RIA: Extensions of Learning Models and Applications to Signal Processing and Geometric Reconstruction

RIA：学习模型及其在信号处理和几何重建中的应用的扩展

• 批准号: 9209577
• 负责人: Sanjeev Kulkarni
• 金额: $ 6万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9209577&HistoricalAwards=false
• 关键词: RIA; Extensions; Learning; Models; Applications

Recently there has been a great deal of work on formal models of machine learning such as the probably approximately correct (or PAC learning model. This model is a precise framework attempting to capture the notion of learning from examples. Recent progress in machine learning and statistical inference on paradigms such as the PAC model has provided fundamental results on the amount of data needed for function approximation in a completely nonparametric setting. The applicability of these paradigms is limited by the assumptions on the data gathering mechanisms and the performance criteria. Some of these assumptions will be relaxed to allow the extended learning paradigm to be applied to areas such as signal/image processing and geometric reconstruction. The approach is to place mild assumptions on the function classes while allowing more flexibility in the sampling and error criteria. Specifically, the extensions proposed are to allow deterministic sampling strategies, sampling over noncompact domains, and learning with respect to general performance criterion. The extended model will be applied to a variety of problems in signal processing and geometric reconstruction to provide information complexity results for some classical and new reconstruction/estimation problems. In the area of signal processing, the framework will be applied to problems dealing with tomographic image reconstruction, multiresolution signal processing, and classical sampling theorems. In the area of geometric reconstruction, applications to stochastic geometry and shape form probing problems. The approach will provide results on the fundamental capabilities and limitations of reconstruction as well as sample size bounds for these applications.

最近，在机器学习的形式模型方面已经有了大量的工作，例如可能近似正确(或PAC学习模型)。这个模型是一个精确的框架，试图抓住从例子中学习的概念。在机器学习和关于范例的统计推理方面的最新进展，例如PAC模型，已经提供了关于在完全非参数设置下的函数逼近所需的数据量的基本结果。这些范例的适用性受到对数据收集机制和业绩标准的假设的限制。其中一些假设将被放宽，以便将扩展的学习范例应用于信号/图像处理和几何重建等领域。方法是对函数类进行温和的假设，同时允许在采样和误差标准方面有更大的灵活性。具体地说，提出的扩展是允许确定性抽样策略，非紧域上的抽样，以及关于一般性能准则的学习。扩展的模型将应用于信号处理和几何重建中的各种问题，为一些经典的和新的重建/估计问题提供信息复杂性结果。在信号处理领域，该框架将应用于处理层析图像重建、多分辨率信号处理和经典采样定理的问题。在几何重建领域，随机几何和形状的应用形成了探测问题。该方法将提供关于重建的基本能力和局限性以及这些应用的样本大小界限的结果。