Top-10 rejected images in the MNIST testing set found by two methods.

Top-10 rejected images in the MNIST testing set found by two methods.

We present first results from the use of XGBoost, a highly effective machine learning (ML) method, within the Bristol Betting Exchange (BBE), an open-source agent-based model (ABM) designed to simulate a contemporary sports-betting exchange with in-play betting during track-racing events such as horse races. We use the BBE ABM and its array of minimally-simple bettor-agents as a synthetic data generator which feeds into our XGBoost ML system, with the intention that XGBoost discovers profitable dynamic betting strategies by learning from the more profitable bets made by the BBE bettor-agents. After this XGBoost training, which results in one or more decision trees, a bettor-agent with a betting strategy determined by the XGBoost-learned decision tree(s) is added to the BBE ABM and made to bet on a sequence of races under various conditions and betting-market scenarios, with profitability serving as the primary metric of comparison and evaluation. Our initial findings presented here show that XGBoost trained in this way can indeed learn profitable betting strategies, and can generalise to learn strategies that outperform each of the set of strategies used for creation of the training data. To foster further research and enhancements, the complete version of our extended BBE, including the XGBoost integration, has been made freely available as an open-source release on GitHub.

In the race for artificial intelligence dominance, it is currently just a two horse race when looked at on a national level. As our chart shows, when looking at patent applications, investment, talent, research and companies in the sector, the United States and China are top of the charts when it comes to these key metrics. Between these two leaders, there are areas in which one or the other is far stronger, with China well ahead in terms of investment and financing - China accounted for 60 percent of global investment since 2013. The U.S. on the other hand is most dominant from the perspective of the number of companies operating in the field. This chart shows the countries most dominant in key areas of artificial intelligence in 2018.

In the race for artificial intelligence dominance, it is currently just a two horse race when looked at on a national level. As our chart shows, when looking at patent applications, investment, talent, research and companies in the sector, the United States and China are top of the charts when it comes to these key metrics. Between these two leaders, there are areas in which one or the other is far stronger, with China well ahead in terms of investment and financing - China accounted for 60 percent of global investment since 2013. The U.S. on the other hand is most dominant from the perspective of the number of companies operating in the field.

We deal with the \textit{selective classification} problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original $m$-class classification problem to $(m+1)$-class where the $(m+1)$-th class represents the model abstaining from making a prediction due to uncertainty. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. We show that minimizing this loss function has a natural interpretation as maximizing the return of a \textit{horse race}, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the uncertainty of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or neural architecture. Experimentally, we show that our method can identify both uncertain and outlier data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.