Hands-On Machine Learning for Algorithmic Trading

DL and manifold learning

There is an important conceptual reason why DL works is the manifold hypothesis, which we encountered in Chapter 12, Unsupervised Learning. The idea is that high-dimensional phenomena can often be represented well in lower dimensions, and if we can find this representation, then we can reduce or even avoid the challenges posed by the curse of dimensionality.

A manifold refers to a connected set of points, typically in high-dimensional space, that can be approximated well using only a much smaller number of dimensions. In other words, the lower-dimensional manifold is embedded in a higher-dimensional space. The example of a street as a one-dimensional manifold in a three-dimensional space illustrates how house numbers ...