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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.

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  • $\begingroup$ Why do you have the distribution as 60/40? Is it because you observed those conditions 100 times and observed 60 instances of one category and 40 of the other? $\endgroup$
    – Dave
    Commented May 18 at 16:38

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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

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