Farzana Yusuf

Sam Ganzfried, Farzana Yusuf

A problem faced by many instructors is that of designing exams that accurately assess the abilities of the students. Typically these exams are prepared several days in advance, and generic question scores are used based on rough approximation of the question difficulty and length. For example, for a recent class taught by the author, there were 30 multiple choice questions worth 3 points, 15 true/false with explanation questions worth 4 points, and 5 analytical exercises worth 10 points. We describe a novel framework where algorithms from machine learning are used to modify the exam question weights in order to optimize the exam scores, using the overall class grade as a proxy for a student's true ability. We show that significant error reduction can be obtained by our approach over standard weighting schemes, and we make several new observations regarding the properties of the "good" and "bad" exam questions that can have impact on the design of improved future evaluation methods.

Sam Ganzfried, Farzana Yusuf

Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In many situations, we would like to compute strategies that can actually be implemented by humans, who may have computational limitations and may only be able to remember a small number of features or components of the strategies that have been computed. We study poker games where private information distributions can be arbitrary. We create a large training set of game instances and solutions, by randomly selecting the information probabilities, and present algorithms that learn from the training instances in order to perform well in games with unseen information distributions. We are able to conclude several new fundamental rules about poker strategy that can be easily implemented by humans.

Sam Ganzfried, Farzana Yusuf

In many settings people must give numerical scores to entities from a small discrete set. For instance, rating physical attractiveness from 1--5 on dating sites, or papers from 1--10 for conference reviewing. We study the problem of understanding when using a different number of options is optimal. We consider the case when scores are uniform random and Gaussian. We study computationally when using 2, 3, 4, 5, and 10 options out of a total of 100 is optimal in these models (though our theoretical analysis is for a more general setting with $k$ choices from $n$ total options as well as a continuous underlying space). One may expect that using more options would always improve performance in this model, but we show that this is not necessarily the case, and that using fewer choices---even just two---can surprisingly be optimal in certain situations. While in theory for this setting it would be optimal to use all 100 options, in practice this is prohibitive, and it is preferable to utilize a smaller number of options due to humans' limited computational resources. Our results could have many potential applications, as settings requiring entities to be ranked by humans are ubiquitous. There could also be applications to other fields such as signal or image processing where input values from a large set must be mapped to output values in a smaller set.