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Activity Number:
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413
- Section on Statistics in Sports Cpapers
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Type:
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Contributed
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Date/Time:
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Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistics in Sports
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Abstract #330026
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Presentation
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Title:
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Removing Absorbing States from Markov Chain Models
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Author(s):
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Li-Hsuan Huang* and Harish S. Bhat and Sebastian Rodriguez
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Companies:
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and University of California, Merced and Northwestern University
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Keywords:
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Markov chains;
equilibrium distribution;
time series;
optimization;
linear programming ;
basketball
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Abstract:
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Suppose we have data consisting of repeated discrete-state time series. When the length of these series is smaller than the dimension of the state space, maximum likelihood estimation (MLE) often produces absorbing states. In this case, the estimated Markov chain's equilibrium distribution assigns zero probability to all non-absorbing states. We seek the sparsest perturbation to the MLE that yields a Markov chain whose equilibrium is the empirical fraction of time spent in each state. We formulate and solve this problem using linear programming. We apply this method to continuous-time Markov chain models for NBA games, where each 5-man unit is a state and the model tracks how long each unit plays on the court. Using the linear programming method, we produce models with nearly zero training error and test error that is significantly less than that of simple MLE models.
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Authors who are presenting talks have a * after their name.
