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Not quite sure if this is what your question actually is. However, when you have a data generating process such as $y = 3 + 2x$ (with some zero-mean "gaussian noise"), your model could look like: $$y = \beta_0 + \beta_1 x + u,$$ and you will find the $\beta_0 = 3$ and $\beta_1 = 2$. When you have a data generating process such as $y=3+2x+3x^2$ you ...

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It is quite simple to understand (and to implement using matrices). Consider a specific example (to generalise later). You have a polynomial function of a single feature $x$): $$f(x) = \omega_0 x^0 + \omega_1 x^1 + \ldots \omega_n x^n$$ You can organise coefficients and features in vectors and get $f$ by a scalar product:  \mathbf{\omega} = \begin{...

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There are two ways to do that: Scale your output data from [0, 2] to [0, 1] and apply Sigmoid activation at the end. Make your own custom activation function that output everything in [0, 2] I strongly suggest you no. 1, it's way faster to implement.

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Yes - it is $d\times l$. There would be 6 $β$ coefficients for 2*3: $β_1x_1 + β_2x_1^2 + β_3x_2 + β_4x_2^2 + β_5x_3 + β_6x_3^2$ That does not include an intercept or any interaction terms.

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Any machine learning algorithm could possibly learn a solution once the problem properly defined. One technique that could aid in learning is to bin the locations. Instead of predicting a specific x and y (and being precisely wrong), predict a more general region. Based on the topological structure of the location, bin similar location points together. One ...

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