Reproducing kernel Hilbert spaces
Reproducing kernel Hilbert spaces
复制标题
DOI：
10.1017/9781108627771.012
复制
发表时间：
2019-02
期刊：
影响因子：
--
通讯作者：
L. Rosasco
中科院分区：
文献类型：
--
作者：
L. Rosasco
在前两节课中，我们讨论了学习问题和统计推断之间的联系。然而，与传统统计学不同的是，我们学习的主要目标是预测未来，而不是描述手头的数据。我们通常在更高维度的空间中拥有更小的数据样本，所以我们不能盲目地选择一个模型并假设它是准确的。如果模型的参数化程度太高，那么它对数据的反应就会太强烈，我们就会对数据进行过拟合，并且我们将无法学习到潜在的现象（参见图1中这种行为的一个例子）。然而，参数太少的模型甚至可能不能充分描述训练数据，并且会提供类似的糟糕性能。正则化为我们提供了一种在创建模型时取得适当平衡的方法。它需要一个（可能很大的）模型类和一种评估类中每个模型复杂性的方法。“核”的概念将为我们提供一种灵活的、计算上可行的方法来实现这个方案。
In the previous two lectures, we’ve discussed the connections of the learning problem to statistical inference. However, unlike in traditional statistics, our primary goal with learning is to predict the future rather than describe the data at hand. We also typically have a much smaller sample of data in a much higher-dimensional space, so we cannot blindly choose a model and assume it will be accurate. If the model is too highly-parameterized, it will react too strongly to the data, we will overfit the data, and we will fail to learn the underlying phenomenon (see Figure 1 for an example of this behavior). However, models with too few parameters may not even describe the training data adequately, and will provide similarly bad performance. Regularization provides us with one way to strike the appropriate balance in creating our model. It requires a (possibly large) class of models and a method for evaluating the complexity of each model in the class. The concept of “kernels” will provide us with a flexible, computationally feasible method for implementing this scheme.