the importance sampling with TP (ISTP) shows generally\u0000better results than off-the-shelf MCMC methods, as seen in the compute time and\u0000trace plots, it is also seen that finding a TP which is necessary for the\u0000method may not be easy. On the other hand, the pseudo-TP method shows a mixed\u0000result and room for improvement since it relies on an approximation, which may\u0000not be adequate for a given model and dataset.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189506","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: 0

$statcheck$ is flawed by design and no valid spell checker for statistical results $statcheck$ 的设计存在缺陷，没有有效的统计结果拼写检查器

arXiv - STAT - Computation Pub Date : 2024-08-15 DOI: arxiv-2408.07948

Ingmar Böschen

{"title":"$statcheck$ is flawed by design and no valid spell checker for statistical results","authors":"Ingmar Böschen","doi":"arxiv-2408.07948","DOIUrl":"https://doi.org/arxiv-2408.07948","url":null,"abstract":"The R package $statcheck$ is designed to extract statistical test results\u0000from text and check the consistency of the reported test statistics and\u0000corresponding p-values. Recently, it has also been featured as a spell checker\u0000for statistical results, aimed at improving reporting accuracy in scientific\u0000publications. In this study, I perform a check on $statcheck$ using a\u0000non-exhaustive list of 187 simple text strings with arbitrary statistical test\u0000results. These strings represent a wide range of textual representations of\u0000results including correctly manageable results, non-targeted test statistics,\u0000variable reporting styles, and common typos. Since $statcheck$'s detection\u0000heuristic is tied to a specific set of statistical test results that strictly\u0000adhere to the American Psychological Association (APA) reporting guidelines, it\u0000is unable to detect and check any reported result that even slightly deviates\u0000from this narrow style. In practice, $statcheck$ is unlikely to detect many\u0000statistical test results reported in the literature. I conclude that the\u0000capabilities and usefulness of the $statcheck$ software are very limited and\u0000that it should not be used to detect irregularities in results nor as a spell\u0000checker for statistical results. Future developments should aim to incorporate\u0000more flexible algorithms capable of handling a broader variety of reporting\u0000styles, such as those provided by $JATSdecoder$ and Large Language Models,\u0000which show promise in overcoming these limitations but they cannot replace the\u0000critical eye of a knowledgeable reader.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189507","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: 0

Modeling of Measurement Error in Financial Returns Data 金融收益数据测量误差建模

arXiv - STAT - Computation Pub Date : 2024-08-14 DOI: arxiv-2408.07405

Ajay Jasra, Mohamed Maama, Aleksandar Mijatović

引用次数: 0

Gaussian mixture Taylor approximations of risk measures constrained by PDEs with Gaussian random field inputs 受高斯随机场输入 PDE 约束的风险度量的高斯混合泰勒近似值

arXiv - STAT - Computation Pub Date : 2024-08-13 DOI: arxiv-2408.06615

Dingcheng Luo, Joshua Chen, Peng Chen, Omar Ghattas

{"title":"Gaussian mixture Taylor approximations of risk measures constrained by PDEs with Gaussian random field inputs","authors":"Dingcheng Luo, Joshua Chen, Peng Chen, Omar Ghattas","doi":"arxiv-2408.06615","DOIUrl":"https://doi.org/arxiv-2408.06615","url":null,"abstract":"This work considers the computation of risk measures for quantities of\u0000interest governed by PDEs with Gaussian random field parameters using Taylor\u0000approximations. While efficient, Taylor approximations are local to the point\u0000of expansion, and hence may degrade in accuracy when the variances of the input\u0000parameters are large. To address this challenge, we approximate the underlying\u0000Gaussian measure by a mixture of Gaussians with reduced variance in a dominant\u0000direction of parameter space. Taylor approximations are constructed at the\u0000means of each Gaussian mixture component, which are then combined to\u0000approximate the risk measures. The formulation is presented in the setting of\u0000infinite-dimensional Gaussian random parameters for risk measures including the\u0000mean, variance, and conditional value-at-risk. We also provide detailed\u0000analysis of the approximations errors arising from two sources: the Gaussian\u0000mixture approximation and the Taylor approximations. Numerical experiments are\u0000conducted for a semilinear advection-diffusion-reaction equation with a random\u0000diffusion coefficient field and for the Helmholtz equation with a random wave\u0000speed field. For these examples, the proposed approximation strategy can\u0000achieve less than $1%$ relative error in estimating CVaR with only\u0000$mathcal{O}(10)$ state PDE solves, which is comparable to a standard Monte\u0000Carlo estimate with $mathcal{O}(10^4)$ samples, thus achieving significant\u0000reduction in computational cost. The proposed method can therefore serve as a\u0000way to rapidly and accurately estimate risk measures under limited\u0000computational budgets.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189570","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: 0

Exploring the generalizability of the optimal 0.234 acceptance rate in random-walk Metropolis and parallel tempering algorithms 探索随机漫步 Metropolis 算法和并行调节算法中 0.234 最佳接受率的通用性

arXiv - STAT - Computation Pub Date : 2024-08-13 DOI: arxiv-2408.06894

Aidan Li, Liyan Wang, Tianye Dou, Jeffrey S. Rosenthal

{"title":"Exploring the generalizability of the optimal 0.234 acceptance rate in random-walk Metropolis and parallel tempering algorithms","authors":"Aidan Li, Liyan Wang, Tianye Dou, Jeffrey S. Rosenthal","doi":"arxiv-2408.06894","DOIUrl":"https://doi.org/arxiv-2408.06894","url":null,"abstract":"For random-walk Metropolis (RWM) and parallel tempering (PT) algorithms, an\u0000asymptotic acceptance rate of around 0.234 is known to be optimal in the\u0000high-dimensional limit. Yet, the practical relevance of this value is uncertain\u0000due to the restrictive conditions underlying its derivation. We synthesise\u0000previous theoretical advances in extending the 0.234 acceptance rate to more\u0000general settings, and demonstrate the applicability and generalizability of the\u00000.234 theory for practitioners with a comprehensive empirical simulation study\u0000on a variety of examples examining how acceptance rates affect Expected Squared\u0000Jumping Distance (ESJD). Our experiments show the optimality of the 0.234\u0000acceptance rate for RWM is surprisingly robust even in lower dimensions across\u0000various proposal and multimodal target distributions which may or may not have\u0000an i.i.d. product density. Experiments on parallel tempering also show that the\u0000idealized 0.234 spacing of inverse temperatures may be approximately optimal\u0000for low dimensions and non i.i.d. product target densities, and that\u0000constructing an inverse temperature ladder with spacings given by a swap\u0000acceptance of 0.234 is a viable strategy. However, we observe the applicability\u0000of the 0.234 acceptance rate heuristic diminishes for both RWM and PT\u0000algorithms below a certain dimension which differs based on the target density,\u0000and that inhomogeneously scaled components in the target density further\u0000reduces its applicability in lower dimensions.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189568","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: 0