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I'm a newbie at data science and I want to ask how can I predict a set of coordinates from a set of input coordinates? That is (x1, y1) -> (x2, y2).

To give a bit of context, I am developing an eye tracker and I trying to map the coordinates of my eye to the coordinates of my gaze. My current implementation uses 2 linear regression models, 1 to predict x values and 1 to predict y values, but I am wondering if it is possible to directly predict both x and y values with 1 model.

Would appreciate any help! Thanks!

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Using 2 different models for X and Y is not a good idea, since you are missing the correlation between the two. You are predicting new X coordinates based on old X coordinates and new Y coordinates based on old Y coordinates. What you want to do is predict new (x,y) based on old (x,y). So your intuition is correct that you should use one model and it is possible. What I would recommend is using a Kalman filter - you can read more about it here and an example implementation is found here.

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    $\begingroup$ Hi @Nemo_the_scientist, correct me if I'm wrong, but a Kalman filter estimates the current state based on the previous, for example, estimating the coordinates and/or velocity of a car based on the previous measured coordinates/velocity. In this case, I want to measure the gaze coordinates based on the eye coordinates. If I were to use a Kalman Filter, wouldn't I be using previously measured gaze coordinates to estimate the gaze coordinates? How would I then map the eye coordinates to the gaze coordinates? $\endgroup$
    – tayron.vikranth
    Jan 4, 2023 at 14:27
  • $\begingroup$ Yes, I believe you are right. In this case, you can use a multi-output regression algorithm, instead of the two models. I think that this tutorial might be of help. $\endgroup$
    – Nemo_the_scientist
    Jan 5, 2023 at 7:19

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