Model-based Supervised Numeric-Value Prediction Task

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A Model-based Supervised Numeric-Value Prediction Task is a supervised numeric-value prediction task that is a model-based supervised learning task.



References

2011

  • http://en.wikipedia.org/wiki/Linear_least_squares_%28mathematics%29#Motivational_example
    • As a result of an experiment, four [math]\displaystyle{ (x, y) }[/math] data points were obtained, [math]\displaystyle{ (1, 6), }[/math] [math]\displaystyle{ (2, 5), }[/math] [math]\displaystyle{ (3, 7), }[/math] and [math]\displaystyle{ (4, 10) }[/math] (shown in red in the picture on the right). It is desired to find a line [math]\displaystyle{ y=\beta_1+\beta_2 x }[/math] that fits "best" these four points. In other words, we would like to find the numbers [math]\displaystyle{ \beta_1 }[/math] and [math]\displaystyle{ \beta_2 }[/math] that approximately solve the overdetermined linear system [math]\displaystyle{ \begin{alignat}{3} \beta_1 + 1\beta_2 &&\; = \;&& 6 & \\ \beta_1 + 2\beta_2 &&\; = \;&& 5 & \\ \beta_1 + 3\beta_2 &&\; = \;&& 7 & \\ \beta_1 + 4\beta_2 &&\; = \;&& 10 & \\ \end{alignat} }[/math] of four equations in two unknowns in some "best" sense.

2006