Efficient bayesian inference and recycling of features in data analysis problems

数据分析问题中的高效贝叶斯推理和特征回收

• 批准号: 2671809
• 金额: --
• 依托单位: University of Bath
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2671809
• 关键词: Efficient; bayesian; inference; recycling; features

The project is in collaboration with BT where large amounts of time-series data are collected along with vast amounts of potential predictors e.g. monthly telecommunications data with location and weather. With an increasing number of data generated and stored in many fields, applying statistical analysis to these data sets gives insight on the relationships between predictors and the response of interest. However, difficulties arise in situations where too many predictors exist as model fitting and prediction become challenging in the high dimensional setting with potentially many predictors being strongly correlated. Subset selection methods provide an attractive solution to ensure the statistical model produced is interpretable by reducing the number of predictors, however the difficulty is in identifying the relevant combination of predictors which best explain the response. Furthermore, evaluating all potential models as the number of predictors increases is computationally expensive and so requires methods which can greatly reduce this cost.In addition, time-discretised data display seasonalities with complex non-linear relationships which can change over time. Therefore, it is crucial to keep track of the changes in predictors which potentially causes the changes in the relationship. This could be achieved using the Bayesian framework for parameter estimation which models uncertainty and prior beliefs about predictors as probability distributions. Additional information about predictors from observed data are then incorporated to update the distribution such that this reflects changes in parameter information. Traditional Markov Chain Monte Carlo methods used in Bayesian inference require target distributions to be known up to some proportionality however, such methods are infeasible for time dependent data due to the intractability of the likelihood function. Therefore, particle filtering methods offer numerical approximations for dynamic time series models with complex structures and intractable likelihoods. The aim of this project is to incorporate subset selection methods and appropriate particle filter Bayesian methodology for dynamic time series models. Traditional statistical models are fit by hand which is time consuming and costly so automating the process of model fitting and predictor selection should be taken into consideration. The developed method would be applied in BT with the aims to improve insight and predictive ability in comparison to the current methods used in industry. This project is relevant to EPSRC as we are developing and applying statistical methods which can improve the predictive ability and decision-making process in industrial settings. In addition, the developed method also aims to reduce the computational cost of the relevant methods that are currently used, and so falls within the mathematics and data science focus of EPSRC.

该项目与英国电信合作，收集了大量的时间序列数据沿着大量的潜在预测因素，例如每月的位置和天气电信数据。随着越来越多的数据在许多领域中生成和存储，对这些数据集进行统计分析可以深入了解预测因子与感兴趣的响应之间的关系。然而，在存在太多预测因子的情况下出现困难，因为模型拟合和预测在高维环境中变得具有挑战性，其中潜在的许多预测因子是强相关的。子集选择方法提供了一种有吸引力的解决方案，以确保通过减少预测因子的数量来解释所产生的统计模型，但是困难在于识别最能解释响应的相关预测因子组合。此外，评估所有潜在的模型作为预测因子的数量增加是计算昂贵的，因此需要的方法，可以大大降低这种cost.In此外，时间离散化的数据显示季节性与复杂的非线性关系，可以随着时间的推移而改变。因此，跟踪可能导致关系变化的预测变量的变化至关重要。这可以通过使用贝叶斯参数估计框架来实现，该框架将不确定性和关于预测因子的先验信念建模为概率分布。然后将来自观测数据的关于预测因子的附加信息并入以更新分布，使得这反映参数信息的变化。传统的马尔可夫链蒙特卡罗方法中使用的贝叶斯推理要求目标分布是已知的一些比例，然而，这种方法是不可行的时间依赖的数据，由于棘手的似然函数。因此，粒子滤波方法为具有复杂结构和难以处理的可能性的动态时间序列模型提供了数值近似。这个项目的目的是将子集选择方法和适当的粒子滤波贝叶斯方法用于动态时间序列模型。传统的统计模型是手工拟合的，这是耗时和昂贵的，因此自动化的模型拟合和预测器的选择过程中应考虑。开发的方法将应用于BT，目的是与当前工业中使用的方法相比，提高洞察力和预测能力。该项目与EPSRC相关，因为我们正在开发和应用统计方法，这些方法可以提高工业环境中的预测能力和决策过程。此外，开发的方法还旨在降低目前使用的相关方法的计算成本，因此福尔斯属于EPSRC的数学和数据科学重点。