Differential Model Inference with Imperfect Information

不完全信息的微分模型推理

• 批准号: 2592959
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2592959
• 关键词: Differential; Model; Inference; Imperfect; Information

Density Ratio estimation (DRE) is the practice of estimating the ratio between two probability density functions (PDFs). DRE's ability to characterise the relationship between two PDFs naturally lends itself to many applications such as outlier detection, Generative Adversarial Networks (GANs) , and general binary classification. Furthermore, DRE is a technique which can be applied to the EPSRC research area of Natural Language Processing. In our research we aim to adapt various DRE methods, and downstream applications of these methods, to be robust when working with imperfect data. Imperfect data itself can take many forms such as missing data, corrupted data, and even adversarial data each of which need to be taken into careful consideration when trying to adapt DRE approaches. Imperfect data is a key issue within DRE as "few key points" can have a large impact on estimates making DRE very sensitive to any irregularities within the data. While there is a vast number of DRE approaches, very few of them explicitly account for the any case of imperfect data. Some work has been done regarding the impact of missing data on DRE, however this work exclusively focuses on the case of uniform missing patterns. There are many applications in which such an assumption is unrealistic and the probability of an observation being missing depends in some way in the value of the observation itself. For example, many measuring instruments are more likely to err when when attempting to measure more extreme values, while in questionnaires, participants are less likely to answer a question if they deem their answer to be embarrassing or unfavourable. Both of these examples lead to non-uniform missing patterns within the data. In such a case, naive implementation of a complete case approach with any DRE procedure can lead to estimating a different density ratio to our true density ratio and thus give inconsistent estimations. Our initial aim is therefore to adapt DRE procedures to this scenario of non-uniform missing data. When doing so there are multiple considerations An additional aim of the PhD will be to adapt downstream applications of DRE to the case of imperfect data. One of these applications we are looking to adapt is Neyman-Pearson (NP) classification. Neyman-Pearson (NP) classification is an application of DRE in which one wants to create a classification procedure which strictly controls miss-classification for one class. A potential application of NP classification is for use in disease diagnosis. Within this setting, falsely classifying a diseased individual as healthy could be far more damaging than classifying an individual who is healthy as diseased. As such we would like to construct a procedure for classifying individuals which has a strict control on the probability of miss-classifying a healthy individual as diseased. While major NP classification procedures leverage DRE, there is still opportunity for imperfect data to impact the procedure outside of the DRE. Therefore, we aim to address this and make the entirety of the NP classification procedure robust to non-uniform missing data. Again we will look to expand this to multi-dimensional settings. Another way we intend to extend this work is to look into cases where the missingness structure is in some way unknown. In this case we will explore how this missingness structure can be first learned before we perform our adapted DRE procedure or any downstream applications.

密度比估计(DRE)是估计两个概率密度函数(PDF)之间的比率的实践。DRE描述两个PDF之间的关系的能力自然适用于许多应用，例如孤立点检测、生成性对手网络(GANS)和一般二进制分类。DRE是一种可以应用于EPSRC自然语言处理研究领域的技术。在我们的研究中，我们的目标是适应各种DRE方法，以及这些方法的下游应用，以使其在处理不完美数据时具有健壮性。不完美的数据本身可以采取多种形式，例如丢失数据、损坏的数据，甚至是敌对数据，在尝试采用DRE方法时，需要仔细考虑每一种形式。不完美的数据是DRE中的一个关键问题，因为“几个关键点”可能会对估计产生很大影响，使DRE对数据中的任何违规非常敏感。虽然有大量的DRE方法，但很少有方法明确地解释任何不完美数据的情况。关于缺失数据对DRE的影响已经做了一些工作，但本工作主要集中在均匀缺失模式的情况。在许多应用中，这样的假设是不现实的，观测丢失的概率在某种程度上取决于观测本身的价值。例如，许多测量仪器在试图测量更极端的值时更有可能出错，而在问卷调查中，如果参与者认为自己的答案令人尴尬或不利，他们回答问题的可能性就会降低。这两个例子都会导致数据中不一致的缺失模式。在这种情况下，用任何DRE程序天真地实施完整的案例方法可能会导致估计出与我们真实密度比不同的密度比，从而给出不一致的估计。因此，我们的初始目标是使DRE过程适应这种非均匀丢失数据的情况。在这样做时，有多方面的考虑，PHD的另一个目标将是使DRE的下游应用适应不完美数据的情况。我们正在寻求适应的这些应用之一是Neyman-Pearson(NP)分类。Neyman-Pearson(NP)分类是DRE的一种应用，在DRE中，人们想要创建一个严格控制某一类的漏分的分类过程。NP分类的一个潜在应用是用于疾病诊断。在这种情况下，错误地将一个患病的人归类为健康的人，可能比将一个健康的人归类为患病的人的破坏性要大得多。因此，我们希望建立一个个人分类程序，严格控制遗漏的可能性--将健康的个人归类为疾病。虽然主要的NP分类程序利用DRE，但不完美的数据仍有可能影响DRE以外的程序。因此，我们的目标是解决这个问题，并使整个NP分类过程对非均匀缺失数据具有健壮性。同样，我们将寻求将其扩展到多维设置。我们打算扩展这项工作的另一种方式是调查缺失结构在某种程度上未知的情况。在这种情况下，我们将探索如何在执行调整后的DRE程序或任何下游应用之前首先学习这种失配结构。