  We introduce LAMP: the Linear Additive Markov Process. Transitions in LAMP
may be influenced by states visited in the distant history of the process, but
unlike higher-order Markov processes, LAMP retains an efficient
parametrization. LAMP also allows the specific dependence on history to be
learned efficiently from data. We characterize some theoretical properties of
LAMP, including its steady-state and mixing time. We then give an algorithm
based on alternating minimization to learn LAMP models from data. Finally, we
perform a series of real-world experiments to show that LAMP is more powerful
than first-order Markov processes, and even holds its own against deep
sequential models (LSTMs) with a negligible increase in parameter complexity.
