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Take Figure 1 showing point interpolation, where point L0 is being interpolated using points L2 and L1 and the distances L11, L12, L21, and L22.

Figure 1. Interpolation of point L0

Table 1. Dataframe representation for Figure 1.

Whilst the graph shows a linear interpolation example, it is just to demo the idea whilst the Target variable is a product sum of arrays (non-linear)

Target/L0 = L1_Lag_Point * L11 + L1_Lead_Point * L12 + L2_Lag_Point * L21 + L2_Lead_Point * L22

Can a Machine Learning Algorithm understand that L11 is associated ONLY with Lagging Point L1, L12 with Leading Point L1, L21 with Lagging Point L2, and L22 with Leading Point L2?!

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  • $\begingroup$ It's not clear what you want to achieve. If you have formula for your interpolation points a machine learning can learn that formula yes. But its not clear what having a ML algo would achieve here. $\endgroup$
    – Lucas Morin
    Commented Jan 25 at 12:30
  • $\begingroup$ @LucasMorin, a study on the ability of different ML algorithms to understand feature association. $\endgroup$
    – Emad Ezzeldin
    Commented Jan 25 at 12:34
  • $\begingroup$ Well that's the whole point of modern ML. However, as is, it not clear that your point are uniquely defined. $\endgroup$
    – Lucas Morin
    Commented Jan 25 at 12:42
  • $\begingroup$ In the case of this interpolation problem for instance, the question is Can a Machine Learning Algorithm understand that L11 is associated ONLY with Lagging Point L1, L12 with Leading Point L1, L21 with Lagging Point L2, and L22 with Leading Point L2?! That is a close-ended question, answered in a Yes/No manner. I understand that the general answer is yes, but for instance in case simple linear regression, the answer is no. $\endgroup$
    – Emad Ezzeldin
    Commented Jan 25 at 12:43
  • $\begingroup$ your question is not clear enough for a human to understand how is the interpolation performed. If L12 is the middle point between L1 and L2, sure, there is a closed formula and a ML algo can learn that provided you have enough exemple. If the interpolation is more complex you'll need more info. $\endgroup$
    – Lucas Morin
    Commented Jan 25 at 13:01

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Will borrow Luca Morin's answer from the comments :

"yeah some algo can't learn that and need feature engineering. And some algo can, typically NN are universal function approximators (see: en.wikipedia.org/wiki/Universal_approximation_theorem), trees too."

Almost all non-linear ML Algorithms can understand Feature Association, but they are much slower than linear ones. Thus Feature Engineering like adding interaction and high-order features with Linear Algorithms is recommended. Would recommend for scikit-learn poly = PolynomialFeatures(degree=2,interaction_only=True, include_bias=False) for adding interactive features.

Keeping in mind that whilst the graph shows a linear interpolation example, it is just to demo the idea whilst the Target variable is a product sum of arrays (non-linear), and thus a linear solution will not fit well without feature engineering mentioned in the above paragraph.

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