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Suppose I set [Smin, Smax] to be the limits of slope of a regression, are they hyperparameter? If not, what are they called?

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  • $\begingroup$ I don't see what is unclear about this. $\endgroup$ – Peter Flom Feb 27 '18 at 12:22
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Hyperparameters are much more broadly defined than @Ben's post would suggest. He's not incorrect, but I would say Smax and Smin are hyperparameters. I was taught anything you have to set for your model to work that doesn't involve the data itself is a hyperparameter that can be set to achieve different model performance.

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  • $\begingroup$ I agree. You are constraining the parameter—how is this different from a hyper-parameter $\lambda$ in lasso, for example? $\endgroup$ – user0 Feb 27 '18 at 18:35
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Hyperparameters occur in hierarchical Bayesian models; they are parameters that occur in the prior distribution for the initial parameters that occur in the sampling distribution.

If you are undertaking a Bayesian regression model then you have a choice of how you want to impose limits on the slope parameters in the regression. If you are comfortable imposing fixed bounds on the slope parameters then you could treat $S_{\text{max}}$ and $S_{\text{min}}$ as fixed values that are specified by you, in which case they would be constants. Alternatively, you could take them as unknown, in which case they would be hyperparameters with a specified prior distribution. So the short answer is: they are hyperparameters if you choose to treat them as unknown.

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