Conditional Logistic Regression with Frailty applied to predicting horse race winners in Hong Kong.

http://www.helios.ai

Since first proposed by Bill Benter in 1994, the Conditional Logistic Regression has been an extremely popular tool for estimating the probability of horses winning a race.

I propose a new prediction process that is composed of two innovations to the common CLR model and a unique goal for parameter tuning . First, I modify the likelihood function to include a "frailty" parameter borrowed from epidemiological use of the Cox Proportional Hazards model. Secondly, I use a LASSO penalty on the likelihood, where profit is the target to be maximized. (As opposed to the much more common goal of maximizing likelihood.)

Finally, I implemented a Cyclical Coordinate Descent algorithm to fit the model in high-speed parallelized code that runs on a Graphics Processing Unit (GPU), allowing me to rapidly test many tuning parameter settings.

Historical data from 3681 races in Hong Kong were collected and a 10-fold cross validation was used to find the optimal outcome. Simulated betting on a hold out set of 20% of races yielded a return on investment of 36.73%.