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In the equation:


Is there a reason that $\theta$ might be a subscript of $f$ and not either a second parameter or left out of the left side of the equation altogether? Does it differ from the following?


(I've been following the Machine Learning class and the instructor uses this notation that I've not seen before)

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The notations are equivalent, but using a subscript sort of suggests that it's fixed for most of the discussion, and $x$ is the one that's changing. Leaving it out means for sure that it's fixed for the discussion (i.e., all the $f$'s you see should be taken with the same $\theta$.) – Ted Oct 5 '11 at 5:38
up vote 6 down vote accepted

As you note, this is mostly notational choice. I might call the $\theta$ a parameter, rather than an independent variable. That is to say, you are meant to think of $\theta$ as being fixed, and $x$ as varying.

As an example (though I am not sure of the context you saw this notation), maybe you are interested in describing the collection of functions $$f(x) = x^2+c$$, where $c$ is a real number. I might call this function $f_c(x)$, so that I can later say that for $c\leq 0$, the function $f_c$ has two real roots, while for $c>0$ the roots are uniformly convex. I think these statements would be much more opaque if I made them about the function $f(x,c)$.

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