Using unsupervised learning anomoly detection to detect fraud? How can I ensure that the detected class will correspond to fraud rather than another outcome, given that this is an unsupervised learning approach? To my understanding, such algorithms (e.g., Isolation Forest) work by learning the joint probability distribution of the covariates/input variables, then flags observations that deviate greatly from the mean of this distribution. So how can I ensure that anomalies will correspond to what I want to detect?
My approach to this is to use PCA to obtain the vectors that maximize the variance of the input matrix, then only choose those principal components that have a high correlation to the covariates that are associated with fraud, so that observations that are detected as anomalous using these PCs will correspond to fraudulent observation.
How statistically sound is the above approach? .

You are right, unsupervised anomaly detection (UAD) methods like isolation forest "only" detect anomalies in the data, also known as outliers or isolated points. And, of course, not all isolated points correspond to the special type of anomaly you are looking for, in your case, fraud.
That's why you usually perform some kind of vetting of the output of the UAD. UAD only reduces the amount of data you have to check.
And often there is a chance of doing this vetting automatically, e.g. as in the situation you have described. If you know some fraud data and are relatively sure that other points in this direction will be fraud, too, this is an appropriate approach (the word "sound" is usually used for inference that is never wrong, so I would not use it here).
