How can I solve a classification problem where the label for the same input is probabilistic?

Question

In the usual classification problems, the label for the same input is usually the same. For example, if I have an image of a dog, then the true label for that exact input is dog every time.

However, for my dataset, the label for the same (or very similar) input is probabilistic, i.e. if I have the same input (or very similar inputs), the label follow a statistical distribution, e.g. 60% of the time it is a dog, 40% of the time it is a cat

How should I solve such a machine learning task?

Example: given a sequence of stock prices p[t-T:t], if you buy at time t, the chance that you will make 2% profit in 1 hour is 60%, and 40% otherwise.

Answer 1

Usually you use cross entropy loss for classification, and you can use class probabilities as the label instead of hard labels.

https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html