arXiv - STAT - Computation最新文献

英文中文

Counting $N$ Queens 数出 N$ 皇后

arXiv - STAT - Computation

Pub Date : 2024-07-11 DOI: arxiv-2407.08830

Nick Polson, Vadim Sokolov

Gauss proposed the problem of how to enumerate the number of solutions forplacing $N$ queens on an $Ntimes N$ chess board, so no two queens attack eachother. The N-queen problem is a classic problem in combinatorics. We describe avariety of Monte Carlo (MC) methods for counting the number of solutions. Inparticular, we propose a quantile re-ordering based on the Lorenz curve of asum that is related to counting the number of solutions. We show his approachleads to an efficient polynomial-time solution. Other MC methods includevertical likelihood Monte Carlo, importance sampling, slice sampling, simulatedannealing, energy-level sampling, and nested-sampling. Sampling binary matricesthat identify the locations of the queens on the board can be done with aSwendsen-Wang style algorithm. Our Monte Carlo approach counts the number ofsolutions in polynomial time.

高斯提出了这样一个问题：如何枚举出在一个 N 次 N 元的棋盘上摆放 N 个皇后的解的个数，从而避免两个皇后互相攻击。N 皇后问题是组合数学中的一个经典问题。我们介绍了各种计算解数的蒙特卡罗（MC）方法。特别是，我们提出了一种基于洛伦兹曲线的量子重排序方法，它与计算解的数量有关。我们证明了他的方法能带来高效的多项式时间解决方案。其他 MC 方法包括理论似然蒙特卡罗、重要性采样、切片采样、模拟嵌套、能量级采样和嵌套采样。对确定棋盘上皇后位置的二进制矩阵进行采样，可采用斯文森-旺（Swendsen-Wang）式算法。我们的蒙特卡罗方法可以在多项式时间内计算出解决方案的数量。

引用次数: 0

The 2023/24 VIEWS Prediction Challenge: Predicting the Number of Fatalities in Armed Conflict, with Uncertainty 2023/24 VIEWS 预测挑战赛：在不确定情况下预测武装冲突中的死亡人数

arXiv - STAT - Computation

Pub Date : 2024-07-08 DOI: arxiv-2407.11045

Håvard HegrePeace Research Institute OsloDepartment of Peace and Conflict Research, Uppsala University, Paola VescoPeace Research Institute OsloDepartment of Peace and Conflict Research, Uppsala University, Michael ColaresiDepartment of Peace and Conflict Research, Uppsala UniversityUniversity of Pittsburgh, Jonas VestbyPeace Research Institute Oslo, Alexa TimlickPeace Research Institute Oslo, Noorain Syed KazmiPeace Research Institute Oslo, Friederike BeckerInstitute of Statistics, Marco BinettiCenter for Crisis Early Warning, University of the Bundeswehr Munich, Tobias BodentienInstitute of Statistics, Tobias BohneCenter for Crisis Early Warning, University of the Bundeswehr Munich, Patrick T. BrandtSchool of Economic, Political, and Policy Sciences, University of Texas, Dallas, Thomas ChadefauxTrinity College Dublin, Simon DrauzInstitute of Statistics, Christoph DworschakUniversity of York, Vito D'OrazioWest Virginia University, Cornelius FritzPennsylvania State University, Hannah FrankTrinity College Dublin, Kristian Skrede GleditschUniversity of EssexPeace Research Institute Oslo, Sonja HäffnerCenter for Crisis Early Warning, University of the Bundeswehr Munich, Martin HoferUniversity College London, Finn L. KlebeUniversity College London, Luca MacisDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Alexandra MalagaInstitute for Economic Analysis, Barcelona, Marius MehrlUniversity of Leeds, Nils W. MetternichUniversity College London, Daniel MittermaierCenter for Crisis Early Warning, University of the Bundeswehr Munich, David MuchlinskiGeorgia Tech, Hannes MuellerInstitute for Economic Analysis, BarcelonaBarcelona School of Economics, Christian OswaldCenter for Crisis Early Warning, University of the Bundeswehr Munich, Paola PisanoDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, David RandahlDepartment of Peace and Conflict Research, Uppsala University, Christopher RauhUniversity of Cambridge, Lotta RüterInstitute of Statistics, Thomas SchincariolTrinity College Dublin, Benjamin SeimonFundació Economia Analitica, Elena SilettiDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Marco TagliapietraDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Chandler ThornhillGeorgia Tech, Johan VegeliusDepartment of Medical Sciences, Uppsala University, Julian WalterskirchenCenter for Crisis Early Warning, University of the Bundeswehr Munich

This draft article outlines a prediction challenge where the target is toforecast the number of fatalities in armed conflicts, in the form of the UCDP`best' estimates, aggregated to the VIEWS units of analysis. It presents theformat of the contributions, the evaluation metric, and the procedures, and abrief summary of the contributions. The article serves a function analogous toa pre-analysis plan: a statement of the forecasting models made publiclyavailable before the true future prediction window commences. More informationon the challenge, and all data referred to in this document, can be found athttps://viewsforecasting.org/research/prediction-challenge-2023.

