ac米兰官方网站 用于函数逼近和优化的混合阶超网络

引用

斯文勒 K (2016)用于函数逼近和优化的混合阶超网络。哲学博士。milan米兰体育。 http://hdl.handle.net/1893/25349

摘要
Many systems take inputs, which can be measured and sometimes controlled, and outputs, which can also be measured and which depend on the inputs. Taking numerous measurements from such systems produces data, which may be used to either model the system with the goal of predicting the output associated with a given input (function approximation, or regression) or of finding the input settings required to produce a desired output (optimisation, or search). Approximating or optimising a function is central to the field of computational intelligence. There are many existing methods for performing regression and optimisation based on samples of data but they all have limitations. Multi layer perceptrons (MLPs) are universal approximators, but they suffer from the black box problem, which means their structure and the function they implement is opaque to the user. They also suffer from a propensity to become trapped in local minima or large plateaux in the error function during learning. A regression method with a structure that allows models to be compared, human knowledge to be extracted, optimisation searches to be guided and model complexity to be controlled is desirable. This thesis presents such as method. This thesis presents a single framework for both regression and optimisation: the mixed order hyper network (MOHN). A MOHN implements a function f:{-1,1}^n ->R 到任意精度。 MOHN 的结构使得输入变量相互作用以确定函数输出的方式变得明确，这允许人类洞察和复杂性控制，这在具有隐藏单元的神经网络中是非常困难的。显式结构表示还允许有效的算法来搜索导致所需输出的输入模式。提出了许多基于数据样本估计权重的学习规则，以及用于选择模型中包含哪些连接的启发式方法。比较了几种在 MOHN 中搜索输入并产生所需输出的方法。 实验在回归任务上将 MOHN 与 MLP 进行比较。研究发现 MOHN 可以达到与 MLP 相当的准确度水平，但受误差函数局部最小值的影响较小，并且在多个训练试验中显示出较小的方差。它也更容易从整体中解释和组合。模型与其训练数据的拟合度与独立的测试数据集的拟合度之间的权衡在 MOHN 中比在 MLP 中更容易控制。 MOHN 还与许多现有的优化方法进行了比较，包括使用分布估计算法、遗传算法和模拟退火的方法。对于从文献中选择的任务，MOHN 能够以比这些方法少得多的功能评估找到最佳解决方案。

关键字
机器学习；优化;神经网络