Prediction of hierarchical time series using structured regularization and its application to artificial neural networks

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that the forecast for an upper-level time series equals the sum of forecasts for corresponding lower-level time series. Previous methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts and then reconciling those forecasts based on their inherent hierarchical structure. With the aim of improving time series predictions, we propose a structured regularization method for completing both phases simultaneously. The proposed method is based on a prediction model for bottom-level time series and uses a structured regularization term to incorporate upper-level forecasts into the prediction model. We also develop a backpropagation algorithm specialized for application of our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate the superiority of our method in terms of prediction accuracy and computational efficiency

Endoscopic Discectomy for Extraforaminal Lumbar Disc Herniation

Summary. The microendoscopic discectomy (MED) technique has been one of the promising surgeries for lumbar disc herniation in the last few years. The purpose of this study is to report the feasibility of a minimally invasive technique for extraforaminal lumbar disc herniation. Ten patients with extraforaminal lumbar disc herniation (one at L3-4, four at L4-5, and five at L5-S1) underwent MED using the METRx system. A tubular retractor was inserted posterolaterally adjacent to the caudal base of the transverse process at the level of the affected disc. The nerve root was carefully distinguished from its surrounding tissues, and then the herniated disc was excised. The mean length of the preoperative clinical course was 7 months. The pain in the lower extremity was relieved in all patients. The clinical results in the MED group were the same as those in the open surgery group. Endoscopic herniotomy requires much less extensive muscle dissection than open surgery. The MED technique for extraforaminal lumbar disc herniation can be performed safely and effectively. There is a learning curve to this procedure