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Is there any method of calculating sample size for a machine learning model/problem?

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In general? No.

Take into account that the amount of data need for an ML model to achieve a certain level of performance in a task is totally dependent on the task, the specific dataset, and the model itself.

Of course, you may find studies to understand how different machine learning models behave under low-resource settings. For instance, in text classification tasks, there are studies of how a specific neural network model called BERT behaves with datasets of different sizes. This gives practitioners an idea of how much data was needed by a specific model to achieve X performance on task T, but does not set a rule or method to compute the minimum amount of data needed in general.

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As Noe mentioned, no. But you can study how much data is needed to certain algorithm converge. For example assuming that one has 10 iid normal distributed IV and the DV is a linear combination of them, how much data is some algorithm you need until convergence. With this study is possible to see if there is pattern or no.

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