Machine Learning Methods with Time Series Dependence

We introduce the PrAGMaTiSt: Prediction and Analysis for Generalized Markov Time Series of States, a methodology which enhances classification algorithms so that they can accommodate sequential data. The PrAGMaTiSt can model a wide variety of time series structures including arbitrary order Markov chains, generalized and transition dependent generalized Markov chains, and variable length Markov chains. We subject our method as well as competitor methods to a rigorous set of simulations in order to understand its properties. We find, for very low or high levels of noise in $Y_t|X_t$, complexity of $Y_t|X_t$, or complexity of the time series structure, simple methods that either ignore the time series structure or model it as first order Markov can perform as well or better than more complicated models even when the latter are true; however, in moderate settings, the more complicated models tend to dominate. Furthermore, even with little training data, the more complicated models perform about as well as the simple ones when the latter are true. We also apply the PrAGMaTiSt to the important problem of sleep scoring of mice based on video data. Our procedure provides more accurate differentiation of the NREM and REM sleep states compared to any previous method in the field. The improvements in REM classification are particularly beneficial, as the dynamics of REM sleep are of special interest to sleep scientists. Furthermore, our procedure provides substantial improvements in capturing the sleep state bout duration distributions relative to other methods.