Why does my model's output look correct pattern-wise but with a consistent offset?

Question

I'm having an issue where my AutoML model's output is having a consistent offset from the test dataset (image below). I'm wondering if anybody has any input on what could be causing this? My initial thought is that it's an elevation related issue. The predictors are from weather models and the dependent variables are from station data. The weather models have a slightly different elevation than some of the stations' recorded elevations as the models go off of a grid.

I'm using auto-sklearn and the model input can be simulated by the following simplified matrix: \begin{bmatrix}Temp_{loc1,\ time1}&Wind_{loc1,\ time1}&Temp_{loc2,\ time1}&Wind_{loc2,\ time1} \\ Temp_{loc1,\ time2}&Wind_{loc1,\ time2}&Temp_{loc2,\ time2}&Wind_{loc2,\ time2} \\ Temp_{loc1,\ time3}&Wind_{loc1,\ time3}&Temp_{loc2,\ time3}&Wind_{loc2,\ time3}\end{bmatrix}

And the output is: \begin{bmatrix}Pressure_{loc1,\ time1}&Pressure_{loc2,\ time1} \\ Pressure_{loc1,\ time2}&Pressure_{loc2,\ time2} \\ Pressure_{loc1,\ time3}&Pressure_{loc2,\ time3}\end{bmatrix}

I've tried including elevation in the predictor matrix, but it did not do anything to change the output (I'm guessing because it's a constant?) I'm just curious if anyone has any suggestions, or sees something I don't? Ideally I'd like to solve this problem before the output happens as I don't want to do a post-process downscale method to adjust the output.

Answer 1

Given the relationship between temperature, pressure and volume, your theory about elevation differences might be valid. Altitude of course affects those measurements.

Scaling

Are you scaling your inputs to be between [0, 1]? If you do so using the sklearn StandardScaler (or equivalent scale function), you will keep the distribution of your data, but at least the scale is then brought into the same range for all your data.

You apply the transformation to the predictions to move them back into the target range (see linked documentation above).

Simplification

Perhaps you could first train a model only on ${\{Temp,Wind,Pressure\}}_{loc1}$ data first, to rule effects between the two locations.

Visualisation

If the above don't help, I would suggest plotting some of the input data to see if there are clear correlations or consistent differences that might affect your model. You can then try to account for these somehow (scaling, subtracting them, etc).

I don't know which class of model you are using (not familiar with auto-sklearn model selection), but you might consider using a model such as a neural network that would likely learn to compensate for the bias you are seeing.