Uncertainty in Statistical Computing

统计计算中的不确定性

• 批准号: RGPIN-2019-05115
• 负责人: Campbell, David
• 金额: $ 2.62万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=765749
• 关键词: Uncertainty; Statistical; Computing

Machine Learning methods have exploded in utility with the availability of software and graphics cards. Dealing with huge amounts of data requires approximations to statistical models, often relying on asymptotic arguments that likelihoods have decayed to near delta function shapes. The break down of traditional statistical methods for assessing models and assumptions are challenged by the size and the complexity of new data sources such as video, and text. Quantifying uncertainty from machine learning requires updating the underlying statistical models to consider the unique challenges from different data types. The overarching theme of this proposal is to advanced methods for dealing with large data sets while improving the measures of uncertainty and assessing assumptions therein. The research themes in this proposal consider i-Statistical Models for Video Data, ii-Spatial Models for Text Data, iii-Regression Models for Distributions of Covariates, and iv-Assessing Appropriateness of Model Assumptions in Machine Learning. Project i With a combined 50 years worth of video of eagle behaviour from cameras inside dozens of nests around Coastal British Columbia, the Hancock Wildlife Foundation aims to understand eagle nesting, feeding, and rearing behaviour patterns as well as the factors influencing these behaviours. This work will smooth the output from machine learning models applied to video data to improve insights. Project ii Here we intend inference on the geographic differences related to flavour characteristics of beer based on text reviews. Extensions to current Latent Dirichlet Allocation models will consider model beer style, brewery effects, and spatial variables in the topic allocations. The methods are expected to be extensible to topic model clusters for health records with physician, seasonal, long term time, and geographic effects. Project iii Functional Regression (FR) has extended the statisticians toolbox by accounting for the smooth underlying process of some time series data sets and allowing them to be modelling in a regression context. This project considers extensions to FR to the case where some or all of the variables are smooth densities. Bernstein polynomials are a natural way to estimate densities and provide uncertainty thereof while respecting properties of densities. The associated uncertainty for different individuals based on different amounts of data would also be carried through the model allowing a natural weighted least squares regression. Project iv Probabilistic integration methods are fast ways of approximately numerically integrating functions while accounting for the approximation uncertainty. In this work we propose to use the Laplace approximation as a null hypothesis and then interrogate the likelihood at a set of points so as to check if the Laplace approximation falls within the uncertainty of the integrator.

随着软件和显卡的出现，机器学习方法在实用方面取得了爆炸性的进展。处理海量数据需要对统计模型进行近似，通常依赖于概率已衰减到接近增量函数形状的渐近论点。视频和文本等新数据来源的规模和复杂性对评估模型和假设的传统统计方法的崩溃提出了挑战。量化机器学习的不确定性需要更新基础统计模型，以考虑来自不同数据类型的独特挑战。这项提案的主要主题是提出先进的方法来处理大数据集，同时改进不确定性的衡量标准并评估其中的假设。本提案中的研究主题包括：I-视频数据的统计模型，II-文本数据的空间模型，III-协变量分布的回归模型，以及IV-评估模型假设在机器学习中的适当性。项目一，汉考克野生动物基金会从不列颠哥伦比亚省海岸附近的几十个巢穴中拍摄了一段长达50年的鹰行为视频，旨在了解鹰的筑巢、觅食和饲养行为模式以及影响这些行为的因素。这项工作将平滑应用于视频数据的机器学习模型的输出，以提高洞察力。项目二在此，我们打算在文本评论的基础上推断与啤酒风味特征相关的地理差异。对当前潜在Dirichlet分配模型的扩展将在主题分配中考虑模型啤酒风格、啤酒厂效应和空间变量。这些方法有望扩展到具有医生、季节性、长期和地理影响的健康记录的主题模型簇。项目III功能回归(FR)扩展了统计学家工具箱，说明了一些时间序列数据集的平稳基本过程，并允许在回归环境中对它们进行建模。本项目考虑将FR扩展到部分或全部变量为光滑密度的情况。伯恩斯坦多项式是一种在考虑密度性质的同时估计密度并提供其不确定性的自然方法。基于不同数据量的不同个人的相关不确定性也将通过该模型进行，从而允许进行自然加权最小二乘回归。项目四：概率积分方法是在考虑近似不确定性的同时，对函数进行近似数值积分的快速方法。在这项工作中，我们建议使用拉普拉斯近似作为零假设，然后在一组点上询问似然性，以检查拉普拉斯近似是否落在积分器的不确定性之内。