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Imagine you have to create a model to explain to stakeholders e.g. to predict price, weight, sales etc.. Which regression models offer the best in terms of explainability and interprability? ... Which model is best for this?

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I think linear (through model's coefficients/weights) and tree-based models (gain importance) are the best for explainability.

But this is not restricted to those models since you can use model agnostic techniques to explain any model, even those considered as "black-box."

Like:

  1. SHAP Values
  2. Partial Dependence plot
  3. LIME

You can check this good resource to learn more.

You cannot forget that an essential part of model explainability is model performance. It does not make sense to have an easily explainable model but with a deficient performance since those structures found by the model do not generalise well. So a suitable model version will lead you to the "correct" conclusions when explaining it.

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  • $\begingroup$ agreed on that, but for linear regression alot of assumptons are made about underlying data, don't you need to standarize the data and remove correlated variables etc for these models? $\endgroup$
    – Maths12
    Commented Feb 5, 2021 at 17:38
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    $\begingroup$ Every model has assumptions, in case of linear models, as you mention multicollinearity is something to take into account as it change completely the interpretation of the coefficients (This also affects PD Plots) I propose using PCA regression so that you guarantee that the is no correlation in your features $\endgroup$
    – Multivac
    Commented Feb 5, 2021 at 17:48
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For this scenario, I would vouch for symbolic regression (https://en.wikipedia.org/wiki/Symbolic_regression#:~:text=Symbolic%20Regression%20(SR)%20is%20a,starting%20point%20to%20the%20algorithm.) which allows you to evolve human interpretable mathematical equations as a population. You could then choose a single model that has the best trade-off between performance and interpretability.

There are some commercial packages available for this such as DataModeler (https://evolved-analytics.com/) which allow you to evolve populations of models and you can explore the Pareto front which gives you the models with the best trade-off between simplicity (explainability) and accuracy and you can choose which one best fits your needs. DataModeler has additional features that let you further explore models to determine variable importance, etc. that could help you explain the model to stakeholders.

There is also Eureqa (https://www.datarobot.com/nutonian/) that was recently bought out by Nutonian, but I'm less familiar with this implementation since it has been packaged into DataRobot as one of many different features.

There are some open-source implementations mentioned on the symbolic regression Wikipedia page linked previously, but I am not familiar enough to know how user-friendly those implementations are.

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