What is the best way to ensure your machine learning models are statistically valid?

Differences between Verification and Validation? Verification?is the process of checking that a software achieves its goal without any bugs. It is the process to ensure whether the product that is developed is right or not. It verifies whether the developed product fulfills the requirements that we have. Verification is static testing.? Verification means?Are we building the product right?? Validation?is the process of checking whether the software product is up to the mark or in other words product has high level requirements. It is the process of checking the validation of product i.e. it checks what we are developing is the right product. it is validation of actual and expected product. Validation is the dynamic testing.?

The best way to ensure statistical validity in machine learning models is through robust data preprocessing, appropriate feature selection, cross-validation, and careful evaluation metrics selection. Regular validation on independent datasets and addressing issues like overfitting are also crucial for maintaining model integrity.

Metric curation is an art, a very subjective one. Even in the most obvious seeming conditions. For instance, MSE has a statistical and an algebraic root for optimizing for certain things with assumptions, but even that does not translate into real world objectives. So, whatever metric you choose, please remind yourself, it is very likely that it is not the best objective function you have chosen.

One needs to understand that choice of validation strategy, metrics and sets are always statistically arbitrary. There is no correct answer. Therefore, one needs to understand fundamentals of statistics and hypothesis evaluation thoroughly to propose his/her ideas. Cox's claim on "all models are wrong, some are useful" is also valid for this aspect as many of other statistical concepts.

It is important to understand cross validation from a pure statistical perspective, regarding the sampling formulations, bootstrapping etc. Try to infer probablities and confidence intervals at least while you are learning at first step.

Implement k-fold cross-validation (e.g., 5-fold or 10-fold) to assess the model's performance across different subsets of the data. This helps identify potential overfitting.

In practice you will need to challenge the arbitrary choices for the test metric thresholds for the tests like shapiro etc. Based on your use case and the context, you may accept normality for a feature for a value above the rule of thumb threshold, whilst for another specific case you may need to reconsider even the test yields a recommended metric.

The ultimate question is will you go "quantile regression" or "conformalized regression". Now, you don't have to choose as Stanford researchers have developed the "Conformal Quantile Regression".

Most models that modern data scientists deploy are based on simple regression when you look under the hood. As a result, in my experience, it's wise to pair a complex model (e.g. XGBoost) with a simple linear/logistic regression to see where the models agree and disagree in terms of feature importance and accuracy. If the models generally agree, you're probably safe to simply choose the most accurate model. However, if you find disagreement in the models, dig a little deeper to find out why. Are there assumptions in the models that are being violated? Are your data high fidelity? Are there third factors contributing to your model that you haven't explicitly included? Etc.

Again this seems a very ambiguous topic, what part of machine learning modeling is not statistical modeling? May I ask what is the best way to ensure your Statistical model is statistically valid? And then what is the definition of Statistical validity? A room full of ten statisticians can have ten different models/opinions on a specific topic some of which may or may not match in approach, but that doesn't necessarily mean some of those are invalid.

Subject matter experts might be required for several ML models, but the training set, test set, and cross validation should take you a long way!

Copulas are awesome statistical tools to convert multiple conditions on dependent variables to yield a single probability of meeting them. So, it makes them useful to define single metrics out of dependent variables.