Linear Model Diagnostics via Machine Learning Are there any approaches to checking diagnostics of statistical models, in particular linear regression, by machine learning methods? Many of the standard frequentist tests for numerical estimation of residual diagnostics are insufficient in my opinion. Therefore, I am looking for advanced methods to assess assumptions.
 A: If you wanted to test somehow the assumptions of linear regression using some method that employs machine learning, you would first need to fit the machine learning algorithm to your data. You would face the problem of assessing the fit of the machine learning algorithm to the data and you would possibly need to check the assumptions of the machine learning algorithm that was used. In machine learning we often do not check the assumptions, people often do not even state them explicitly, but it is not true that those methods do not have any assumptions -- any method does. So by employing machine learning in here, you change the problem definition from checking the assumptions of method A, to checking the assumptions of method B, to verify is assumptions of method A are met. So now two things may go wrong: you may wrongly assume that method B has "converged", or you may make wrong conclusions from the output of method B. Now instead of single test that went wrong, two things may fail! That was the first problem.
The second problem is that when fitting machine learning algorithms, you need to choose, and/or tune the hyperparameters of the model, prepare the features etc., so the result depends on your actions. You don't want to have a "test" that depends on your actions (i.e. if you believe the hypothesis is true, you tune the parameters until the test proves your hypothesis and if you don't, you stop with using default parameters and proclaim you win).
The third problem is that machine learning algorithms are not designed for hypothesis testing. They are designed for classifying, making predictions, clustering etc. They will make their predictions "at all cost", leading to problems like overfitting if something goes wrong. They are not designed for making optimal decisions, since they do not optimize anything that is related to making such decisions (unless you made a classification problem of it, but I'd still argue that it is not how you do testing). Hypothesis tests are designed for testing. Machine learning algorithm return predictions and to make any decision based on the predictions, you need to interpret them. Tests give you clear-cur criteria for this, machine learning don't, so you'd rely on more or less subjective interpretations of the results.
