Probabilistic Machine Learning for Finance and Investing

Chapter 8. Making Probabilistic Decisions with Generative Ensembles

But I realized that the odds as the game progressed actually depended on which cards were still left in the deck and that the edge would shift as play continued, sometimes favoring the casino and sometimes the player.

—Dr. Edward O. Thorp, the greatest quantitative gambler and trader of all time

In the previous chapter, we designed, developed, trained, and tested a generative ensemble of linear regression lines. Probabilistic linear regression is fundamentally different from frequentist or conventional linear regression, introduced in Chapter 4. For starters, frequentist linear regression produces a single regression line with parameters optimized to fit a noisy financial dataset generated by a stochastic process that is neither stationary nor ergodic. Probabilistic linear regression generates many regression lines, each corresponding to different combinations of possible parameters, which can fit the observed data distribution with various plausibilities while remaining consistent with prior knowledge and model assumptions.

Generative ensembles have the desirable characteristics of being capable of continually learning and revising model parameters from data and explicitly stated past knowledge. What truly distinguishes generative ensembles from their conventional counterparts are their capabilities of seamlessly simulating new data and counterfactual knowledge conditioned on the observed data and model assumptions ...