I want to know analytical machine learning methods (the more innovative, the better!) to calculate contributions of sectors (ex. financials, consumer staples, industirals indices) to the market (ex. s&p index).
In other words, I want to answer this question: which sector had the biggest return and risk contribution to the market from t = t1 to t= t2? What percentage of total return and risk is coming from the TMT sector from t = t1 to t = t2?
Performing simple multiple regression is one way, but what are other advanced/innovative ways which make use of machine learnings?