本文草案概述了一项预测挑战，其目标是以 UCDP "最佳 "估计值的形式预测武装冲突中的死亡人数，并将其汇总到 VIEWS 分析单元。文章介绍了贡献的格式、评估指标和程序，并对贡献进行了简要总结。这篇文章的作用类似于分析前计划：在真正的未来预测窗口开始之前，公布预测模型的说明。有关挑战赛的更多信息以及本文件中提到的所有数据，请访问：https://viewsforecasting.org/research/prediction-challenge-2023。

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引用次数: 0

posteriordb: Testing, Benchmarking and Developing Bayesian Inference Algorithms 后ordb：测试、基准测试和开发贝叶斯推理算法

arXiv - STAT - Computation

Pub Date : 2024-07-06 DOI: arxiv-2407.04967

Måns Magnusson, Jakob Torgander, Paul-Christian Bürkner, Lu Zhang, Bob Carpenter, Aki Vehtari

The generality and robustness of inference algorithms is critical to thesuccess of widely used probabilistic programming languages such as Stan, PyMC,Pyro, and Turing.jl. When designing a new general-purpose inference algorithm,whether it involves Monte Carlo sampling or variational approximation, thefundamental problem arises in evaluating its accuracy and efficiency across arange of representative target models. To solve this problem, we proposeposteriordb, a database of models and data sets defining target densities alongwith reference Monte Carlo draws. We further provide a guide to the bestpractices in using posteriordb for model evaluation and comparison. To providea wide range of realistic target densities, posteriordb currently comprises 120representative models and has been instrumental in developing several generalinference algorithms.

推理算法的通用性和鲁棒性是 Stan、PyMC、Pyro 和 Turing.jl 等广泛使用的概率编程语言取得成功的关键。在设计新的通用推理算法时，无论是蒙特卡罗抽样还是变分近似，最基本的问题是在一系列有代表性的目标模型中评估其准确性和效率。为了解决这个问题，我们提出了posteriordb，这是一个定义目标密度的模型和数据集数据库，并附有参考蒙特卡罗抽样。我们还提供了使用 posteriordb 进行模型评估和比较的最佳实践指南。为了提供广泛的现实目标密度，posteriordb 目前包括 120 个代表性模型，并在开发几种通用推断算法方面发挥了重要作用。

引用次数: 0

Gaussian process regression with log-linear scaling for common non-stationary kernels 普通非稳态核的对数线性缩放高斯过程回归

arXiv - STAT - Computation

Pub Date : 2024-07-04 DOI: arxiv-2407.03608

P. Michael Kielstra, Michael Lindsey

We introduce a fast algorithm for Gaussian process regression in lowdimensions, applicable to a widely-used family of non-stationary kernels. Thenon-stationarity of these kernels is induced by arbitrary spatially-varyingvertical and horizontal scales. In particular, any stationary kernel can beaccommodated as a special case, and we focus especially on the generalizationof the standard Mat'ern kernel. Our subroutine for kernel matrix-vectormultiplications scales almost optimally as $O(Nlog N)$, where $N$ is thenumber of regression points. Like the recently developed equispaced FourierGaussian process (EFGP) methodology, which is applicable only to stationarykernels, our approach exploits non-uniform fast Fourier transforms (NUFFTs). Weoffer a complete analysis controlling the approximation error of our method,and we validate the method's practical performance with numerical experiments.In particular we demonstrate improved scalability compared to tostate-of-the-art rank-structured approaches in spatial dimension $d>1$.

我们介绍了一种用于低维度高斯过程回归的快速算法，它适用于广泛使用的非稳态核系列。这些核的非稳态性是由任意空间变化的垂直和水平尺度引起的。特别是，任何静止核都可以作为特例来处理，我们尤其关注标准 Mat'ern 核的广义化。我们的核矩阵-向量乘法子程序几乎以最优方式缩放为 $O(N/log N)$，其中 $N$ 是回归点的数量。最近开发的等距傅立叶高斯过程（EFGP）方法只适用于静态核，而我们的方法则利用了非均匀快速傅立叶变换（NUFFT）。我们提供了控制我们方法近似误差的完整分析，并通过数值实验验证了该方法的实用性能，特别是在空间维度 $d>1$ 的情况下，与最先进的秩结构方法相比，我们证明了该方法具有更好的可扩展性。

引用次数: 0

Geometric statistics with subspace structure preservation for SPD matrices 为 SPD 矩阵保留子空间结构的几何统计

arXiv - STAT - Computation

Pub Date : 2024-07-02 DOI: arxiv-2407.03382

Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre

We present a geometric framework for the processing of SPD-valued data thatpreserves subspace structures and is based on the efficient computation ofextreme generalized eigenvalues. This is achieved through the use of theThompson geometry of the semidefinite cone. We explore a particular geodesicspace structure in detail and establish several properties associated with it.Finally, we review a novel inductive mean of SPD matrices based on thisgeometry.

