g=h(x)
this should depend on \theta for consistency
9 Matching Annotations
- Last 7 days
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introml.mit.edu introml.mit.edu
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the parameters will have been “picked” or “fixed” already.
why not write the test error as \mathcal{E}(h, \theta) = ... and then say for a fixed $\theta \in \Theta$ instead of burying the dependence on \theta? This is partially addressed in the note but it might make the note more intuitive. Also, \Theta is typically reserved for parameter space and \theta are instantiations of the parameters. Since we are not adopting this convention making we can introduce notation for a fixed \Theta and still incorporate it
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where Θ stands for all the parameters in our model (i.e., all possible choices over parameters).
Why not place this above where we first introduce this notation (i.e. for training error)?
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est error
why do we hide the dependence on \Theta here? I think some students could find that confusing.
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- Jan 2026
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introml.mit.edu introml.mit.edu
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To make this discussion more concrete, we need a loss function to express how unhappy we are when we guess an output g given an input x for which the desired output was a.
why not have h map to g here explicitly (h(x) = g). I think we do this a bit further down but it might be helpful and less abstract to start connecting all the notation.
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R
We could section/paragraph this as "The Regression Problem"
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Real
Maybe this should be a new paragraph?
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B
For example, x^{(i)} might represent the size of a house and y^{(i)} its sale price
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A hypothesis h is employed as a model for solving the regression problem, in that it maps inputs x to outputs y,
I think the original sentence could be vague for some readers. We could improve clarity by framing it more concretely. For example: “A hypothesis h is a model, represented mathematically as a function h: R^d -> R. It maps an input vector x to a predicted output h(x), which we hope closely matches an observed or future output y.” This wording makes the mapping x↦h(x) explicit and states the goal of matching the true outputs.
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