What is multicollinearity in machine learning validation and how can you handle it?

Multicollinearity in machine learning and statistical modelling refers to a situation where two or more predictor variables (also known as features or independent variables) in a regression model are highly correlated. This means that one predictor variable can be linearly predicted from the others with a substantial degree of accuracy, which can lead to several problems. One way to deal with this is to get the Variance Inflation Factor (VIF) for each feature, which tells us the amount of multicollinearity of each feature. A common rule of thumb is that if VIF is greater than 5 or 10, that indicates high multicollinearity. Dropping features with a VIF beyond this range can help mitigate the problems that can stem from multicollinearity.

Multicollinearity occurs when independent variables in a regression model are highly correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results. To fix multicollinearity, one can remove one of the highly correlated variables, combine them into a single variable, or use a dimensionality reduction technique such as principal component analysis to reduce the number of variables while retaining most of the information. Another way is to collect additional data under different experimental or observational conditions.

Multicollinearity can skew your models. Looking at a correlation plot of all the variables helps identify them. This can be visualized with a heatmap. Dropping highly collinear features can help avoid issues of multicollinearity.

Multicollinearity can be detected through various methods: 1) Correlation matrices to spot high correlations between predictors. (Easiest way to follow as preprocessing) 2) Variance Inflation Factor (VIF) values exceeding 10 indicate strong multicollinearity. (Regression output) 3) Eigenvalues of the correlation matrix near zero signal multicollinearity.

ALWAYS START WITH A CORRELATION MATRIX Before starting any model, understanding your variables is crucial. A simple yet effective approach is to begin with a correlation matrix of the variables. You might explore sophisticated hierarchical clustering methods, but a straightforward technique I favor for multicollinearity is ordering by the sum of the absolute values in your matrix. By ordering your correlation matrix this way, the first variables will exhibit the most multicollinearity, while the last ones will likely have the least. This method offers a solid and simple starting point for understanding your data.

In tackling multicollinearity, a comprehensive approach involves combining visual tools like the correlation matrix, heatmap, and scatter plots with numerical metrics such as the variance inflation factor (VIF) and the condition number. While visual checks provide a quick overview, the VIF quantifies the impact of multicollinearity on individual features, and the condition number assesses the data's sensitivity to errors. Integrating these methods ensures a thorough and nuanced understanding, aiding in the identification of specific features contributing to multicollinearity. This holistic strategy enhances decision-making in addressing this common challenge in statistical modeling.

SOLVING MULTICOLLINEARITY WITH LASSO In my experience with financial balance sheet analysis, I found multicollinearity among various accounting metrics that often provided overlapping signals regarding a company's ability to pay dividends—a crucial factor in equity valuation—or service its debt. To address this, I applied regularization methods, specifically Lasso Regression, where it could identify the most pertinent balance sheet metrics and ratios. They effectively managed multicollinearity while also highlighting key variables. This not only solved the multicollinearity issue but also gave insights useful for qualitative analysts that facilitated more informed decision-making processes for stakeholders that consumed the outcome.

Multicollinearity in machine learning is like interwoven threads in fabric—too entangled, and the pattern gets lost. To handle it, think like a tailor: trim excess (feature selection), weave complexity into clarity (feature extraction like PCA), or stitch in new designs (feature engineering). For instance, in real estate pricing models, removing correlated features like 'nearby schools' and 'school district quality' can make the model more interpretable and robust. The goal is a sleek, structured dataset where each feature stands out with individual significance.

Once multicollinearity has been detected in a regression model, there are a number of things that can be done to deal with it. The best approach will depend on the specific data set and the model being used. Remove one or more of the independent variables from the model, Use a different statistical method, such as ridge regression or LASSO regression, Transform the independent variables or Collect more data. It is important to note that there is no single "best" way to handle multicollinearity. The best approach will vary depending on the specific data set and the model being used. However, by using a combination of the methods described above, the researcher can effectively address potential problems with multicollinearity.

Keep in mind that multicollinearity doesn't necessarily invalidate the model's output since it affects individual model parameters but, all else equal, if the holistic metrics (F-Testing etc.) are good your model as a whole is useful for many things. Taking a page from my past econometrics books, if the model is for forecasting or a component of a larger model, you can live with multicollinearity. It the aim of the model is to test the impact of each input separately, you need to keep working until you have a model without multicollinearity.

CHECK OUT YOUR MODEL! When modeling, always check the hypotheses behind your model. Many statistical techniques require that the data used be treated for multicollinearity, while other models are more or less affected by it. Understanding the sensitivity of each model to various data problems (multicollinearity, heteroscedasticity, autocorrelation, presence of dummy variables, etc.) will make you a better modeler :)

Multicollinearity is when a feature is linearly correlated with more then one feature. Multicollinearity inflates the parameters of the features. Let's say parameters b1 and b2 are highly correlated. b1 and b2 will be volatile in nature, standard deviation will not be minimum. Parameters properties of unbiased is met but parameters should be of minimum variance is not met. So b1 and b2 will not be best linear estimator. So parameters which has high vif needs to be removed from features to meet the rule of properties of estimator.