我们提出了一个处理 SPD 值数据的几何框架，该框架保留了子空间结构，并以高效计算极端广义特征值为基础。这是通过使用半定锥的汤普森几何来实现的。我们详细探讨了一种特殊的大地空间结构，并建立了与之相关的几个属性。最后，我们回顾了基于这种几何的 SPD 矩阵的一种新颖的归纳平均值。

引用次数: 0

Scalable expectation propagation for generalized linear models 广义线性模型的可扩展期望传播

arXiv - STAT - Computation

Pub Date : 2024-07-02 DOI: arxiv-2407.02128

Niccolò Anceschi, Augusto Fasano, Beatrice Franzolini, Giovanni Rebaudo

Generalized linear models (GLMs) arguably represent the standard approach forstatistical regression beyond the Gaussian likelihood scenario. When Bayesianformulations are employed, the general absence of a tractable posteriordistribution has motivated the development of deterministic approximations,which are generally more scalable than sampling techniques. Among them,expectation propagation (EP) showed extreme accuracy, usually higher than manyvariational Bayes solutions. However, the higher computational cost of EP posedconcerns about its practical feasibility, especially in high-dimensionalsettings. We address these concerns by deriving a novel efficient formulationof EP for GLMs, whose cost scales linearly in the number of covariates p. Thisreduces the state-of-the-art O(p^2 n) per-iteration computational cost of theEP routine for GLMs to O(p n min{p,n}), with n being the sample size. We alsoshow that, for binary models and log-linear GLMs approximate predictive meanscan be obtained at no additional cost. To preserve efficient moment matchingfor count data, we propose employing a combination of log-normal Laplacetransform approximations, avoiding numerical integration. These novel resultsopen the possibility of employing EP in settings that were believed to bepractically impossible. Improvements over state-of-the-art approaches areillustrated both for simulated and real data. The efficient EP implementationis available at https://github.com/niccoloanceschi/EPglm.

广义线性模型（GLM）可以说是超越高斯似然情景的标准统计回归方法。在使用贝叶斯公式时，由于普遍缺乏可操作的后分布，因此人们开发了确定性近似方法，这种方法通常比抽样技术更具可扩展性。其中，期望传播（EP）显示出极高的准确性，通常高于许多变量贝叶斯解决方案。然而，EP 较高的计算成本使人们对其实际可行性产生了担忧，尤其是在高维环境中。为了解决这些问题，我们为 GLMs 推导了一种新的高效 EP 方案，其成本与协方差的数量 p 成线性比例，从而将 GLMs 的 EP 例程的最新 O(p^2 n) 每次迭代计算成本降至 O(p,n)，n 为样本大小。我们还证明，对于二元模型和对数线性 GLM，可以在不增加成本的情况下获得近似预测均值。为了保持计数数据的有效矩匹配，我们建议采用对数正态拉普变换近似的组合，避免数值积分。这些新颖的结果为在人们认为实际上不可能的情况下使用 EP 提供了可能性。在模拟数据和真实数据方面，与最先进的方法相比都有很大改进。高效的 EP 实现可在 https://github.com/niccoloanceschi/EPglm 上获取。

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引用次数: 0

A General Purpose Approximation to the Ferguson-Klass Algorithm for Sampling from Lévy Processes Without Gaussian Components 从无高斯成分的莱维过程采样的弗格森-克拉斯算法的通用近似值

arXiv - STAT - Computation

Pub Date : 2024-07-01 DOI: arxiv-2407.01483

Dawid Bernaciak, Jim E. Griffin

We propose a general-purpose approximation to the Ferguson-Klass algorithmfor generating samples from L'evy processes without Gaussian components. Weshow that the proposed method is more than 1000 times faster than the standardFerguson-Klass algorithm without a significant loss of precision. This methodcan open an avenue for computationally efficient and scalable Bayesiannonparametric models which go beyond conjugacy assumptions, as demonstrated inthe examples section.

