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   Huang, Xiang; Lutz, Jack H.; Migunov, Andrei N. (September 2019, 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton))
2. Entropy Rate Estimation for Markov Chains with Continuous Distributions

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   Gotovos, Alkis; Burkholz, Rebekka; Quackenbush, John; Jegelka, Stefanie (December 2021, Advances in neural information processing systems)

   Modeling the time evolution of discrete sets of items (e.g., genetic mutations) is a fundamental problem in many biomedical applications. We approach this problem through the lens of continuous-time Markov chains, and show that the resulting learning task is generally underspecified in the usual setting of cross-sectional data. We explore a perhaps surprising remedy: including a number of additional independent items can help determine time order, and hence resolve underspecification. This is in sharp contrast to the common practice of limiting the analysis to a small subset of relevant items, which is followed largely due to poor scaling of existing methods. To put our theoretical insight into practice, we develop an approximate likelihood maximization method for learning continuous-time Markov chains, which can scale to hundreds of items and is orders of magnitude faster than previous methods. We demonstrate the effectiveness of our approach on synthetic and real cancer data. 

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4. Scaling up Continuous-Time Markov Chains Helps Resolve Underspecification

   Gotovos, Alkis; Burkholz, Rebekka; Quackenbush, John; Jegelka, Stefanie (January 2021, 35th Conference on Neural Information Processing Systems (NeurIPS 2021))
5. Predictive Modeling and Analysis of Hockey Using Markov Chains

   Campos-Chavez, Harvey; deBolt, Will; Mena, Miles; Prince, Jacob; Alramahi, Alia; Dudzinski, Robert; Thrawl, Soren; DeLegge, Anthony; Harsy, Amanda (January 2022, Mathematics and Sports)

   The fast-paced, volatile nature of hockey makes it a challenging sport to analyze and predict the final outcome. This paper presents two continuous-time Markov process models that predict the probability that a team will win a hockey game given particular states during the game. These states incorporate shot and goal differential relative to the opposing team and are used to approximate the probability that the home team would win depending on the state they are currently 

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