Theory of Family of Learnings-From a Single Learning to Infinitely Many Learning-

在现有的大多数监督学习研究中，对个体学习方法的性质进行了研究，如误差反向传播学习方法或投影学习方法。然而，学习问题的本质并不能用这种个别的理论来解释。例如，误差反向传播算法只需要记忆，但它可以提供高水平的泛化能力。为了理解这种现象，重要的是要发展一种同时处理无限多个学习的学习家族理论，而不仅仅是发展一种个体学习理论。本项目首席研究员针对训练输入点固定的情况，引入了SL投影学习的概念，构建了学习家族理论。这一理论使我们能够阐明许多尚未解决的问题，例如为什么记忆学习可以产生高泛化能力。然而，当训练输入点发生变化时，例如在增量学习或主动学习的情况下，More理论不容易应用。为了扩展这一理论，使其适用于训练输入点发生变化的情况，我们在今年进行了以下研究。首先，我们严格定义了不同训练输入点的“相同学习”概念。在我们小组之前的工作中，我们实际上给出了三种不同的投影学习族的定义，并选择了SL投影学习，因为它在固定的训练输入点下是最自然的。我们从“相同学习”的角度重新审视了这个问题，并表明当训练输入点发生变化时，T投影学习比SL投影学习更有效。我们还阐明了T算子所构成的空间的结构。要讨论的另一个重要问题是渐进式主动学习，其中下一个最优输入点是根据迄今为止获得的学习结果确定的。我们也澄清了这个问题。少

In most of the existing supervised learning research, properties of individual learning methods such as the error back-propagation learning method or projection learning have been studied. However, the essence of learning problem can not be elucidated by such individual theories. For example, the error back-propagation algorithm just requires memorization, but it can provide a high level of generalization capability. In order to understand such phenomena, it is important to develop a theory of family of learnings for dealing with infinitely many learnings at the same time, rather than just developing a theory of individual learnings. The head investigator of this project introduced the concept of SL projection learning for the cases where the training input points are fixed, and constructed a theory of family of learnings. This theory enabled us to elucidate many unsolved problems such as the reason why the memorization learning can yield high generalization capability. However, the th … More eory was not easy to apply when the training input points are changing, e.g., in the cases of incremental learning or active learning.In order to extend this theory so that it is applicable to the cases where training input points change, we carried out the following research this year. First, we rigorously defined the notion of "same learning" for different training input points. In the previous work of our group, we have actually given three different definitions of the family of projection learning, and chose the SL projection learning because it is the most natural under fixed training input points. We gave a fresh look at this problem from the viewpoint of "same learning" and showed that T projection learning is more effective than SL projection learning when training input points change. We also elucidated the structure of the space which T operators form. Another important issue to be discussed is incremental active learning, where the next optimal input points are determined based on the learned results obtained so far. We also clarified this problem. Less