我们提出了一种通用的近似弗格森-克拉斯算法，用于从没有高斯成分的 L'evy 过程中生成样本。结果表明，所提出的方法比标准的弗格森-克拉斯算法快 1000 多倍，而且精度没有明显下降。正如示例部分所展示的，这种方法可以为计算高效、可扩展的贝叶斯非参数模型开辟一条途径，这些模型超越了共轭假设。

引用次数: 0

Structured Sketching for Linear Systems 线性系统结构草图

arXiv - STAT - Computation

Pub Date : 2024-06-30 DOI: arxiv-2407.00746

Johannes J Brust, Michael A Saunders

For linear systems $Ax=b$ we develop iterative algorithms based on asketch-and-project approach. By using judicious choices for the sketch, such asthe history of residuals, we develop weighting strategies that enable shortrecursive formulas. The proposed algorithms have a low memory footprint anditeration complexity compared to regular sketch-and-project methods. In a setof numerical experiments the new methods compare well to GMRES, SYMMLQ andstate-of-the-art randomized solvers.

对于线性系统 $Ax=b$，我们开发了基于 "求取和项目 "方法的迭代算法。通过对草图（如残差的历史）的明智选择，我们开发出了加权策略，从而实现了短递归公式。与常规的草图-项目法相比，所提出的算法具有较低的内存占用和运算复杂度。在一组数值实验中，新方法与 GMRES、SYMMLQ 和最先进的随机求解器相比都有很好的效果。

引用次数: 0

Deterministic and Stochastic Frank-Wolfe Recursion on Probability Spaces 概率空间上的确定性和随机性弗兰克-沃尔夫递推

arXiv - STAT - Computation

Pub Date : 2024-06-29 DOI: arxiv-2407.00307

Di Yu, Shane G. Henderson, Raghu Pasupathy

Motivated by applications in emergency response and experimental design, weconsider smooth stochastic optimization problems over probability measuressupported on compact subsets of the Euclidean space. With the influencefunction as the variational object, we construct a deterministic Frank-Wolfe(dFW) recursion for probability spaces, made especially possible by a lemmathat identifies a ``closed-form'' solution to the infinite-dimensionalFrank-Wolfe sub-problem. Each iterate in dFW is expressed as a convexcombination of the incumbent iterate and a Dirac measure concentrating on theminimum of the influence function at the incumbent iterate. To address commonapplication contexts that have access only to Monte Carlo observations of theobjective and influence function, we construct a stochastic Frank-Wolfe (sFW)variation that generates a random sequence of probability measures constructedusing minima of increasingly accurate estimates of the influence function. Wedemonstrate that sFW's optimality gap sequence exhibits $O(k^{-1})$ iterationcomplexity almost surely and in expectation for smooth convex objectives, and$O(k^{-1/2})$ (in Frank-Wolfe gap) for smooth non-convex objectives.Furthermore, we show that an easy-to-implement fixed-step, fixed-sample versionof (sFW) exhibits exponential convergence to $varepsilon$-optimality. We endwith a central limit theorem on the observed objective values at the sequenceof generated random measures. To further intuition, we include severalillustrative examples with exact influence function calculations.

受应急响应和实验设计应用的启发，我们考虑了欧几里得空间紧凑子集上支持的概率度量的平稳随机优化问题。以影响函数作为变分对象，我们构建了概率空间的确定性弗兰克-沃尔夫（dFW）递归，特别是通过一个确定无穷维弗兰克-沃尔夫子问题的 "封闭形式 "解的定理，使之成为可能。dFW 中的每个迭代都表示为现任迭代的凸组合和集中于现任迭代处影响函数最小值的狄拉克度量。为了解决只能获得目标和影响函数的蒙特卡罗观测结果的常见应用问题，我们构建了一种随机弗兰克-沃尔夫（sFW）变量，它能生成一系列随机概率度量，这些概率度量是利用对影响函数越来越精确的估计的最小值构建的。我们证明，对于平滑凸目标，sFW 的最优性差距序列几乎肯定地在期望值上表现出 $O(k^{-1})$ 的迭代复杂性，而对于平滑非凸目标，则表现出 $O(k^{-1/2})$ 的迭代复杂性（在 Frank-Wolfe 差距中）。此外，我们还证明，一个易于实现的固定步长、固定样本版本的 (sFW) 表现出指数级收敛到 $varepsilon$ 的最优性。最后，我们提出了一个关于在生成的随机度量序列中观察到的目标值的中心极限定理。为了进一步加深直觉，我们列举了几个具有精确影响函数计算的示例。

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引用次数: 0

A note on the relationship between PDE-based precision operators and Matérn covariances 关于基于 PDE 的精确算子与马特恩协方差之间关系的说明

arXiv - STAT - Computation

Pub Date : 2024-06-29 DOI: arxiv-2407.00471

Umberto Villa, Thomas O'Leary-Roseberry

The purpose of this technical note is to summarize the relationship betweenthe marginal variance and correlation length of a Gaussian random field withMat'ern covariance and the coefficients of the correspondingpartial-differential-equation (PDE)-based precision operator.

本技术说明旨在总结具有马特协方差的高斯随机场的边际方差和相关长度与相应的基于偏微分方程（PDE）的精确算子的系数之间的关系。

引用次数: 0

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