Using FHE one could implement a distributed storage system, with replication, conflict resolution, error correction and so on, without ever revealing the plaintext to the storage and compute provider.
If the homomorphic encryption scheme allows for arbitrary functions to be computed, it could work for particular functions of statistical model fitting (perhaps appallingly slowly).
The output model will be encoded as cyphertext.
It would be possible to evaluate the fitted cyphertext model on new features to make predictions, also output as cyphertext.
> the library can evaluate a net-list of binary gates homomorphically at a rate of about 76 gates per second per core, without decrypting its input. It suffices to provide the sequence of gates, as well as ciphertexts of the input bits. And the library computes ciphertexts of the output bits.