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

最近有大量的工作正式模型的 机器学习，例如可能近似正确（或 PAC学习模式 这个模型是一个精确的框架， to capture捕获the notion概念of learning学习from examples例子. 最新进展 在机器学习和统计推理的范例，如 PAC模型提供了关于 在一个完整的函数近似所需的数据 非参数设置 这些范例的适用性是 由于对数据收集机制和 性能标准。 其中一些假设将被放宽 让延伸学习模式应用于 如信号/图像处理和几何重建。 的 方法是对函数类进行温和的假设， 从而允许在采样和误差标准方面具有更大的灵活性。 具体来说，所提出的扩展是允许确定性的 抽样策略、非紧域上的抽样和学习 关于一般性能标准。 扩展模型 将应用于信号处理中的各种问题， 提供信息复杂度结果的几何重构 一些经典的和新的重建/估计问题。 在 信号处理领域，该框架将应用于 处理层析成像图像重建的问题， 多分辨率信号处理和经典采样定理。 在几何重建领域， 几何和形状形成探测问题。 该办法将 提供关于基本能力和局限性的结果 重建以及样本大小界限，这些 应用.

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.