Semiparametric learning in signal processing, communication systems and pattern recognition

信号处理、通信系统和模式识别中的半参数学习

• 批准号: 8131-2007
• 负责人: Pawlak, Miroslaw
• 金额: $ 2.7万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=420545
• 关键词: Semiparametric; learning; signal; processing; communication; Semiparametric; learning; signal; processing; communication

Learning is the process of moving from concrete examples (training data) to models that can explain and predict the underlying process. Formally learning is the problem of recovering (from the training data) a mapping from input signals to output ones. The accuracy of the mapping to be learned from the data depends on the a priori knowledge of the process. Fully nonparametric learning methods do not need any a priori information and therefore are robust and do not suffer from risk of misspecification. On the other hand they exhibit slow learning rate, which deteriorates considerably with the dimensionality of the underlying objects, e.g., images. In contrast, classical parametric learning algorithms carries a great risk of misspecification, but if they are correctly specified they will enjoy fast learning rates with no deterioration caused by multivariate data. These two basic learning schemes have found numerous applications in such diverse areas as: medical diagnostics, data mining, qualitative economics, communication engineering, speech and pattern recognition. In practice, the dimensionality and sparseness of data force us to accept an intermediate model (semiparametric model) which lies between parametric and fully nonparametric cases. The parametric part of the model defines parameters of finite-dimensional projections of multivariate nonlinearities, whereas nonlinear characteristics run through a nonparametric class of univariate functions. This semiparametric model allows one to design practical learning algorithms which share the efficiency of parametric modeling while preserving the high flexibility of the nonparametric case, i.e., we wish to take the best of both worlds. In fact, in semiparametric models the curse of dimensionality can be entirely eliminated. The purpose of this research is twofold. First we propose to examine theoretical advancements, numerical implementations, and testing the accuracy of specific learning schemes within the aforementioned semiparametric framework. Second, we intend to apply this methodology to concrete cases beyond the traditional AI field such as: signal processing, communication systems, pattern recognition , and image analysis.

学习是从具体示例（培训数据）转变为可以解释和预测基础过程的模型的过程。 正式学习是（从培训数据中）从输入信号到输出信号的映射的问题。从数据中学到的映射的准确性取决于该过程的先验知识。完全非参数学习方法不需要任何先验信息，因此很健壮，并且不会遭受指定的风险。另一方面，它们表现出缓慢的学习率，这会随着基础物体的维度（例如图像）的维度大大恶化。相比之下，经典的参数学习算法具有错误指定的很大风险，但是如果正确指定了它们，他们将享受快速学习率，而不会导致多变量数据引起的恶化。这两个基本的学习方案在不同领域发现了许多应用：医学诊断，数据挖掘，定性经济学，通信工程，语音和模式识别。实际上，数据的维度和稀疏性迫使我们接受参数和完全非参数案例之间的中间模型（半参数模型）。该模型的参数部分定义了多元非线性的有限维投影的参数，而非线性特征则通过非参数类单变量函数运行。这种半参数模型允许设计实用的学习算法，这些算法具有参数建模的效率，同时保留非参数案例的高灵活性，即我们希望尽可能地利用这两个世界。实际上，在半参数模型中，可以完全消除维度的诅咒。这项研究的目的是双重的。首先，我们建议研究理论的进步，数值实现，并测试上述半参数框架内特定学习方案的准确性。其次，我们打算将此方法应用于传统AI领域以外的具体案例，例如：信号处理，通信系统，模式识别和图像分析。