How does Monte Carlo simulation for linear regression differ from quantile regression?

I have been studying research papers on machine learning and one topic that I have come across is the use of Monte Carlo simulations to make predictions on quantile regression problems. This piqued my interest and I decided to delve deeper into Monte Carlo simulations and how they are used in both linear and quantile regression.

Monte Carlo simulation is a computational technique used in machine learning to estimate uncertain outcomes and probabilities in complex systems or models. It involves using random sampling to generate a large number of possible scenarios, each with random variations, and then aggregating the results to approximate statistical measures of interest.

In the context of machine learning, Monte Carlo simulation is particularly useful in the following scenarios:

1. Uncertainty Quantification: Machine learning models make predictions based on learned patterns from data. However, the predictions are not always certain, especially in cases with limited data or noisy input. Monte Carlo simulation allows us to quantify the uncertainty in model predictions by generating multiple random samples and observing the variation in predicted outcomes.
2. Bayesian Inference: In Bayesian machine learning, the goal is to…