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Problem

Consider a regression task of mapping inputs $X$ to outputs $y$ where $y \in [0,1]$.

Two linear models that we can use to model this input-output relationships are logistic regression $f_\theta$ and linear regression $g_\theta$:

$$f_\theta(X) = \sigma(XW_\theta+b_\theta)$$

$$g_\theta(X) = XW_\theta+b_\theta $$

With $\sigma$ being the sigmoid function.

Question

In this case is there a practical or a theoretical reason for choosing one over the other? My question arises because logistic regression is mainly used for classification, but my intuition tells me it has a good property of natively producing values between 0 and 1.

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  • $\begingroup$ Do you know observe values across the interval (e.g., $0.3$ and $0.8$ are values you can observe), or do you want to predict the probability of an event occurring? $\endgroup$
    – Dave
    Nov 15, 2023 at 4:34

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