I’m new to ML and I’m doing the Unsupervised Learning course Week 1, where in Anomaly Detection we have to do the density estimation of product of random variables. I’m not aware of the mathematic behind how it happens and also why the correlation of the variables not included, because most of the real-world data has correlated variables. Can we use chi-square approximation to do the Anomaly detection?

We assume that the features (RVs) are independent for simplicity, then we can model the joint probability as the product of individual probs. This may not model real-world scenarios but it’s a practical simplification that works well in most of the cases.

I think Chi-square is used in cases where we have a theoretical distribution to compare against, rather than density estimation directly.

Hope it helps! Feel free to ask if you need further assitance.