How is Machine Learning in finance different from Machine Learning in other fields?
In my view, the main differences stem from differences in data. In finance, data are (very) noisy, and often non-stationary. 'Signals' cannot be split from 'noise' in any unique way, as a matter of principle. This is very different from, say, image processing, where the level of noise can be controlled, at least in principle. Also, the notion of non-stationary data is non-existent for image processing. Because of a pronounced role of noise, some machine learning models, for example non-probabilistic models, are not very useful in finance.
The other difference is the amount of data. Many interesting problems of finance are problems with small-to-medium datasets, which makes applications of data-hungry methods such as deep learning problematic. Therefore, in finance enforcing some prior knowledge is often necessary, via (depending on a method used) choices of regularization, Bayesian priors, or other general principles such as analysis of symmetries.
One more important difference is that the 'true' state space in finance is not well defined. There are so-called black swan events-things that are outside of financial models, for example political risk, that nevertheless might have severe impact on security prices. There is a difference between uncertainty and probability (risk). Most machine learning models (as well as most of classical financial models) deal with probabilistic systems with a well defined state space, they do not admit black swans. They are models of risk but not models of uncertainty.