Estimating the Memory Order of Electrocorticography Recordings

This paper presents a data-driven method for estimating the memory order (the average length of the statistical dependence of a given sample on previous samples) of a recorded electrocorticography (ECoG) sequence. Methods: The proposed inference method is based on the relationship between the loss in predicting the next sample in a time-series and the dependence of this sample on the previous samples. Specifically, the memory order is estimated to be the number of past samples that minimize the least squares error (LSE) in predicting the next sample. To deal with the lack of an analytical model for ECoG recordings, the proposed method combines a collection of different predictors, thereby achieving LSE at least as low as the LSE achieved by each of the different predictors. Results: ECoG recordings from six patients with epilepsy were analyzed, and the empirical cumulative density functions (ECDFs) of the memory orders estimated from these recordings were generated, for rest as well as pre-ictal time intervals. For pre-ictal time intervals, the electrodes corresponding to the seizure-onset-zone were separately analyzed. The estimated ECDFs were different between patients and between different types of blocks. For all the analyzed patients, the estimated memory orders were on the order of tens of milliseconds (up to 100 ms). Significance: The proposed method facilitates the estimation of the causal associations between ECoG recordings, as these associations strongly depend on the recordings' memory. An improved estimation of causal associations can improve the performance of algorithms that use ECoG recordings to localize the epileptogenic zone. Such algorithms can aid doctors in their pre-surgical planning for the surgery of patients with epilepsy.