Semiparametric learning in signal processing, communication systems and pattern recognition

学习是从具体的例子（训练数据）转移到可以解释和预测底层过程的模型的过程。 从形式上讲，学习是从训练数据中恢复从输入信号到输出信号的映射的问题。从数据中学习的映射的准确性取决于过程的先验知识。完全非参数学习方法不需要任何先验信息，因此是鲁棒的，并且不会遭受错误指定的风险。另一方面，它们表现出缓慢的学习速率，这随着底层对象的维度而显著恶化，例如，图像.相比之下，经典的参数学习算法具有很大的错误指定风险，但如果它们被正确指定，它们将享受快速的学习速度，而不会因多变量数据而恶化。这两个基本的学习方案已经在不同的领域找到了许多应用，如：医疗诊断，数据挖掘，定性经济学，通信工程，语音和模式识别。在实践中，数据的维数和稀疏性迫使我们接受介于参数和完全非参数情况之间的中间模型（半参数模型）。模型的参数部分定义了多元非线性的有限维投影的参数，而非线性特征贯穿于单变量函数的非参数类。这种半参数模型允许设计实用的学习算法，其共享参数建模的效率，同时保留非参数情况的高灵活性，即，我们希望两全其美。事实上，在半参数模型中，维数灾难可以完全消除。这项研究的目的是双重的。首先，我们建议检查理论的进步，数值实现，并在上述半参数框架内测试特定学习方案的准确性。其次，我们打算将这种方法应用于传统人工智能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。

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.