check_fit2d_1sample and check_fit2d_1feature are part of the check_estimator test suite.

To pass those checks, the estimator either has to run gracefully, or raise ValueError with an error message containing some predefined substrings:

msgs = ["1 sample", "n_samples = 1", "n_samples=1", "one sample", "1 class", "one class"]

and

msgs = ["1 feature(s)", "n_features = 1", "n_features=1"]

This is quite restrictive. For example:

I have a custom estimator that does early stopping and X is split into train and validation data with train_test_split.

Passing only 1 sample (as in check_fit2d_1sample) to train_test_split will cause the train data to be empty. Of course an exception should be raised. But the appropriate message here is something along the lines of:
"Not enough training data to perform early stopping. Use more training data or adjust 'test_size'".

There are many ways to get an empty train data from train_test_split, passing only one training sample is just one of them. Another way would be to set the test_size param to e.g. .99 when n_samples < 100.

Using one of the required substrings would not make sense here.

So if I want to pass estimator_checks I'm bound to have a very specific check in my code that checks when n_samples==1 and raises a message with one of the appropriate substrings. I guess in my case I could add something like "got n_samples={n_samples}" to the message. But I'm still not sure if forcing a given substring makes sense in all situations.

TLDR: the reason the estimator fails in the context of those checks may be much more general than just because we passed 1 sample (or 1 feature). To pass the tests though, the error message is restricted to a very small subset of causes.

Happy to submit a PR.