One point of confusion I still have is what a natural latent screens off information relative to the prediction capabilities of.
Let’s say one of the models “YTDA” in the ensemble knows the beginning-of-year price of each stock, and uses “average year-to-date market appreciation” as its latent., and so learning the average year-to-date market appreciation of the S&P250odd will tell it approximately everything about that latent, and learning the year-to-date appreciation of ABT will give it almost no information it knows how to use about the year-to-date appreciation of AMGN.
So relative to the predictive capabilities of the YTDA model, I think it is true that “average year-to-date market appreciation” is a natural latent.
However, another model “YTDAPS” in the ensemble might use “per-sector average year-to-date market appreciation” as its latent. Since both the S&P250even and S&P250odd contain plenty of stocks in each sector, it is again the case that once you know the YTDAPS’ latent conditioning on S&P250odd, learning the price of ABT will not tell the YTDAPS model anything about the price of AMGN.
But then if both of these are latents, does that mean that your theorem proves that any weighted sum of natural latents is also itself a natural latent?
Nailed it, well done.
One point of confusion I still have is what a natural latent screens off information relative to the prediction capabilities of.
Let’s say one of the models “YTDA” in the ensemble knows the beginning-of-year price of each stock, and uses “average year-to-date market appreciation” as its latent., and so learning the average year-to-date market appreciation of the S&P250odd will tell it approximately everything about that latent, and learning the year-to-date appreciation of ABT will give it almost no information it knows how to use about the year-to-date appreciation of AMGN.
So relative to the predictive capabilities of the YTDA model, I think it is true that “average year-to-date market appreciation” is a natural latent.
However, another model “YTDAPS” in the ensemble might use “per-sector average year-to-date market appreciation” as its latent. Since both the S&P250even and S&P250odd contain plenty of stocks in each sector, it is again the case that once you know the YTDAPS’ latent conditioning on S&P250odd, learning the price of ABT will not tell the YTDAPS model anything about the price of AMGN.
But then if both of these are latents, does that mean that your theorem proves that any weighted sum of natural latents is also itself a natural latent?